Add scripts and inp files.
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390 changed files with 6580687 additions and 10 deletions
31
Unpublished/3D_Voxel_Assign/CorrosionFaces.py
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31
Unpublished/3D_Voxel_Assign/CorrosionFaces.py
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# Python Preprocessor Script for Abaqus Corrosion Model
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# J. Grogan, D. Gastaldi - Created. 19-07-11
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# Import abaqus modules
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from abaqusConstants import *
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from abaqus import *
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import random
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# Create Model, Assembly and Instance objects
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modelNames=mdb.models.keys()
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corModel=mdb.models[modelNames[0]]
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corAssembly=corModel.rootAssembly
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corSurf=corAssembly.surfaces['Corrode']
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surfFaces=corSurf.faces
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incFile=open('CorSurf.dat','w')
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for i in range(0,len(surfFaces)):
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eachFace=surfFaces[i]
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elemFaces=eachFace.getElementFaces()
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for j in range(0,len(elemFaces)):
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eachElemFace=elemFaces[j]
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faceNodes=eachElemFace.getNodes()
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centx=0.
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centy=0.
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centz=0.
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for k in range(0,len(faceNodes)):
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centx=centx+faceNodes[k].coordinates[0]
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centy=centy+faceNodes[k].coordinates[1]
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centz=centz+faceNodes[k].coordinates[2]
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centx=centx/float(len(faceNodes))
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centy=centy/float(len(faceNodes))
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centz=centz/float(len(faceNodes))
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incFile.write ("%f %f %f \n"%(centx,centy,centz))
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incFile.close()
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193
Unpublished/3D_Voxel_Assign/DistMinPre.f90
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193
Unpublished/3D_Voxel_Assign/DistMinPre.f90
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! This program generates a micro-strucutre mask and applies it to
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! an existing mesh.
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! J.Grogan 05/08/11
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program Voronoi3DPost
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!
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! Parameters
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parameter(max_elements=100000,max_cells=20000,max_fc=100)
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parameter(max_elem_in_cell=50000,max_neigh_per_elem=6,max_neighbours=50)
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!
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! Variables
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character(len=256)input
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character(len=256)input2(2)
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integer num_neighbours(100000),neighbour(100000,max_neighbours)
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real nbr_dist(100000,max_neighbours)
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real cor_faces(100000,3),cor_dist(100000)
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double precision,allocatable,dimension(:,:)::ele_centroid
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!
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allocate(ele_centroid(max_elements,3))
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mesh_type=3
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call elem_centroids(num_elements,ele_centroid,mesh_type)
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rmax_dist=0.020
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neighbour=0
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!
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! Get neighbouring elements
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do i=1,num_elements
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icount=1
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do j=1,num_elements
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if(icount>max_neighbours)then
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rmaxdist=0.
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do k=1,max_neighbours
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if(nbr_dist(i,k)>rmaxdist)then
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rmaxdist=nbr_dist(i,k)
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index_max_dist=k
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endif
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enddo
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endif
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cent1x=ele_centroid(i,1)
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cent1y=ele_centroid(i,2)
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cent1z=ele_centroid(i,3)
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cent2x=ele_centroid(j,1)
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cent2y=ele_centroid(j,2)
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cent2z=ele_centroid(j,3)
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dist=sqrt((cent1x-cent2x)*(cent1x-cent2x)+(cent1y-cent2y)*(cent1y-cent2y)&
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&+(cent1z-cent2z)*(cent1z-cent2z))
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if(icount>max_neighbours)then
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if(dist<rmaxdist)then
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nbr_dist(i,index_max_dist)=dist
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neighbour(i,index_max_dist)=j
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endif
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else
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nbr_dist(i,j)=dist
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neighbour(i,j)=j
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endif
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icount=icount+1
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enddo
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! print *,float(i)/float(num_elements)
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enddo
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!
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! Get corrosion surface distances
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open(unit=20,file='CorSurf.dat',status='unknown')
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read(20,*)num_faces
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ierr=0
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num_faces=1
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do while (ierr==0)
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read(20,*,iostat=ierr)cor_faces(num_faces,1),cor_faces(num_faces,2),&
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&cor_faces(num_faces,3)
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if(ierr==0)num_faces=num_faces+1
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enddo
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close(unit=20)
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do i=1,num_elements
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centx=ele_centroid(i,1)
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centy=ele_centroid(i,2)
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centz=ele_centroid(i,3)
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distmin=1000.
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do j=1,num_faces-1
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facex=cor_faces(j,1)
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facey=cor_faces(j,2)
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facez=cor_faces(j,3)
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dist=sqrt((centx-facex)*(centx-facex)+(centy-facey)*(centy-facey)&
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&+(centz-facez)*(centz-facez))
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if(dist<distmin)distmin=dist
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enddo
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cor_dist(i)=distmin
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enddo
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! Write New Input File
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rewind(10)
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open(unit=13,file='Corrosion.inp',status='unknown')
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input2(1)='**'
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do while (index(input2(1),'*End Assembly')==0)
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read(10,'(a)')input2(2)
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write(13,'(a)')input2(1)
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input2(1)=input2(2)
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enddo
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write(13,'(a)')'*End Assembly'
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write(13,*)'*INITIAL CONDITIONS,TYPE=SOLUTION'
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do i=1,num_elements
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write(13,'(3(a,i6),2(a,f18.6),3(i6,a))')'Assembly.CorPart.',i,',',i,',',&
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& max_neighbours,',',0.,',',cor_dist(i),0,',',0,',',0,','
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write(13,'(8(i6,a))')0,',',0,',',0,',',0,',',0,',',0,',',0,',',1,','
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do j=1, max_neighbours
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if(mod(j,8)/=0)then
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if(j/=max_neighbours)then
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write(13,'(i6,a)',advance='no')neighbour(i,j),','
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else
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write(13,'(i6)')neighbour(i,j)
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endif
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else
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if(j/=max_neighbours)then
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write(13,'(i6,a)')neighbour(i,j),','
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else
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write(13,'(i6)')neighbour(i,j)
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endif
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endif
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enddo
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enddo
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ierr=0
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do while (ierr==0)
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read(10,'(a)',iostat=ierr)input2(1)
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if(ierr==0)write(13,'(a)')input2(1)
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enddo
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end program
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!~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
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! Get Element Centroids
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!~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
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subroutine elem_centroids(ne,ele_centroid,mesh_type)
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!
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! Parameters
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parameter(max_nodes=1000000,max_elements=100000,max_node_in_elem=8)
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!
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! Variables
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character(len=256)input
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integer,dimension(max_elements,max_node_in_elem)::elements
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double precision,dimension(max_nodes,3)::nodes
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double precision,dimension(max_elements,3)::ele_centroid
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!
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! Open Input File and read node and element co-ordinates
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open(unit=10,file='Corrosion_Temp.inp',status='unknown')
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do while (index(input,'*Node')==0)
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read(10,'(a)')input
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end do
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nn=0
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do while(1==1)
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read(10,'(a)')input
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if(index(input,'*')==0)then
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backspace(10)
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nn=nn+1
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if(mesh_type==3)then
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read(10,*)dummy,nodes(nn,1),nodes(nn,2),nodes(nn,3)
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else
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read(10,*)dummy,nodes(nn,1),nodes(nn,2)
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endif
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else
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if(mesh_type==2)then
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nele_type=4
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else
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if(index(input,'C3D8')/=0)nele_type=8
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if(index(input,'C3D4')/=0)nele_type=4
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endif
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exit
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endif
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end do
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ne=0
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do while(1==1)
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read(10,'(a)')input
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if(index(input,'*')==0)then
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backspace(10)
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ne=ne+1
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if(nele_type==8)then
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read(10,*)dummy,elements(ne,1),elements(ne,2),elements(ne,3),elements(ne,4)&
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& ,elements(ne,5),elements(ne,6),elements(ne,7),elements(ne,8)
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elseif(nele_type==4)then
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read(10,*)dummy,elements(ne,1),elements(ne,2),elements(ne,3),elements(ne,4)
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endif
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else
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exit
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endif
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end do
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!
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! Get element centroid
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do i=1,ne
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centroidx=0.d0
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centroidy=0.d0
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centroidz=0.d0
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do j=1,nele_type
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centroidx=centroidx+nodes(elements(i,j),1)
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centroidy=centroidy+nodes(elements(i,j),2)
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if(mesh_type==3)centroidz=centroidz+nodes(elements(i,j),3)
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enddo
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ele_centroid(i,1)=centroidx/float(nele_type)
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ele_centroid(i,2)=centroidy/float(nele_type)
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if(mesh_type==3)ele_centroid(i,3)=centroidz/float(nele_type)
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enddo
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end subroutine
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164
Unpublished/3D_Voxel_Assign/GeoGen.py
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164
Unpublished/3D_Voxel_Assign/GeoGen.py
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@ -0,0 +1,164 @@
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# GrainGen V2.0
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# This script generates idealised and representative meshed micro-structure geometries
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# in 2-D and 3-D through the Abaqus geometry kernel. - J. Grogan, 09/06/2011
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#
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# Import Abaqus and External Modules
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from abaqusConstants import *
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from abaqus import *
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import random
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import subprocess
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import regionToolset
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import mesh
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import step
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import part
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import interaction
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import GeomModules
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#
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# Create Model Database
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VerFile=Mdb(pathName="MStructure")
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VerModel=VerFile.models['Model-1']
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VerAssembly=VerModel.rootAssembly
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#
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# Assign Model Parameters
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shape=4 # 1 - Square, 2- Hex, 3 -Dodec, 4- Voronoi
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part_type=2 # 2 - Shell, 3 - Solid
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dimension=2 # 2 - 2D, 3 - 3D
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rad=0.00595 # Characteristic Dimension (except Voronoi)
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meshsize=0.0005 # Global Mesh Seed Size
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num_high=16 # Number of Grains in X-Dir
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num_wide=6 # Number of Grains in Y-Dir
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num_thick=1 # Number of Grains in Z-Dir
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num_grains=25 # Target Number of Grains (Voronoi Only)
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scalex=1. # Voronoi Part Scale X-Dir (Voronoi Only)
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scaley=3.5 # Voronoi Part Scale Y-Dir (Voronoi Only)
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scalez=1. # Voronoi Part Scale Z-Dir (Voronoi Only)
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ana_type=1 # 1 - Crystal Plasticity, 2 - Corrosion
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hard_rad=0.0 # Hardcore voronoi min. radius (Voronoi Only)
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random_seed=92271 # Random seed for voronoi grain generation or random vector generation
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#
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# Choose Script Function - Set to 1 to activate
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assemble_grains = 1 # Assemble Multiple Grains and Merge Them
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boolean_cut = 1 # Perform Boolean Cut Operation
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mesh_part = 1 # Mesh the Final Geometry
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mat_props = 1 # Assign Material Properties
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bound_conds = 1 # Generate steps and apply BCs
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write_output =1 # Write Output File
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post_proc = 0 # Postprocess INP file (Corrosion Only)
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#
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# For 2-D Solids thickness is set equal to one element
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if dimension==3:
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extrude_depth=rad
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else:
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extrude_depth=meshsize
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num_thick=1
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#
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# Draw a Square Grain
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if shape==1:
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GeomModules.DrawSquare(VerModel,part_type,rad,extrude_depth)
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#
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# Draw a Hexagonal Grain
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if shape==2:
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GeomModules.DrawHexagon(VerModel,part_type,rad,extrude_depth)
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#
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# Draw a Dodecahedral Grain
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if shape==3:
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GeomModules.DrawDodec(VerModel,rad)
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#
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# Draw a Voronoi Tessellation
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if shape==4:
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if dimension==2:
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maxsize=max(scalex,scaley)
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GeomModules.Voronoi2D(VerModel,part_type,extrude_depth,num_grains,maxsize,hard_rad,random_seed)
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else:
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maxsize=max(scalex,scaley,scalez)
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GeomModules.Voronoi3D(VerModel,num_grains,maxsize,hard_rad,random_seed)
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#
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# Assemble Base Parts
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if assemble_grains==1:
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if shape<=3:
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VerPart=VerModel.parts['Base']
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GeomModules.PatternParts(num_high,num_wide,num_thick,VerPart,rad,shape,VerModel)
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#
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# Make a Boolean Template
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if boolean_cut==1:
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if shape>1:
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GeomModules.BooleanPart(VerModel,part_type,rad,extrude_depth,num_high,
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num_wide,num_thick,shape,dimension,scalex,scaley,scalez)
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BoolPart=VerModel.parts['Template']
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#
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#Perform Boolean Cut
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if shape==1:
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VerPart=VerModel.parts['Merged']
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del VerAssembly.instances['Merged-1']
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else:
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VerAssembly.InstanceFromBooleanCut(name='FinalPart',
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instanceToBeCut=VerAssembly.instances['Merged-1'],
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cuttingInstances=(VerAssembly.instances['Template-1'], ),
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originalInstances=DELETE)
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del VerAssembly.instances['FinalPart-1']
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VerPart=VerModel.parts['FinalPart']
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#
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# Mesh Part
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if mesh_part==1:
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if shape<3:
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VerPart.setMeshControls(regions=VerPart.cells, elemShape=HEX, technique=STRUCTURED)
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if shape==3:
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VerPart.setMeshControls(regions=VerPart.cells, elemShape=TET, technique=FREE)
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if shape==4:
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if dimension==2:
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VerPart.setMeshControls(regions=VerPart.cells, elemShape=HEX, technique=SWEEP,
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algorithm=ADVANCING_FRONT)
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else:
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VerPart.setMeshControls(regions=VerPart.cells, elemShape=TET, technique=FREE)
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VerPart.seedPart(size=meshsize)
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VerPart.generateMesh()
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#
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# For Corrosion Analysis Output Part Vertices and Element Connectivity
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if ana_type==2:
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GeomModules.VertsConn(VerPart,dimension)
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ecor=open('ecor.dat','w')
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for eachface in VerPart.faces:
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if len(eachface.getAdjacentFaces())<7.:
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xnor=eachface.getNormal()[0]
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ynor=eachface.getNormal()[1]
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znor=eachface.getNormal()[2]
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if (xnor==0.)and(znor==0.):
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# if (ynor==1.)or(ynor==-1.):
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if (ynor==1.):
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ecor.write("%6.4f %6.4f %6.4f\n"%(xnor,ynor,znor))
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ecor.close()
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#
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#Generate Materials and Sections
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if mat_props==1:
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GeomModules.MatGen(ana_type,VerPart,VerModel,part_type,meshsize,random_seed)
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#
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#Steps and Boundary Conditions
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if bound_conds==1:
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VerModel.ExplicitDynamicsStep(name='Corrode', previous='Initial',
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massScaling=((SEMI_AUTOMATIC, MODEL, AT_BEGINNING, 0.0, 1e-06,
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BELOW_MIN, 0, 0, 0.0, 0.0, 0, None), ))
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VerModel.ExplicitDynamicsStep(name='Load', previous='Corrode',
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timePeriod=1.)
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VerModel.steps['Corrode'].Restart(numberIntervals=2,overlay=OFF,timeMarks=OFF)
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VerModel.steps['Load'].Restart(numberIntervals=2,overlay=OFF, timeMarks=OFF)
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VerModel.FieldOutputRequest(name='F-Output-1',
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createStepName='Corrode', variables=('A', 'CSTRESS', 'LE', 'PE',
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'PEEQ', 'RF', 'S', 'SDV', 'STATUS', 'U','V'), numIntervals=100)
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#
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#Loads and BCs
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VerAssembly.Instance(name='CorPart',part=VerPart, dependent=ON)
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iNodes=VerAssembly.instances['CorPart'].nodes
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# GeomModules.S1BCs(iNodes,VerModel,num_high,num_wide,num_thick,shape,
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# dimension,extrude_depth,rad,scalex,scaley,scalez)
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#
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#VerAssembly.Instance(name='CorPart',part=VerPart, dependent=ON)
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#Create Job and write input file
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if write_output ==1:
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VerFile.Job(name='GeomGenTemp', model='Model-1', type=ANALYSIS,
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explicitPrecision=SINGLE, nodalOutputPrecision=SINGLE,userSubroutine='',
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parallelizationMethodExplicit=DOMAIN,numDomains=1,multiprocessingMode=DEFAULT, numCpus=1)
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VerFile.jobs['GeomGenTemp'].writeInput(consistencyChecking=OFF)
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#
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# Perform Postprocessing for corrosion analysis
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if post_proc ==1:
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retcode=subprocess.call("GeomGenPost2.exe")
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173
Unpublished/3D_Voxel_Assign/GeomGen.f90
Normal file
173
Unpublished/3D_Voxel_Assign/GeomGen.f90
Normal file
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@ -0,0 +1,173 @@
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!This program calculates the distance from each element
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!to its nearest grain boundary
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Program GeomConnectivity
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!
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! Parameters
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parameter(max_nodes=1000000,max_elements=1000000,max_node_in_elem=8)
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parameter(max_cells=1000,max_elem_in_cell=10000,max_neigh_per_elem=6)
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parameter(max_faces_in_cell=100)
|
||||
!
|
||||
! Declare Variables
|
||||
character*256 input,input2(2)
|
||||
integer elements(max_elements,max_node_in_element)
|
||||
integer active(max_elements)
|
||||
integer num_elements(max_cells)
|
||||
integer elem_label=(max_cells,max_elem_in_cell)
|
||||
integer num_neighbours=(max_cells,max_elem_in_cell)
|
||||
integer elem_neighbours=(max_cells,max_elem_in_cell,max_neigh_per_elem)
|
||||
integer num_faces(max_cells)
|
||||
real nodes(max_nodes,3)
|
||||
real face_coords(max_cells,max_faces_in_cell,9)
|
||||
real dotprod(max_node_in_element,max_faces_in_cell)
|
||||
real average(max_faces_in_cell)
|
||||
real distance(max_cells,max_elem_in_cell)
|
||||
!
|
||||
! Initialise Variables
|
||||
nodes=0.
|
||||
face_coords=0.
|
||||
dotprod=0.
|
||||
average=0.
|
||||
distance=0.
|
||||
elements=0
|
||||
active=0
|
||||
num_elements=0
|
||||
elem_label=0
|
||||
num_neighbours=0
|
||||
elem_neighbours=0
|
||||
num_faces=0
|
||||
!
|
||||
! Open Input File and read node and element co-ordinates
|
||||
open(unit=10,file='GeomGenTemp.inp',status='unknown')
|
||||
do while (index(input,'*Node')==0)
|
||||
read(10,'(a)')input
|
||||
end do
|
||||
nn=0
|
||||
do while(1==1)
|
||||
read(10,'(a)')input
|
||||
if(index(input,'*')==0)then
|
||||
backspace(10)
|
||||
nn=nn+1
|
||||
read(10,*)nodes(nn,1),nodes(nn,2),nodes(nn,3)
|
||||
else
|
||||
exit
|
||||
endif
|
||||
end do
|
||||
ne=0
|
||||
do while(1==1)
|
||||
read(10,'(a)')input
|
||||
if(index(input,'*')==0)then
|
||||
backspace(10)
|
||||
ne=ne+1
|
||||
read(10,*)dummy,elements(ne,1),elements(ne,2),elements(ne,3),elements(ne,4)&
|
||||
& ,elements(ne,5),elements(ne,6),elements(ne,7),elements(ne,8)
|
||||
else
|
||||
exit
|
||||
endif
|
||||
end do
|
||||
!
|
||||
! Open GeomGen output file and read element connectivity, cell, face and
|
||||
! vertice data.
|
||||
open(unit=11,file='vertout.dat',status='old')
|
||||
read(11,*)idimension
|
||||
read(11,*)num_cells
|
||||
do i=1,num_cells
|
||||
read(11,*)num_elements(i)
|
||||
do j=1,num_elements(i)
|
||||
read(11,*)elem_label(i,j)
|
||||
read(11,*)num_neighbours(i,j)
|
||||
do k=1,num_neighbours(i,j)
|
||||
read(11,*)elem_neighbours(i,j,k)
|
||||
enddo
|
||||
enddo
|
||||
read(11,*)num_faces(i)
|
||||
do j=1,num_faces(i)
|
||||
read(11,*)face_coords(i,j,1),face_coords(i,j,2),face_coords(i,j,3)
|
||||
read(11,*)face_coords(i,j,4),face_coords(i,j,5),face_coords(i,j,6)
|
||||
read(11,*)face_coords(i,j,7),face_coords(i,j,8),face_coords(i,j,9)
|
||||
enddo
|
||||
enddo
|
||||
!
|
||||
! Determine normal distance between element centroid and closest face
|
||||
do i=1,num_cells
|
||||
do j=1,num_elements(i)
|
||||
do k=1,8
|
||||
nodex=nodes(elements(elem_label(i,j),k),1)
|
||||
nodey=nodes(elements(elem_label(i,j),k),2)
|
||||
nodez=nodes(elements(elem_label(i,j),k),3)
|
||||
do m=1,num_faces(i)
|
||||
vert1x=face_coords(i,m,1)
|
||||
vert1y=face_coords(i,m,1)
|
||||
vert1z=face_coords(i,m,1)
|
||||
vert2x=face_coords(i,m,2)
|
||||
vert2y=face_coords(i,m,2)
|
||||
vert2z=face_coords(i,m,2)
|
||||
vert3x=face_coords(i,m,3)
|
||||
vert3y=face_coords(i,m,3)
|
||||
vert3z=face_coords(i,m,3)
|
||||
v1v2i=vert1x-vert2x
|
||||
v1v2j=vert1y-vert2y
|
||||
v1v2k=vert1z-vert2z
|
||||
v1v3i=vert1x-vert3x
|
||||
v1v3j=vert1y-vert3y
|
||||
v1v3k=vert1z-vert3z
|
||||
v1ni=vert1x-nodex
|
||||
v1nj=vert1y-nodey
|
||||
v1nk=vert1z-nodez
|
||||
crossi=v1v2j*v1v3k-v1v2k*v1v3j
|
||||
crossj=v1v2k*v1v3i-v1v2i*v1v3k
|
||||
crossk=v1v2i*v1v3j-v1v2j*v1v3i
|
||||
dotprod(k,m)=v1ni*crossi+v1nj*crossj+v1nk*crossk
|
||||
enddo
|
||||
enddo
|
||||
min_average=1000.
|
||||
do m=1,num_faces(i)
|
||||
average(m)=0.
|
||||
do k=1,8
|
||||
average(m)=average(m)+dotprod(k,m)
|
||||
enddo
|
||||
average(m)=average(m)/8.
|
||||
if(average(m)<min_average)min_average=average(m)
|
||||
enddo
|
||||
distance(i,j)=min_average
|
||||
enddo
|
||||
enddo
|
||||
!
|
||||
! Copy new data into updated input file
|
||||
rewind(unit=10)
|
||||
open(unit=12,file='GeomGenINP.inp',status='unknown')
|
||||
input2(1)='**'
|
||||
do while (index(input2(1),'*End Assembly')==0)
|
||||
read(10,'(a)')input2(2)
|
||||
write(12,'(a)')input2(1)
|
||||
input2(1)=input2(2)
|
||||
enddo
|
||||
write(12,'(a)')'*End Assembly'
|
||||
write(12,*)'*INITIAL CONDITIONS,TYPE=SOLUTION'
|
||||
open(unit=13,file='ecor.dat',status='old')
|
||||
active=0
|
||||
ierr=0
|
||||
do while (ierr==0)
|
||||
read(13,*,iostat=ierr)ielnum
|
||||
if(ierr==0)active(ielnum)=1
|
||||
enddo
|
||||
do i=1,num_cells
|
||||
do j=1,num_elements(i)
|
||||
write(12,'(a,8(i6,a))')'Assembly.CorPart.',elem_label(i,j),',',elem_neighbours(i,j,1),&
|
||||
& ',',elem_neighbours(i,j,2),',',elem_neighbours(i,j,3),',',elem_neighbours(i,j,4),&
|
||||
& ',',elem_neighbours(i,j,5),',',elem_neighbours(i,j,6),',',0,','
|
||||
write(12,'(2(i6,a),f18.6,a,5(i6,a))')elem_label(i,j),',',active(elem_label(i,j)),',',&
|
||||
& distance(i,j),',',0,',',0,',',0,',',0,',',0,','
|
||||
write(12,'(8(i6,a))')0,',',0,',',0,',',0,',',1,',',0,',',0,',',0,','
|
||||
write(12,'(6(i6,a),f18.6)')0,',',0,',',0,',',0,',',0,',',0,',',0.
|
||||
enddo
|
||||
enddo
|
||||
ierr=0
|
||||
do while (ierr==0)
|
||||
read(10,'(a)',iostat=ierr)input2(1)
|
||||
if(ierr==0)write(12,'(a)')input2(1)
|
||||
enddo
|
||||
close(unit=10)
|
||||
close(unit=11)
|
||||
close(unit=12)
|
||||
close(unit=13)
|
||||
End Program
|
||||
190
Unpublished/3D_Voxel_Assign/GeomGenPost.f90
Normal file
190
Unpublished/3D_Voxel_Assign/GeomGenPost.f90
Normal file
|
|
@ -0,0 +1,190 @@
|
|||
!This program calculates the distance from each element
|
||||
!to its nearest grain boundary
|
||||
Program GeomGenPost
|
||||
!
|
||||
! Parameters
|
||||
parameter(max_nodes=1000000,max_elements=1000000,max_node_in_elem=8)
|
||||
parameter(max_cells=1000,max_elem_in_cell=10000,max_neigh_per_elem=6)
|
||||
parameter(max_faces_in_cell=100)
|
||||
!
|
||||
! Declare Variables
|
||||
character*256 input,input2(2)
|
||||
integer elements(max_elements,max_node_in_elem)
|
||||
integer active(max_elements)
|
||||
integer num_elements(max_cells)
|
||||
integer elem_label(max_cells,max_elem_in_cell)
|
||||
integer num_neighbours(max_cells,max_elem_in_cell)
|
||||
integer elem_neighbours(max_cells,max_elem_in_cell,max_neigh_per_elem)
|
||||
integer num_faces(max_cells)
|
||||
integer fstatus(max_cells,max_faces_in_cell)
|
||||
real nodes(max_nodes,3)
|
||||
real fnorm(max_cells,max_faces_in_cell,3)
|
||||
real fpoint(max_cells,max_faces_in_cell,3)
|
||||
real dotprod(max_node_in_elem,max_faces_in_cell)
|
||||
real average(max_faces_in_cell)
|
||||
real distance(max_cells,max_elem_in_cell)
|
||||
!
|
||||
! Initialise Variables
|
||||
nodes=0.
|
||||
fnorm=0.
|
||||
fpoint=0.
|
||||
dotprod=0.
|
||||
average=0.
|
||||
distance=0.
|
||||
elements=0
|
||||
active=0
|
||||
num_elements=0
|
||||
elem_label=0
|
||||
num_neighbours=0
|
||||
elem_neighbours=0
|
||||
num_faces=0
|
||||
fstatus=0
|
||||
!
|
||||
! Open Input File and read node and element co-ordinates
|
||||
open(unit=10,file='GeomGenTemp.inp',status='unknown')
|
||||
do while (index(input,'*Node')==0)
|
||||
read(10,'(a)')input
|
||||
end do
|
||||
nn=0
|
||||
do while(1==1)
|
||||
read(10,'(a)')input
|
||||
if(index(input,'*')==0)then
|
||||
backspace(10)
|
||||
nn=nn+1
|
||||
read(10,*)dummy,nodes(nn,1),nodes(nn,2),nodes(nn,3)
|
||||
else
|
||||
if(index(input,'C3D8')/=0)nele_type=8
|
||||
if(index(input,'C3D4')/=0)nele_type=4
|
||||
exit
|
||||
endif
|
||||
end do
|
||||
ne=0
|
||||
do while(1==1)
|
||||
read(10,'(a)')input
|
||||
if(index(input,'*')==0)then
|
||||
backspace(10)
|
||||
ne=ne+1
|
||||
if(nele_type==8)then
|
||||
read(10,*)dummy,elements(ne,1),elements(ne,2),elements(ne,3),elements(ne,4)&
|
||||
& ,elements(ne,5),elements(ne,6),elements(ne,7),elements(ne,8)
|
||||
elseif(nele_type==4)then
|
||||
read(10,*)dummy,elements(ne,1),elements(ne,2),elements(ne,3),elements(ne,4)
|
||||
endif
|
||||
else
|
||||
exit
|
||||
endif
|
||||
end do
|
||||
!
|
||||
! Open GeomGen output file and read element connectivity, cell, face and
|
||||
! vertice data.
|
||||
open(unit=11,file='vertout.dat',status='old')
|
||||
read(11,*)idimension
|
||||
read(11,*)num_cells
|
||||
do i=1,num_cells
|
||||
read(11,*)num_elements(i)
|
||||
do j=1,num_elements(i)
|
||||
read(11,*)elem_label(i,j)
|
||||
read(11,*)num_neighbours(i,j)
|
||||
do k=1,num_neighbours(i,j)
|
||||
read(11,*)elem_neighbours(i,j,k)
|
||||
enddo
|
||||
enddo
|
||||
read(11,*)num_faces(i)
|
||||
do j=1,num_faces(i)
|
||||
read(11,*)vert1x,vert1y,vert1z
|
||||
read(11,*)vert2x,vert2y,vert2z
|
||||
read(11,*)vert3x,vert3y,vert3z
|
||||
v1v2i=vert1x-vert2x
|
||||
v1v2j=vert1y-vert2y
|
||||
v1v2k=vert1z-vert2z
|
||||
v1v3i=vert1x-vert3x
|
||||
v1v3j=vert1y-vert3y
|
||||
v1v3k=vert1z-vert3z
|
||||
crossi=v1v2j*v1v3k-v1v2k*v1v3j
|
||||
crossj=v1v2k*v1v3i-v1v2i*v1v3k
|
||||
crossk=v1v2i*v1v3j-v1v2j*v1v3i
|
||||
cmag=sqrt(crossi*crossi+crossj*crossj+crossk*crossk)
|
||||
fnorm(i,j,1)=crossi/cmag
|
||||
fnorm(i,j,2)=crossj/cmag
|
||||
fnorm(i,j,3)=crossk/cmag
|
||||
fpoint(i,j,1)=vert1x
|
||||
fpoint(i,j,2)=vert1y
|
||||
fpoint(i,j,3)=vert1z
|
||||
if(idimension==2)then
|
||||
if(int(fnorm(i,j,1))==0.and.int(fnorm(i,j,2))==0.and.int(abs(fnorm(i,j,3)))==1)then
|
||||
fstatus(i,j)=1
|
||||
endif
|
||||
endif
|
||||
enddo
|
||||
enddo
|
||||
!
|
||||
! Determine normal distance between element centroid and closest face
|
||||
do i=1,num_cells
|
||||
do j=1,num_elements(i)
|
||||
do k=1,nele_type
|
||||
rnodex=nodes(elements(elem_label(i,j),k),1)
|
||||
rnodey=nodes(elements(elem_label(i,j),k),2)
|
||||
rnodez=nodes(elements(elem_label(i,j),k),3)
|
||||
do m=1,num_faces(i)
|
||||
if(fstatus(i,m)/=1)then
|
||||
v1ni=fpoint(i,m,1)-rnodex
|
||||
v1nj=fpoint(i,m,2)-rnodey
|
||||
v1nk=fpoint(i,m,3)-rnodez
|
||||
dotprod(k,m)=v1ni*fnorm(i,m,1)+v1nj*fnorm(i,m,2)+v1nk*fnorm(i,m,3)
|
||||
endif
|
||||
enddo
|
||||
enddo
|
||||
rmin_average=1000.
|
||||
do m=1,num_faces(i)
|
||||
if(fstatus(i,m)/=1)then
|
||||
average(m)=0.
|
||||
do k=1,nele_type
|
||||
average(m)=average(m)+abs(dotprod(k,m))
|
||||
enddo
|
||||
average(m)=average(m)/float(nele_type)
|
||||
if(average(m)<rmin_average)rmin_average=average(m)
|
||||
endif
|
||||
enddo
|
||||
distance(i,j)=rmin_average
|
||||
enddo
|
||||
enddo
|
||||
!
|
||||
! Copy new data into updated input file
|
||||
rewind(unit=10)
|
||||
open(unit=12,file='GeomGenINP.inp',status='unknown')
|
||||
input2(1)='**'
|
||||
do while (index(input2(1),'*End Assembly')==0)
|
||||
read(10,'(a)')input2(2)
|
||||
write(12,'(a)')input2(1)
|
||||
input2(1)=input2(2)
|
||||
enddo
|
||||
write(12,'(a)')'*End Assembly'
|
||||
write(12,*)'*INITIAL CONDITIONS,TYPE=SOLUTION'
|
||||
open(unit=13,file='ecor.dat',status='old')
|
||||
active=0
|
||||
ierr=0
|
||||
do while (ierr==0)
|
||||
read(13,*,iostat=ierr)ielnum
|
||||
if(ierr==0)active(ielnum)=1
|
||||
enddo
|
||||
do i=1,num_cells
|
||||
do j=1,num_elements(i)
|
||||
write(12,'(a,8(i6,a))')'Assembly.CorPart.',elem_label(i,j),',',elem_neighbours(i,j,1),&
|
||||
& ',',elem_neighbours(i,j,2),',',elem_neighbours(i,j,3),',',elem_neighbours(i,j,4),&
|
||||
& ',',elem_neighbours(i,j,5),',',elem_neighbours(i,j,6),',',0,','
|
||||
write(12,'(2(i6,a),f18.6,a,5(i6,a))')elem_label(i,j),',',active(elem_label(i,j)),',',&
|
||||
& distance(i,j),',',0,',',0,',',0,',',0,',',0,','
|
||||
write(12,'(8(i6,a))')0,',',0,',',0,',',0,',',1,',',0,',',0,',',0,','
|
||||
write(12,'(6(i6,a),f18.6)')0,',',0,',',0,',',0,',',0,',',0,',',0.
|
||||
enddo
|
||||
enddo
|
||||
ierr=0
|
||||
do while (ierr==0)
|
||||
read(10,'(a)',iostat=ierr)input2(1)
|
||||
if(ierr==0)write(12,'(a)')input2(1)
|
||||
enddo
|
||||
close(unit=10)
|
||||
close(unit=11)
|
||||
close(unit=12)
|
||||
close(unit=13)
|
||||
End Program
|
||||
74
Unpublished/3D_Voxel_Assign/GeomGenPost2.f90
Normal file
74
Unpublished/3D_Voxel_Assign/GeomGenPost2.f90
Normal file
|
|
@ -0,0 +1,74 @@
|
|||
!This program calculates the distance from each element
|
||||
!to its nearest grain boundary
|
||||
Program GeomGenPost
|
||||
!
|
||||
! Parameters
|
||||
parameter(max_elements=1000000)
|
||||
parameter(max_neigh_per_elem=6)
|
||||
!
|
||||
! Declare Variables
|
||||
character*256 input,input2(2)
|
||||
integer active(max_elements)
|
||||
integer cellstat(max_elements)
|
||||
integer elem_neighbours(max_neigh_per_elem)
|
||||
!
|
||||
! Initialise Variables
|
||||
active=0
|
||||
elem_neighbours=0
|
||||
!
|
||||
! Copy new data into updated input file
|
||||
open(unit=10,file='GeomGenTemp.inp',status='unknown')
|
||||
open(unit=12,file='GeomGenINP.inp',status='unknown')
|
||||
input2(1)='**'
|
||||
do while (index(input2(1),'*End Assembly')==0)
|
||||
read(10,'(a)')input2(2)
|
||||
write(12,'(a)')input2(1)
|
||||
input2(1)=input2(2)
|
||||
enddo
|
||||
write(12,'(a)')'*End Assembly'
|
||||
write(12,*)'*INITIAL CONDITIONS,TYPE=SOLUTION'
|
||||
open(unit=13,file='ecor.dat',status='old')
|
||||
active=0
|
||||
ierr=0
|
||||
do while (ierr==0)
|
||||
read(13,*,iostat=ierr)ielnum
|
||||
if(ierr==0)active(ielnum)=1
|
||||
enddo
|
||||
open(unit=14,file='testout.dat',status='old')
|
||||
ierr=0
|
||||
do while (ierr==0)
|
||||
read(13,*,iostat=ierr)ielnum,icell
|
||||
if(ierr==0)cellstat(ielnum)=icell
|
||||
enddo
|
||||
! Open GeomGen output file and read element connectivity, cell, face and
|
||||
! vertice data.
|
||||
open(unit=11,file='vertout.dat',status='old')
|
||||
read(11,*)num_cells
|
||||
do i=1,num_cells
|
||||
read(11,*)num_elements
|
||||
do j=1,num_elements
|
||||
read(11,*)ielem_label
|
||||
read(11,*)num_neighbours
|
||||
do k=1,num_neighbours
|
||||
read(11,*)elem_neighbours(k)
|
||||
enddo
|
||||
read(11,*)distance
|
||||
write(12,'(a,8(i6,a))')'Assembly.CorPart.',ielem_label,',',elem_neighbours(1),&
|
||||
& ',',elem_neighbours(2),',',elem_neighbours(3),',',elem_neighbours(4),&
|
||||
& ',',elem_neighbours(5),',',elem_neighbours(6),',',0,','
|
||||
write(12,'(2(i6,a),f18.6,a,5(i6,a))')ielem_label,',',active(elem_label),',',&
|
||||
& distance,',',cellstat(ielem_label),',',0,',',0,',',0,',',0,','
|
||||
write(12,'(8(i6,a))')0,',',0,',',0,',',0,',',1,',',0,',',0,',',0,','
|
||||
write(12,'(6(i6,a),f18.6)')0,',',0,',',0,',',0,',',0,',',0,',',0.
|
||||
enddo
|
||||
enddo
|
||||
ierr=0
|
||||
do while (ierr==0)
|
||||
read(10,'(a)',iostat=ierr)input2(1)
|
||||
if(ierr==0)write(12,'(a)')input2(1)
|
||||
enddo
|
||||
close(unit=10)
|
||||
close(unit=11)
|
||||
close(unit=12)
|
||||
close(unit=13)
|
||||
End Program
|
||||
847
Unpublished/3D_Voxel_Assign/GeomModules.py
Normal file
847
Unpublished/3D_Voxel_Assign/GeomModules.py
Normal file
|
|
@ -0,0 +1,847 @@
|
|||
# Draw a Square Grain
|
||||
#
|
||||
def DrawSquare(VerModel,part_type,rad,extrude_depth):
|
||||
from abaqusConstants import *
|
||||
from abaqus import *
|
||||
label='Base'
|
||||
if part_type==3:
|
||||
VerPart=VerModel.Part(name=label, dimensionality=THREE_D,type=DEFORMABLE_BODY)
|
||||
else:
|
||||
VerPart=VerModel.Part(name=label, dimensionality=TWO_D_PLANAR,type=DEFORMABLE_BODY)
|
||||
VerPart.DatumPointByCoordinate((0,0,0))
|
||||
VerPart.DatumPointByCoordinate((1,0,0))
|
||||
VerPart.DatumPointByCoordinate((0,1,0))
|
||||
pdatums=VerPart.datums
|
||||
VerPart.DatumPlaneByThreePoints(point1=pdatums[1], point2=pdatums[2], point3=pdatums[3])
|
||||
VerPart.DatumAxisByTwoPoint(point1=pdatums[1],point2=pdatums[2])
|
||||
partTransform = VerPart.MakeSketchTransform(sketchPlane=pdatums[4], sketchUpEdge=pdatums[5],
|
||||
sketchPlaneSide=SIDE1, sketchOrientation=BOTTOM, origin=(0,0,0))
|
||||
VerSketch = VerModel.ConstrainedSketch(name=label,sheetSize=200, transform=partTransform)
|
||||
VerSketch.Line(point1=(0.,0.),point2=(rad,0.))
|
||||
VerSketch.Line(point1=(rad,0.),point2=(rad,rad))
|
||||
VerSketch.Line(point1=(rad,rad),point2=(0.,rad))
|
||||
VerSketch.Line(point1=(0.,rad),point2=(0.,0.))
|
||||
if part_type==3:
|
||||
VerPart.BaseSolidExtrude(sketch=VerSketch,depth=extrude_depth)
|
||||
else:
|
||||
VerPart.BaseShell(sketch=VerSketch)
|
||||
# Draw a Hexagonal Grain
|
||||
#
|
||||
def DrawHexagon(VerModel,part_type,rad,extrude_depth):
|
||||
from abaqusConstants import *
|
||||
from abaqus import *
|
||||
label='Base'
|
||||
VerAssembly=VerModel.rootAssembly
|
||||
if part_type==3:
|
||||
VerPart=VerModel.Part(name=label, dimensionality=THREE_D,type=DEFORMABLE_BODY)
|
||||
else:
|
||||
VerPart=VerModel.Part(name=label, dimensionality=TWO_D_PLANAR,type=DEFORMABLE_BODY)
|
||||
VerPart.DatumPointByCoordinate((0,0,0))
|
||||
VerPart.DatumPointByCoordinate((1,0,0))
|
||||
VerPart.DatumPointByCoordinate((0,1,0))
|
||||
pdatums=VerPart.datums
|
||||
VerPart.DatumPlaneByThreePoints(point1=pdatums[1], point2=pdatums[2], point3=pdatums[3])
|
||||
VerPart.DatumAxisByTwoPoint(point1=pdatums[1],point2=pdatums[2])
|
||||
partTransform = VerPart.MakeSketchTransform(sketchPlane=pdatums[4], sketchUpEdge=pdatums[5],
|
||||
sketchPlaneSide=SIDE1, sketchOrientation=BOTTOM, origin=(0,0,0))
|
||||
VerSketch = VerModel.ConstrainedSketch(name=label,sheetSize=200, transform=partTransform)
|
||||
yheight=sin(radians(30.))
|
||||
xheight=cos(radians(30.))
|
||||
VerSketch.Line(point1=(0.,0.),point2=(rad*xheight,rad*yheight))
|
||||
VerSketch.Line(point1=(rad*xheight,rad*yheight),point2=(rad*xheight,rad*yheight+rad))
|
||||
VerSketch.Line(point1=(rad*xheight,rad*yheight+rad),point2=(0.,2.*rad*yheight+rad))
|
||||
VerSketch.Line(point1=(0.,2.*rad*yheight+rad),point2=(-rad*xheight,rad*yheight+rad))
|
||||
VerSketch.Line(point1=(-rad*xheight,rad*yheight+rad),point2=(-rad*xheight,rad*yheight))
|
||||
VerSketch.Line(point1=(-rad*xheight,rad*yheight),point2=(0.,0.))
|
||||
if part_type==3:
|
||||
VerPart.BaseSolidExtrude(sketch=VerSketch,depth=extrude_depth)
|
||||
else:
|
||||
VerPart.BaseShell(sketch=VerSketch)
|
||||
BasePart=VerModel.parts['Base']
|
||||
BasePartCells = BasePart.cells
|
||||
BasePartFaces = BasePart.faces
|
||||
BasePartVerts = BasePart.vertices
|
||||
if part_type==3:
|
||||
BasePart.PartitionCellByPlaneThreePoints(point1=BasePartVerts[4], point2=BasePartVerts[10],
|
||||
point3=BasePartVerts[11], cells=BasePartCells)
|
||||
else:
|
||||
BasePart.PartitionFaceByShortestPath(point1=BasePartVerts[4], point2=BasePartVerts[1],
|
||||
faces=BasePartFaces)
|
||||
# Draw a Dodecahedral Grain
|
||||
#
|
||||
def DrawDodec(VerModel,rad):
|
||||
from abaqusConstants import *
|
||||
from abaqus import *
|
||||
label='BaseTemp'
|
||||
VerAssembly=VerModel.rootAssembly
|
||||
VerPart=VerModel.Part(name=label, dimensionality=THREE_D,type=DEFORMABLE_BODY)
|
||||
VerPart.DatumPointByCoordinate((0,0,0))
|
||||
VerPart.DatumPointByCoordinate((1,0,0))
|
||||
VerPart.DatumPointByCoordinate((0,1,0))
|
||||
pdatums=VerPart.datums
|
||||
VerPart.DatumPlaneByThreePoints(point1=pdatums[1], point2=pdatums[2], point3=pdatums[3])
|
||||
VerPart.DatumAxisByTwoPoint(point1=pdatums[1],point2=pdatums[2])
|
||||
partTransform = VerPart.MakeSketchTransform(sketchPlane=pdatums[4], sketchUpEdge=pdatums[5],
|
||||
sketchPlaneSide=SIDE1, sketchOrientation=BOTTOM, origin=(0,0,0))
|
||||
VerSketch = VerModel.ConstrainedSketch(name=label,sheetSize=200, transform=partTransform)
|
||||
VerSketch.Line(point1=(0.,0.),point2=(sqrt(2.)*rad,rad))
|
||||
VerSketch.Line(point1=(sqrt(2.)*rad,rad),point2=(0.,2.*rad))
|
||||
VerSketch.Line(point1=(0.,2.*rad),point2=(-sqrt(2.)*rad,rad))
|
||||
VerSketch.Line(point1=(-sqrt(2.)*rad,rad),point2=(0.,0.))
|
||||
VerPart.BaseShell(sketch=VerSketch)
|
||||
for i in range (1,13):
|
||||
dodecname='dodec'+str(i)
|
||||
VerAssembly.Instance(name=dodecname,part=VerPart, dependent=ON)
|
||||
VerAssembly.translate(instanceList=('dodec2', ), vector=(0.,0.,-2.*sqrt(2.)*rad))
|
||||
VerAssembly.rotate(instanceList=('dodec3','dodec4', ), axisPoint=(0.0, 0.0, 0.0),
|
||||
axisDirection=(0.0, 1., 0.0), angle=90.0)
|
||||
VerAssembly.translate(instanceList=('dodec3', ), vector=(sqrt(2.)*rad,0.,0.))
|
||||
VerAssembly.translate(instanceList=('dodec4', ), vector=(-sqrt(2.)*rad,0.,0.))
|
||||
VerAssembly.translate(instanceList=('dodec3','dodec4', ), vector=(0.,0.,-sqrt(2.)*rad))
|
||||
VerAssembly.rotate(instanceList=('dodec5','dodec6','dodec7','dodec8',),
|
||||
axisPoint=(-sqrt(2.)*rad, rad, 0.0), axisDirection=(0., 0., 1.), angle=90.0)
|
||||
VerAssembly.rotate(instanceList=('dodec5','dodec6','dodec7','dodec8',),
|
||||
axisPoint=(-sqrt(2.)*rad, rad, 0.0), axisDirection=(0., 1., 0.), angle=-45.0)
|
||||
VerAssembly.rotate(instanceList=('dodec5','dodec6','dodec7','dodec8',),
|
||||
axisPoint=(-sqrt(2.)*rad, rad, 0.0), axisDirection=(1., 0., 1.), angle=-45.0)
|
||||
VerAssembly.rotate(instanceList=('dodec6',),
|
||||
axisPoint=(0., rad, -sqrt(2.)*rad), axisDirection=(0., 1., 0.), angle=90.0)
|
||||
VerAssembly.rotate(instanceList=('dodec7',),
|
||||
axisPoint=(0., rad, -sqrt(2.)*rad), axisDirection=(0., 1., 0.), angle=180.0)
|
||||
VerAssembly.rotate(instanceList=('dodec8',),
|
||||
axisPoint=(0., rad, -sqrt(2.)*rad), axisDirection=(0., 1., 0.), angle=270.0)
|
||||
VerAssembly.rotate(instanceList=('dodec9','dodec10','dodec11','dodec12',),
|
||||
axisPoint=(-sqrt(2.)*rad, rad, 0.0), axisDirection=(0., 0., 1.), angle=-90.0)
|
||||
VerAssembly.rotate(instanceList=('dodec9','dodec10','dodec11','dodec12',),
|
||||
axisPoint=(-sqrt(2.)*rad, rad, 0.0), axisDirection=(0., 1., 0.), angle=-45.0)
|
||||
VerAssembly.rotate(instanceList=('dodec9','dodec10','dodec11','dodec12',),
|
||||
axisPoint=(-sqrt(2.)*rad, rad, 0.0), axisDirection=(1., 0., 1.), angle=45.0)
|
||||
VerAssembly.rotate(instanceList=('dodec10',),
|
||||
axisPoint=(0., rad, -sqrt(2.)*rad), axisDirection=(0., -1., 0.), angle=90.0)
|
||||
VerAssembly.rotate(instanceList=('dodec11',),
|
||||
axisPoint=(0., rad, -sqrt(2.)*rad), axisDirection=(0., -1., 0.), angle=180.0)
|
||||
VerAssembly.rotate(instanceList=('dodec12',),
|
||||
axisPoint=(0., rad, -sqrt(2.)*rad), axisDirection=(0., -1., 0.), angle=270.0)
|
||||
VerAssembly.InstanceFromBooleanMerge(name='Base', instances=(
|
||||
VerAssembly.instances['dodec1'],
|
||||
VerAssembly.instances['dodec2'], VerAssembly.instances['dodec3'],
|
||||
VerAssembly.instances['dodec4'], VerAssembly.instances['dodec5'],
|
||||
VerAssembly.instances['dodec6'], VerAssembly.instances['dodec7'],
|
||||
VerAssembly.instances['dodec8'], VerAssembly.instances['dodec9'],
|
||||
VerAssembly.instances['dodec10'],VerAssembly.instances['dodec11'],
|
||||
VerAssembly.instances['dodec12'], ),
|
||||
keepIntersections=ON, originalInstances=SUPPRESS, domain=GEOMETRY)
|
||||
VerPart=VerModel.parts['Base']
|
||||
VerPart.AddCells(faceList = VerPart.faces)
|
||||
for i in range (1,12):
|
||||
dodecname='dodec'+str(i)
|
||||
del VerAssembly.instances[dodecname]
|
||||
del VerAssembly.instances['Base-1']
|
||||
# Draw a 2D Voronoi Tessellation
|
||||
#
|
||||
def Voronoi2D(VerModel,part_type,extrude_depth,num_grains,maxsize,hard_rad,random_seed):
|
||||
from abaqusConstants import *
|
||||
from abaqus import *
|
||||
import random
|
||||
import subprocess
|
||||
xlist=[0.]
|
||||
ylist=[0.]
|
||||
VerAssembly=VerModel.rootAssembly
|
||||
random.seed(random_seed)
|
||||
qhullin=open('qhullin.dat','w')
|
||||
qhullin.write("%i \n"%(2))
|
||||
qhullin.write("%i \n"%(num_grains*9))
|
||||
for i in range(0,num_grains):
|
||||
outside=False
|
||||
while outside==False:
|
||||
xcor=random.random()*maxsize
|
||||
ycor=random.random()*maxsize
|
||||
if hard_rad==0.:
|
||||
outside=True
|
||||
break
|
||||
if len(xlist)>1:
|
||||
distold=1000.
|
||||
for i in range(1,len(xlist)):
|
||||
distnew=(xcor-xlist[i])*(xcor-xlist[i])+(ycor-ylist[i])*(ycor-ylist[i])
|
||||
distnew=sqrt(distnew)
|
||||
if distnew<distold:
|
||||
distold=distnew
|
||||
if distold>=hard_rad:
|
||||
outside=True
|
||||
else:
|
||||
outside=True
|
||||
xlist.append(xcor)
|
||||
ylist.append(ycor)
|
||||
qhullin.write("%18.6f %18.6f \n"%(xcor,ycor))
|
||||
qhullin.write("%18.6f %18.6f \n"%(xcor+maxsize,ycor))
|
||||
qhullin.write("%18.6f %18.6f \n"%(xcor-maxsize,ycor))
|
||||
qhullin.write("%18.6f %18.6f \n"%(xcor,ycor+maxsize))
|
||||
qhullin.write("%18.6f %18.6f \n"%(xcor,ycor-maxsize))
|
||||
qhullin.write("%18.6f %18.6f \n"%(xcor+maxsize,ycor+maxsize))
|
||||
qhullin.write("%18.6f %18.6f \n"%(xcor-maxsize,ycor-maxsize))
|
||||
qhullin.write("%18.6f %18.6f \n"%(xcor+maxsize,ycor-maxsize))
|
||||
qhullin.write("%18.6f %18.6f \n"%(xcor-maxsize,ycor+maxsize))
|
||||
qhullin.close()
|
||||
scales=open('scales.dat','w')
|
||||
scales.write("%18.6f \n"%(maxsize))
|
||||
scales.close()
|
||||
# retcode=subprocess.call("qhull.exe v Qbb TI qhullin.dat o TO qhullout.dat")
|
||||
retcode=subprocess.call("Voronoi2DPost.exe")
|
||||
FortranFile=open('fortranout.dat')
|
||||
num_cells=int(FortranFile.readline())
|
||||
cordx=[]
|
||||
cordy=[]
|
||||
x1=[]
|
||||
y1=[]
|
||||
x2=[]
|
||||
y2=[]
|
||||
k=0
|
||||
for i in range(0,num_cells):
|
||||
label='Cell'+str(i)
|
||||
if part_type==3:
|
||||
VerPart=VerModel.Part(name=label, dimensionality=THREE_D,type=DEFORMABLE_BODY)
|
||||
else:
|
||||
VerPart=VerModel.Part(name=label, dimensionality=TWO_D_PLANAR,type=DEFORMABLE_BODY)
|
||||
# Constuct Datum Point At Each Node
|
||||
VerPart.DatumPointByCoordinate((0,0,0))
|
||||
VerPart.DatumPointByCoordinate((1,0,0))
|
||||
VerPart.DatumPointByCoordinate((0,1,0))
|
||||
pdatums=VerPart.datums
|
||||
# Constuct Datum Plane on Element Face and Datum Axis Along Element Base
|
||||
VerPart.DatumPlaneByThreePoints(point1=pdatums[1],
|
||||
point2=pdatums[2], point3=pdatums[3])
|
||||
VerPart.DatumAxisByTwoPoint(point1=pdatums[1],point2=pdatums[2])
|
||||
# Sketch New Part Geometry Over Original Element
|
||||
partTransform = VerPart.MakeSketchTransform(sketchPlane=pdatums[4],
|
||||
sketchUpEdge=pdatums[5],
|
||||
sketchPlaneSide=SIDE1, sketchOrientation=BOTTOM, origin=(0,0,0))
|
||||
VerSketch = VerModel.ConstrainedSketch(name=label,sheetSize=200,
|
||||
transform=partTransform)
|
||||
num_verts=int(FortranFile.readline())
|
||||
for j in range(0,num_verts):
|
||||
coords=FortranFile.readline().split(',')
|
||||
cordx.append([])
|
||||
cordy.append([])
|
||||
cordx[j]=float(coords[0])
|
||||
cordy[j]=float(coords[1])
|
||||
print i,num_verts
|
||||
for j in range(0,num_verts-1):
|
||||
VerSketch.Line(point1=(cordx[j],cordy[j]),point2=(cordx[j+1],cordy[j+1]))
|
||||
x1.append([])
|
||||
y1.append([])
|
||||
x1[k]=cordx[j]
|
||||
y1[k]=cordy[j]
|
||||
x2.append([])
|
||||
y2.append([])
|
||||
x2[k]=cordx[j+1]
|
||||
y2[k]=cordy[j+1]
|
||||
k=k+1
|
||||
VerSketch.Line(point1=(cordx[num_verts-1],cordy[num_verts-1]),
|
||||
point2=(cordx[0],cordy[0]))
|
||||
x1.append([])
|
||||
y1.append([])
|
||||
x1[k]=cordx[num_verts-1]
|
||||
y1[k]=cordy[num_verts-1]
|
||||
x2.append([])
|
||||
y2.append([])
|
||||
x2[k]=cordx[0]
|
||||
y2[k]=cordy[0]
|
||||
k=k+1
|
||||
print i,num_verts,k
|
||||
if part_type==3:
|
||||
VerPart.BaseSolidExtrude(sketch=VerSketch, depth=extrude_depth)
|
||||
else:
|
||||
VerPart.Shell(sketchPlane=pdatums[4], sketchUpEdge=pdatums[5], sketchPlaneSide=SIDE1,
|
||||
sketchOrientation=BOTTOM, sketch=VerSketch)
|
||||
VerAssembly.Instance(name=label,part=VerPart)
|
||||
inst=[]
|
||||
inst.append([])
|
||||
for i in range(0,num_cells):
|
||||
inst[i]=VerAssembly.instances['Cell'+str(i)]
|
||||
if i<num_cells-1:
|
||||
inst.append([])
|
||||
VerAssembly.InstanceFromBooleanMerge(name='Merged',
|
||||
instances=inst,originalInstances=DELETE, keepIntersections=ON,domain=GEOMETRY)
|
||||
# Draw a 3D Voronoi Tessellation
|
||||
#
|
||||
def Voronoi3D(VerModel,num_grains,maxsize,hard_rad,random_seed):
|
||||
from abaqusConstants import *
|
||||
from abaqus import *
|
||||
import random
|
||||
import subprocess
|
||||
xlist=[0.]
|
||||
ylist=[0.]
|
||||
zlist=[0.]
|
||||
VerAssembly=VerModel.rootAssembly
|
||||
random.seed(random_seed)
|
||||
qhullin=open('qhullin.dat','w')
|
||||
qhullin.write("%i \n"%(3))
|
||||
qhullin.write("%i \n"%(num_grains*27))
|
||||
for i in range(0,num_grains):
|
||||
outside=False
|
||||
while outside==False:
|
||||
xcor=random.random()*maxsize
|
||||
ycor=random.random()*maxsize
|
||||
zcor=random.random()*maxsize
|
||||
if hard_rad==0.:
|
||||
outside=True
|
||||
break
|
||||
if len(xlist)>1:
|
||||
distold=1000.
|
||||
for i in range(1,len(xlist)):
|
||||
distnew=(xcor-xlist[i])*(xcor-xlist[i])+(ycor-ylist[i])*(ycor-ylist[i])
|
||||
distnew=distnew+(zcor-zlist[i])*(zcor-zlist[i])
|
||||
distnew=sqrt(distnew)
|
||||
if distnew<distold:
|
||||
distold=distnew
|
||||
if distold>=hard_rad:
|
||||
outside=True
|
||||
else:
|
||||
outside=True
|
||||
xlist.append(xcor)
|
||||
ylist.append(ycor)
|
||||
zlist.append(zcor)
|
||||
qhullin.write("%18.6f %18.6f %18.6f \n"%(xcor,ycor,zcor))
|
||||
qhullin.write("%18.6f %18.6f %18.6f \n"%(xcor+maxsize,ycor,zcor))
|
||||
qhullin.write("%18.6f %18.6f %18.6f \n"%(xcor-maxsize,ycor,zcor))
|
||||
qhullin.write("%18.6f %18.6f %18.6f \n"%(xcor,ycor+maxsize,zcor))
|
||||
qhullin.write("%18.6f %18.6f %18.6f \n"%(xcor,ycor-maxsize,zcor))
|
||||
qhullin.write("%18.6f %18.6f %18.6f \n"%(xcor+maxsize,ycor+maxsize,zcor))
|
||||
qhullin.write("%18.6f %18.6f %18.6f \n"%(xcor-maxsize,ycor-maxsize,zcor))
|
||||
qhullin.write("%18.6f %18.6f %18.6f \n"%(xcor+maxsize,ycor-maxsize,zcor))
|
||||
qhullin.write("%18.6f %18.6f %18.6f \n"%(xcor-maxsize,ycor+maxsize,zcor))
|
||||
qhullin.write("%18.6f %18.6f %18.6f \n"%(xcor,ycor,zcor+maxsize))
|
||||
qhullin.write("%18.6f %18.6f %18.6f \n"%(xcor+maxsize,ycor,zcor+maxsize))
|
||||
qhullin.write("%18.6f %18.6f %18.6f \n"%(xcor-maxsize,ycor,zcor+maxsize))
|
||||
qhullin.write("%18.6f %18.6f %18.6f \n"%(xcor,ycor+maxsize,zcor+maxsize))
|
||||
qhullin.write("%18.6f %18.6f %18.6f \n"%(xcor,ycor-maxsize,zcor+maxsize))
|
||||
qhullin.write("%18.6f %18.6f %18.6f \n"%(xcor+maxsize,ycor+maxsize,zcor+maxsize))
|
||||
qhullin.write("%18.6f %18.6f %18.6f \n"%(xcor-maxsize,ycor-maxsize,zcor+maxsize))
|
||||
qhullin.write("%18.6f %18.6f %18.6f \n"%(xcor+maxsize,ycor-maxsize,zcor+maxsize))
|
||||
qhullin.write("%18.6f %18.6f %18.6f \n"%(xcor-maxsize,ycor+maxsize,zcor+maxsize))
|
||||
qhullin.write("%18.6f %18.6f %18.6f \n"%(xcor,ycor,zcor-maxsize))
|
||||
qhullin.write("%18.6f %18.6f %18.6f \n"%(xcor+maxsize,ycor,zcor-maxsize))
|
||||
qhullin.write("%18.6f %18.6f %18.6f \n"%(xcor-maxsize,ycor,zcor-maxsize))
|
||||
qhullin.write("%18.6f %18.6f %18.6f \n"%(xcor,ycor+maxsize,zcor-maxsize))
|
||||
qhullin.write("%18.6f %18.6f %18.6f \n"%(xcor,ycor-maxsize,zcor-maxsize))
|
||||
qhullin.write("%18.6f %18.6f %18.6f \n"%(xcor+maxsize,ycor+maxsize,zcor-maxsize))
|
||||
qhullin.write("%18.6f %18.6f %18.6f \n"%(xcor-maxsize,ycor-maxsize,zcor-maxsize))
|
||||
qhullin.write("%18.6f %18.6f %18.6f \n"%(xcor+maxsize,ycor-maxsize,zcor-maxsize))
|
||||
qhullin.write("%18.6f %18.6f %18.6f \n"%(xcor-maxsize,ycor+maxsize,zcor-maxsize))
|
||||
qhullin.close()
|
||||
scales=open('scales.dat','w')
|
||||
scales.write("%18.6f \n"%(maxsize))
|
||||
scales.close()
|
||||
# retcode=subprocess.call("qvoronoi.exe TI qhullin.dat o Fi TO qhullout.dat")
|
||||
retcode=subprocess.call("Voronoi3DPost.exe")
|
||||
FortranFile=open('fortranout.dat')
|
||||
num_cells=int(FortranFile.readline())
|
||||
cordx=[]
|
||||
cordy=[]
|
||||
cordz=[]
|
||||
x1=[]
|
||||
y1=[]
|
||||
x2=[]
|
||||
y2=[]
|
||||
k=0
|
||||
for k in range(0,num_cells):
|
||||
num_hyp=int(FortranFile.readline())
|
||||
for i in range(0,num_hyp):
|
||||
label='C'+str(k)+'H'+str(i)
|
||||
VerPart=VerModel.Part(name=label, dimensionality=THREE_D,type=DEFORMABLE_BODY)
|
||||
# Constuct Datum Point At Each Node
|
||||
num_verts=int(FortranFile.readline())
|
||||
for j in range(0,num_verts):
|
||||
coords=FortranFile.readline().split(',')
|
||||
cordx.append([])
|
||||
cordy.append([])
|
||||
cordz.append([])
|
||||
cordx[j]=float(coords[0])
|
||||
cordy[j]=float(coords[1])
|
||||
cordz[j]=float(coords[2])
|
||||
VerPart.DatumPointByCoordinate((cordx[j],cordy[j],cordz[j]))
|
||||
pdatums=VerPart.datums
|
||||
p1x=pdatums[1].pointOn[0]
|
||||
p1y=pdatums[1].pointOn[1]
|
||||
p1z=pdatums[1].pointOn[2]
|
||||
tol=1.e-4
|
||||
for m in range(2,num_verts+1):
|
||||
px=pdatums[m].pointOn[0]
|
||||
py=pdatums[m].pointOn[1]
|
||||
pz=pdatums[m].pointOn[2]
|
||||
p1pk=sqrt((p1x-px)*(p1x-px)+(p1y-py)*(p1y-py)+(p1z-pz)*(p1z-pz))
|
||||
if p1pk>tol:
|
||||
index1=m
|
||||
p2x=px
|
||||
p2y=py
|
||||
p2z=pz
|
||||
break
|
||||
for m in range(2,num_verts+1):
|
||||
if m!=index1:
|
||||
px=pdatums[m].pointOn[0]
|
||||
py=pdatums[m].pointOn[1]
|
||||
pz=pdatums[m].pointOn[2]
|
||||
p1pk=sqrt((p1x-px)*(p1x-px)+(p1y-py)*(p1y-py)+(p1z-pz)*(p1z-pz))
|
||||
p2pk=sqrt((p2x-px)*(p2x-px)+(p2y-py)*(p2y-py)+(p2z-pz)*(p2z-pz))
|
||||
if p1pk>tol:
|
||||
if p2pk>tol:
|
||||
index2=m
|
||||
break
|
||||
VerPart.DatumPlaneByThreePoints(point1=pdatums[1], point2=pdatums[index1], point3=pdatums[index2])
|
||||
VerPart.DatumAxisByTwoPoint(point1=pdatums[1],point2=pdatums[index1])
|
||||
partTransform = VerPart.MakeSketchTransform(sketchPlane=pdatums[num_verts+1],
|
||||
sketchUpEdge=pdatums[num_verts+2], sketchPlaneSide=SIDE1, sketchOrientation=BOTTOM, origin=(0.,0.,0.))
|
||||
sklabel='Skbase'+'C'+str(k)+'H'+str(i)
|
||||
VerSketch=VerModel.ConstrainedSketch(name=sklabel,sheetSize=200, transform=partTransform)
|
||||
VerPart.projectReferencesOntoSketch(sketch=VerSketch, filter=COPLANAR_EDGES)
|
||||
verts=VerSketch.vertices
|
||||
centroidx=0.
|
||||
centroidy=0.
|
||||
angle=[]
|
||||
jnum=[]
|
||||
for j in range(0,num_verts):
|
||||
centroidx=centroidx+verts[j].coords[0]
|
||||
centroidy=centroidy+verts[j].coords[1]
|
||||
centroidx=centroidx/float(num_verts)
|
||||
centroidy=centroidy/float(num_verts)
|
||||
for j in range(0,num_verts):
|
||||
pointx=verts[j].coords[0]-centroidx
|
||||
pointy=verts[j].coords[1]-centroidy
|
||||
vertangle=atan2(pointy,pointx)
|
||||
if vertangle<0.:
|
||||
vertangle=2*pi+vertangle
|
||||
angle.append(vertangle)
|
||||
jnum.append(j)
|
||||
icheck=0
|
||||
while icheck==0:
|
||||
icheck=1
|
||||
for j in range(1,num_verts):
|
||||
if angle[j]<angle[j-1]:
|
||||
temp1=angle[j-1]
|
||||
temp2=jnum[j-1]
|
||||
angle[j-1]=angle[j]
|
||||
angle[j]=temp1
|
||||
jnum[j-1]=jnum[j]
|
||||
jnum[j]=temp2
|
||||
icheck=0
|
||||
for j in range(1,num_verts):
|
||||
x1=verts[jnum[j]].coords[0]
|
||||
x2=verts[jnum[j-1]].coords[0]
|
||||
y1=verts[jnum[j]].coords[1]
|
||||
y2=verts[jnum[j-1]].coords[1]
|
||||
VerSketch.Line(point1=(x1,y1),point2=(x2,y2))
|
||||
VerSketch.Line(point1=(verts[jnum[num_verts-1]].coords[0],
|
||||
verts[jnum[num_verts-1]].coords[1]),
|
||||
point2=(verts[jnum[0]].coords[0],verts[jnum[0]].coords[1]))
|
||||
VerPart.Shell(sketchPlane=pdatums[num_verts+1], sketchPlaneSide=SIDE1,
|
||||
sketchUpEdge=pdatums[num_verts+2],sketchOrientation=BOTTOM,sketch=VerSketch)
|
||||
label='Part'+'C'+str(k)+'H'+str(i)
|
||||
VerAssembly.Instance(name=label,part=VerPart)
|
||||
inst=[]
|
||||
inst.append([])
|
||||
for i in range(0,num_hyp):
|
||||
inst[i]=VerAssembly.instances['Part'+'C'+str(k)+'H'+str(i)]
|
||||
if i<num_hyp-1:
|
||||
inst.append([])
|
||||
VerAssembly.InstanceFromBooleanMerge(name='Merged'+str(k),
|
||||
instances=inst,originalInstances=DELETE, keepIntersections=ON,domain=GEOMETRY)
|
||||
shellpart=VerModel.parts['Merged'+str(k)]
|
||||
shellpart.AddCells(faceList = shellpart.faces)
|
||||
VerAssembly.Instance(name='Part'+str(k),part=shellpart, dependent=ON)
|
||||
del VerAssembly.instances['Merged'+str(k)+'-1']
|
||||
for i in range(0,num_hyp):
|
||||
del VerModel.sketches['Skbase'+'C'+str(k)+'H'+str(i)]
|
||||
del VerModel.parts['C'+str(k)+'H'+str(i)]
|
||||
print float(k)/float(num_cells)
|
||||
inst=[]
|
||||
inst.append([])
|
||||
for i in range(0,num_cells):
|
||||
inst[i]=VerAssembly.instances['Part'+str(i)]
|
||||
if i<num_cells-1:
|
||||
inst.append([])
|
||||
VerAssembly.InstanceFromBooleanMerge(name='Merged',
|
||||
instances=inst,originalInstances=DELETE, keepIntersections=ON,domain=GEOMETRY)
|
||||
# Make a Boolean Template Part
|
||||
#
|
||||
def BooleanPart(VerModel,part_type,rad,extrude_depth,
|
||||
num_high,num_wide,num_thick,shape,dimension,scalex,scaley,scalez):
|
||||
from abaqusConstants import *
|
||||
from abaqus import *
|
||||
VerAssembly=VerModel.rootAssembly
|
||||
booSketch=VerModel.ConstrainedSketch(name='BSmall', sheetSize=20.0)
|
||||
if shape==1:
|
||||
vert1x=0.
|
||||
vert1y=0.
|
||||
vert2x=rad*num_high
|
||||
vert2y=0.
|
||||
vert3x=rad*num_high
|
||||
vert3y=rad*num_wide
|
||||
vert4x=0.
|
||||
vert4y=rad*num_wide
|
||||
edepth=extrude_depth*num_thick
|
||||
if shape==2:
|
||||
yheight=sin(radians(30.))
|
||||
xheight=cos(radians(30.))
|
||||
vert1x=0.
|
||||
vert1y=rad*yheight+rad/2.
|
||||
vert2x=rad*xheight*(float(num_high)-1.)*2.
|
||||
vert2y=rad*yheight+rad/2.
|
||||
vert3x=rad*xheight*(float(num_high)-1.)*2.
|
||||
vert3y=rad*yheight+rad/2.+(float(num_wide)-1.)*(rad+rad*yheight)
|
||||
vert4x=0.
|
||||
vert4y=rad*yheight+rad/2.+(float(num_wide)-1.)*(rad+rad*yheight)
|
||||
edepth=extrude_depth*num_thick
|
||||
if shape==3:
|
||||
vert1x=0.
|
||||
vert1y=rad
|
||||
vert2x=sqrt(2.)*rad*(2.*float(num_high)-1.)
|
||||
vert2y=rad
|
||||
vert3x=sqrt(2.)*rad*(2.*float(num_high)-1.)
|
||||
vert3y=rad*(2.*float(num_wide)-1.)
|
||||
vert4x=0.
|
||||
vert4y=rad*(2.*float(num_wide)-1.)
|
||||
edepth=sqrt(2.)*rad*(2.*float(num_thick)-1.)
|
||||
if shape==4:
|
||||
vert1x=0.
|
||||
vert1y=0.
|
||||
vert2x=scalex
|
||||
vert2y=0.
|
||||
vert3x=scalex
|
||||
vert3y=scaley
|
||||
vert4x=0.
|
||||
vert4y=scaley
|
||||
if dimension==2:
|
||||
edepth=extrude_depth
|
||||
else:
|
||||
edepth=scalez
|
||||
booSketch.Line(point1=(vert1x,vert1y), point2=(vert2x, vert2y))
|
||||
booSketch.Line(point1=(vert2x, vert2y), point2=(vert3x, vert3y))
|
||||
booSketch.Line(point1=(vert3x, vert3y), point2=(vert4x, vert4y))
|
||||
booSketch.Line(point1=(vert4x, vert4y), point2=(vert1x, vert1y))
|
||||
if part_type==3:
|
||||
booPart=VerModel.Part(name='BSmall', dimensionality=THREE_D,type=DEFORMABLE_BODY)
|
||||
booPart.BaseSolidExtrude(sketch=booSketch, depth=edepth)
|
||||
else:
|
||||
booPart=VerModel.Part(name='BSmall', dimensionality=TWO_D_PLANAR,type=DEFORMABLE_BODY)
|
||||
booPart.BaseShell(sketch=booSketch)
|
||||
booSketchB=VerModel.ConstrainedSketch(name='BBig', sheetSize=20.0)
|
||||
booSketchB.Line(point1=(vert1x-10.,vert1y-10.), point2=(vert2x+10., vert2y-10.))
|
||||
booSketchB.Line(point1=(vert2x+10., vert2y-10.), point2=(vert3x+10., vert3y+10.))
|
||||
booSketchB.Line(point1=(vert3x+10., vert3y+10.), point2=(vert4x-10., vert4y+10.))
|
||||
booSketchB.Line(point1=(vert4x-10., vert4y+10.), point2=(vert1x-10., vert1y-10.))
|
||||
if part_type==3:
|
||||
booPartb=VerModel.Part(name='BBig', dimensionality=THREE_D,type=DEFORMABLE_BODY)
|
||||
booPartb.BaseSolidExtrude(sketch=booSketchB, depth=edepth*10.)
|
||||
else:
|
||||
booPartb=VerModel.Part(name='BBig', dimensionality=TWO_D_PLANAR,type=DEFORMABLE_BODY)
|
||||
booPartb.BaseShell(sketch=booSketchB)
|
||||
VerAssembly.Instance(name='BSmall',part=booPart, dependent=ON)
|
||||
VerAssembly.Instance(name='BBig',part=booPartb, dependent=ON)
|
||||
if shape==3:
|
||||
if part_type==3:
|
||||
VerAssembly.translate(instanceList=('BSmall', ),
|
||||
vector=(0.,0.,-sqrt(2.)*rad))
|
||||
VerAssembly.translate(instanceList=('BBig', ),
|
||||
vector=(0.,0.,-sqrt(2.)*rad*5.))
|
||||
if shape==4:
|
||||
if part_type==3:
|
||||
VerAssembly.translate(instanceList=('BBig', ),
|
||||
vector=(0.,0.,-edepth*5.))
|
||||
VerAssembly.InstanceFromBooleanCut(name='Template',
|
||||
instanceToBeCut=VerAssembly.instances['BBig'],
|
||||
cuttingInstances=(VerAssembly.instances['BSmall'], ),
|
||||
originalInstances=DELETE)
|
||||
# Pattern base parts for multilpe grains
|
||||
#
|
||||
def PatternParts(num_high,num_wide,num_thick,VerPart,rad,shape,VerModel):
|
||||
from abaqusConstants import *
|
||||
from abaqus import *
|
||||
VerAssembly=VerModel.rootAssembly
|
||||
yheight=sin(radians(30.))
|
||||
xheight=cos(radians(30.))
|
||||
icount=0
|
||||
for i in range(0,num_high):
|
||||
for j in range(0,num_wide):
|
||||
for k in range(0,num_thick):
|
||||
label='Part'+str(icount)
|
||||
VerAssembly.Instance(name=label,part=VerPart, dependent=ON)
|
||||
# Square
|
||||
if shape==1:
|
||||
VerAssembly.translate(instanceList=(label, ),
|
||||
vector=(i*rad,j*rad,k*rad))
|
||||
# Hexagon
|
||||
if shape==2:
|
||||
if j%2==0:
|
||||
VerAssembly.translate(instanceList=(label, ),
|
||||
vector=(i*xheight*rad*2.,j*rad*(1.+yheight),k*rad))
|
||||
else:
|
||||
VerAssembly.translate(instanceList=(label, ),
|
||||
vector=(i*xheight*rad*2.+xheight*rad,j*rad*(1.+yheight),k*rad))
|
||||
# Dodecahedron
|
||||
if shape==3:
|
||||
if j%2==0:
|
||||
VerAssembly.translate(instanceList=(label, ),
|
||||
vector=(i*rad*2.*sqrt(2.),j*2.*rad,2.*k*rad*sqrt(2.)))
|
||||
else:
|
||||
VerAssembly.translate(instanceList=(label, ),
|
||||
vector=(i*rad*2.*sqrt(2.)+sqrt(2.)*rad,j*2.*rad,2.*k*rad*sqrt(2.)+sqrt(2.)*rad))
|
||||
icount=icount+1
|
||||
inst=[]
|
||||
inst.append([])
|
||||
for i in range(0,icount):
|
||||
inst[i]=VerAssembly.instances['Part'+str(i)]
|
||||
if i<icount-1:
|
||||
inst.append([])
|
||||
VerAssembly.InstanceFromBooleanMerge(name='Merged',
|
||||
instances=inst,originalInstances=DELETE, keepIntersections=ON,domain=GEOMETRY)
|
||||
# Output vertices and element connectivity for corrosion analysis
|
||||
#
|
||||
def VertsConn(VerPart,dimension):
|
||||
from abaqusConstants import *
|
||||
from abaqus import *
|
||||
vertout=open('vertout.dat','w')
|
||||
vertout.write("%i\n"%(len(VerPart.cells)))
|
||||
k=1.
|
||||
for eachcell in VerPart.cells:
|
||||
print k/float(len(VerPart.cells))
|
||||
cellElements=eachcell.getElements()
|
||||
vertout.write("%i\n"%(len(cellElements)))
|
||||
cellFaces=eachcell.getFaces()
|
||||
for eachElement in cellElements:
|
||||
vertout.write("%i\n"%(eachElement.label))
|
||||
Adj_Elem=eachElement.getAdjacentElements()
|
||||
vertout.write("%i\n"%(len(Adj_Elem)))
|
||||
for i in range(0,len(Adj_Elem)):
|
||||
vertout.write("%i\n"%(Adj_Elem[i].label))
|
||||
centroidx=0.
|
||||
centroidy=0.
|
||||
centroidz=0.
|
||||
dmin=1000.
|
||||
for eachNode in eachElement.getNodes():
|
||||
centroidx=centroidx+eachNode.coordinates[0]
|
||||
centroidy=centroidy+eachNode.coordinates[1]
|
||||
centroidz=centroidz+eachNode.coordinates[2]
|
||||
num_nodes=float(len(eachElement.getNodes()))
|
||||
centroidx=centroidx/num_nodes
|
||||
centroidy=centroidy/num_nodes
|
||||
centroidz=centroidz/num_nodes
|
||||
for i in range(0,len(cellFaces)):
|
||||
eachFace=VerPart.faces[cellFaces[i]]
|
||||
facex=eachFace.pointOn[0][0]
|
||||
facey=eachFace.pointOn[0][1]
|
||||
facez=eachFace.pointOn[0][2]
|
||||
normalx=eachFace.getNormal()[0]
|
||||
normaly=eachFace.getNormal()[1]
|
||||
normalz=eachFace.getNormal()[2]
|
||||
if dimension==2:
|
||||
if normalx==0.:
|
||||
if normaly==0.:
|
||||
if abs(normalz)==1:
|
||||
continue
|
||||
else:
|
||||
if len(Adj_Elem)<6:
|
||||
if normalx==0.:
|
||||
if normaly==0.:
|
||||
if abs(normalz)==1:
|
||||
continue
|
||||
dfcx=facex-centroidx
|
||||
dfcy=facey-centroidy
|
||||
dfcz=facez-centroidz
|
||||
distance=abs(dfcx*normalx+dfcy*normaly+dfcz*normalz)
|
||||
if distance<dmin:
|
||||
dmin=distance
|
||||
vertout.write("%18.6f\n"%(dmin))
|
||||
k=k+1
|
||||
vertout.close()
|
||||
# Generate Materials and Sections
|
||||
#
|
||||
def MatGen(ana_type,VerPart,VerModel,part_type,meshsize,random_seed):
|
||||
from abaqusConstants import *
|
||||
from abaqus import *
|
||||
import random
|
||||
if ana_type==2:
|
||||
VerModel.Material(name='Magnesium')
|
||||
VerModel.materials['Magnesium'].Density(table=((1e-05, ), ))
|
||||
VerModel.materials['Magnesium'].Depvar(deleteVar=20, n=30)
|
||||
VerModel.materials['Magnesium'].UserMaterial(
|
||||
mechanicalConstants=(44000.0, 0.35, 138.7, 16.0, 165.0,0.5))
|
||||
if part_type==3:
|
||||
regions=VerPart.cells
|
||||
else:
|
||||
regions=VerPart.faces
|
||||
VerModel.HomogeneousSolidSection(name='Magnesium',
|
||||
material='Magnesium', thickness=meshsize)
|
||||
VerPart.SectionAssignment(region=(regions,),
|
||||
sectionName='Magnesium', offset=0.0, offsetField='')
|
||||
else:
|
||||
labelcount=1
|
||||
if part_type==3:
|
||||
regions=VerPart.cells
|
||||
else:
|
||||
regions=VerPart.faces
|
||||
random.seed(random_seed)
|
||||
for eachregion in regions:
|
||||
rand1=(random.random()-0.5)*2.
|
||||
rand2=(random.random()-0.5)*2.
|
||||
rand3=(random.random()-0.5)*2.
|
||||
rand4=(random.random()-0.5)*2.
|
||||
rand5=(random.random()-0.5)*2.
|
||||
rand6=(rand1*rand4+rand2*rand5)/(-rand3)
|
||||
mlabel='Mat'+str(labelcount)
|
||||
VerModel.Material(name=mlabel)
|
||||
VerModel.materials[mlabel].Density(table=((1e-05, ), ))
|
||||
VerModel.materials[mlabel].Depvar(deleteVar=124, n=124)
|
||||
VerModel.materials[mlabel].UserMaterial(
|
||||
mechanicalConstants=(200000.0, 0.3,
|
||||
rand1, rand2, rand3,1.,0.,0.,rand4,rand5,rand6,0.,0.,1.,
|
||||
10.,0.001,541.5,109.5,60.8,1.,1.,0.5,1.))
|
||||
VerModel.HomogeneousSolidSection(name=mlabel,
|
||||
material=mlabel, thickness=meshsize)
|
||||
VerPart.SectionAssignment(region=(eachregion,),
|
||||
sectionName=mlabel, offset=0.0, offsetField='')
|
||||
labelcount=labelcount+1
|
||||
# Shape 1 BCs and Constraints - Uniaxial Tension
|
||||
#
|
||||
def S1BCs(iNodes,VerModel,num_high,num_wide,num_thick,shape,
|
||||
dimension,extrude_depth,rad,scalex,scaley,scalez):
|
||||
from abaqusConstants import *
|
||||
from abaqus import *
|
||||
import regionToolset
|
||||
VerAssembly=VerModel.rootAssembly
|
||||
Min=-0.001
|
||||
Max=0.001
|
||||
fwide=float(num_wide)
|
||||
fhigh=float(num_high)
|
||||
fthick=float(num_thick)
|
||||
if shape==1:
|
||||
# BC LEFT
|
||||
XMnBL=Min
|
||||
XMxBL=Max
|
||||
YMnBL=Min
|
||||
YMxBL=fwide*rad+Max
|
||||
ZMnBL=Min
|
||||
ZMxBL=Max+extrude_depth
|
||||
# BC BACK
|
||||
XMnBBK=Min
|
||||
XMxBBK=fhigh*rad+Max
|
||||
YMnBBK=Min
|
||||
YMxBBK=fwide*rad+Max
|
||||
ZMnBBK=Min
|
||||
ZMxBBK=Max
|
||||
# BC Bottom
|
||||
XMnBBT=Min
|
||||
XMxBBT=fhigh*rad+Max
|
||||
YMnBBT=Min
|
||||
YMxBBT=Max
|
||||
ZMnBBT=Min
|
||||
ZMxBBT=Max+extrude_depth
|
||||
# BC Right
|
||||
XMnBR=fhigh*rad+Min
|
||||
XMxBR=fhigh*rad+Max
|
||||
YMnBR=Min
|
||||
YMxBR=fwide*rad+Max
|
||||
ZMnBR=Min
|
||||
ZMxBR=Max+extrude_depth
|
||||
# RP
|
||||
XRP=fhigh*rad
|
||||
YRP=fwide*rad*0.5
|
||||
ZRP=extrude_depth*0.5
|
||||
if shape==2:
|
||||
yheight=sin(radians(30.))
|
||||
xheight=cos(radians(30.))
|
||||
# BC LEFT
|
||||
XMnBL=Min
|
||||
XMxBL=Max
|
||||
YMnBL=rad*yheight+rad/2.+Min
|
||||
YMxBL=rad*yheight+rad/2.+(fwide-1.)*(rad+rad*yheight)+Max
|
||||
ZMnBL=Min
|
||||
ZMxBL=Max+extrude_depth
|
||||
# BC BACK
|
||||
XMnBBK=Min
|
||||
XMxBBK=rad*xheight*(fhigh-1.)*2.+Max
|
||||
YMnBBK=rad*yheight+rad/2.+Min
|
||||
YMxBBK=rad*yheight+rad/2.+(fwide-1.)*(rad+rad*yheight)+Max
|
||||
ZMnBBK=Min
|
||||
ZMxBBK=Max
|
||||
# BC Bottom
|
||||
XMnBBT=Min
|
||||
XMxBBT=rad*xheight*(fhigh-1.)*2.+Max
|
||||
YMnBBT=rad*yheight+rad/2.+Min
|
||||
YMxBBT=rad*yheight+rad/2.+Max
|
||||
ZMnBBT=Min
|
||||
ZMxBBT=Max+extrude_depth
|
||||
# BC Right
|
||||
XMnBR=rad*xheight*(fhigh-1.)*2.+Min
|
||||
XMxBR=rad*xheight*(fhigh-1.)*2.+Max
|
||||
YMnBR=rad*yheight+rad/2.+Min
|
||||
YMxBR=rad*yheight+rad/2.+(fwide-1.)*(rad+rad*yheight)+Max
|
||||
ZMnBR=Min
|
||||
ZMxBR=Max+extrude_depth
|
||||
# RP
|
||||
XRP=rad*xheight*(fhigh-1.)*2.
|
||||
YRP=rad*yheight+rad/2.+(fwide-1.)*(rad+rad*yheight)*0.5
|
||||
ZRP=extrude_depth*0.5
|
||||
if shape==4:
|
||||
# BC LEFT
|
||||
XMnBL=Min
|
||||
XMxBL=Max
|
||||
YMnBL=Min
|
||||
YMxBL=scaley+Max
|
||||
ZMnBL=Min
|
||||
ZMxBL=Max+extrude_depth
|
||||
# BC BACK
|
||||
XMnBBK=Min
|
||||
XMxBBK=scalex+Max
|
||||
YMnBBK=Min
|
||||
YMxBBK=scaley+Max
|
||||
ZMnBBK=Min
|
||||
ZMxBBK=Max
|
||||
# BC Bottom
|
||||
XMnBBT=Min
|
||||
XMxBBT=scalex+Max
|
||||
YMnBBT=Min
|
||||
YMxBBT=Max
|
||||
ZMnBBT=Min
|
||||
ZMxBBT=Max+extrude_depth
|
||||
# BC Right
|
||||
XMnBR=scalex+Min
|
||||
XMxBR=scalex+Max
|
||||
YMnBR=Min
|
||||
YMxBR=scaley+Max
|
||||
ZMnBR=Min
|
||||
ZMxBR=Max+extrude_depth
|
||||
# RP
|
||||
XRP=scalex
|
||||
YRP=scaley*0.5
|
||||
ZRP=extrude_depth*0.5
|
||||
#
|
||||
total_length=(XMxBR-Max)-(XMnBL-Min)
|
||||
BLeft=iNodes.getByBoundingBox(xMin=XMnBL,xMax=XMxBL,yMin=YMnBL,yMax=YMxBL,zMin=ZMnBL,zMax=ZMxBL)
|
||||
BBack=iNodes.getByBoundingBox(xMin=XMnBBK,xMax=XMxBBK,yMin=YMnBBK,yMax=YMxBBK,zMin=ZMnBBK,zMax=ZMxBBK)
|
||||
BBot=iNodes.getByBoundingBox(xMin=XMnBBT,xMax=XMxBBT,yMin=YMnBBT,yMax=YMxBBT,zMin=ZMnBBT,zMax=ZMxBBT)
|
||||
BRight=iNodes.getByBoundingBox(xMin=XMnBR,xMax=XMxBR,yMin=YMnBR,yMax=YMxBR,zMin=ZMnBR,zMax=ZMxBR)
|
||||
Ref1=VerAssembly.ReferencePoint(point=(XRP,YRP,ZRP))
|
||||
#
|
||||
BLregion=regionToolset.Region(nodes=BLeft)
|
||||
BBregion=regionToolset.Region(nodes=BBot)
|
||||
BBKregion=regionToolset.Region(nodes=BBack)
|
||||
BRregion=regionToolset.Region(nodes=BRight)
|
||||
VerModel.DisplacementBC(name='LeftX', createStepName='Initial',
|
||||
region=BLregion, u1=0.0, u2=UNSET, u3=UNSET, ur1=UNSET, ur2=UNSET,
|
||||
ur3=UNSET, amplitude=UNSET, fixed=OFF, distributionType=UNIFORM)
|
||||
VerModel.DisplacementBC(name='BottomY', createStepName='Initial',
|
||||
region=BBregion, u1=UNSET, u2=0.0, u3=UNSET, ur1=UNSET, ur2=UNSET,
|
||||
ur3=UNSET, amplitude=UNSET, fixed=OFF, distributionType=UNIFORM)
|
||||
VerModel.DisplacementBC(name='BackZ', createStepName='Initial',
|
||||
region=BBKregion, u1=UNSET, u2=UNSET, u3=0.0, ur1=UNSET, ur2=UNSET,
|
||||
ur3=UNSET, amplitude=UNSET, fixed=OFF, distributionType=UNIFORM)
|
||||
#
|
||||
id1=VerAssembly.features['RP-1'].id
|
||||
RPoint=regionToolset.Region(referencePoints=(VerAssembly.referencePoints[id1],))
|
||||
VerAssembly.Set(referencePoints=(VerAssembly.referencePoints[id1],), name='RPoint')
|
||||
VerAssembly.Set(nodes=BRight, name='BRight')
|
||||
VerModel.Equation(name='Constraint-1', terms=((1.0, 'BRight', 1), ( -1.0, 'RPoint', 1)))
|
||||
VerModel.SmoothStepAmplitude(name='Load', timeSpan=STEP, data=((0.0, 0.0), (1.0, 1.0)))
|
||||
VerModel.DisplacementBC(name='RPNode', createStepName='Load',
|
||||
region=RPoint, u1=total_length*0.17, u2=0., u3=UNSET, ur1=UNSET, ur2=UNSET,
|
||||
ur3=UNSET, amplitude='Load', fixed=OFF, distributionType=UNIFORM)
|
||||
750
Unpublished/3D_Voxel_Assign/GrainMask.f90
Normal file
750
Unpublished/3D_Voxel_Assign/GrainMask.f90
Normal file
|
|
@ -0,0 +1,750 @@
|
|||
! This program generates a micro-strucutre mask and applies it to
|
||||
! an existing mesh.
|
||||
! J.Grogan 05/08/11
|
||||
program Voronoi3DPost
|
||||
!
|
||||
! Parameters
|
||||
parameter(max_elements=100000,max_cells=20000,max_fc=100,max_faces=10000)
|
||||
parameter(max_elem_in_cell=50000,max_neigh_per_elem=6,max_neighbours=50)
|
||||
!
|
||||
! Variables
|
||||
character(len=256)input
|
||||
character(len=256)input2(2)
|
||||
integer cell_stat(20000)
|
||||
integer,allocatable,dimension(:)::closest
|
||||
integer,allocatable,dimension(:)::num_ele_cell
|
||||
integer,allocatable,dimension(:)::num_faces
|
||||
integer,allocatable,dimension(:)::cell_status
|
||||
integer,allocatable,dimension(:,:)::cell_ele
|
||||
integer,dimension(max_elements)::num_neighbours
|
||||
integer,dimension(max_elements,max_neighbours)::neighbour
|
||||
integer mesh_type,mask_type,num_x,num_y,num_z,num_grains
|
||||
double precision grain_length,rad_hard,rscale
|
||||
double precision,allocatable,dimension(:,:)::distance
|
||||
double precision,allocatable,dimension(:,:)::nbr_dist
|
||||
double precision,allocatable,dimension(:,:)::cor_faces
|
||||
double precision,dimension(max_elements)::cor_dist
|
||||
double precision,allocatable,dimension(:,:)::ele_centroid
|
||||
double precision,allocatable,dimension(:,:)::cell_centroid
|
||||
double precision,allocatable,dimension(:,:,:)::face
|
||||
!
|
||||
! Mesh Type: 2 = 2D, 3 = 3D
|
||||
mesh_type=3
|
||||
! Mask Type: 1= Square, 2= Hexagon, 3= Dodec, 4=2D Voronoi, 5=3D Voronoi
|
||||
mask_type=5
|
||||
! Grain Length
|
||||
Grain_length=0.025
|
||||
! Num grains x
|
||||
num_x=10
|
||||
! Num grains y
|
||||
num_y=10
|
||||
! Num grains z
|
||||
num_z=1
|
||||
! Hardcore Voronoi Radius
|
||||
rad_hard=0.00
|
||||
num_grains=num_x*num_y*num_z
|
||||
if(mask_type>3)then
|
||||
! Create Tessellation
|
||||
allocate(face(max_cells,max_fc,4),num_faces(max_cells),cell_centroid(max_cells,3))
|
||||
call make_voronoi(mask_type,mesh_type,num_grains,num_x,rad_hard,grain_length)
|
||||
call process_voronoi(face,num_faces,cell_centroid,num_cells,cell_stat)
|
||||
else
|
||||
! Generate Centroids and faces for other geometries
|
||||
icount=1
|
||||
num_cells=num_grains
|
||||
allocate(face(num_cells,6,4),num_faces(num_cells),cell_centroid(num_cells,3))
|
||||
do i=1,num_x
|
||||
do j=1,num_y
|
||||
do k=1,num_z
|
||||
if(mask_type==1)then
|
||||
call make_square(i,j,k,grain_length,num_faces(icount), &
|
||||
& face(icount,:,:),cell_centroid(icount,:),mesh_type)
|
||||
elseif(mask_type==2)then
|
||||
call make_hexagon(i,j,k,grain_length,num_faces(icount), &
|
||||
& face(icount,:,:),cell_centroid(icount,:),mesh_type)
|
||||
else
|
||||
if(mod(j,2)==0)then
|
||||
cell_centroid(icount,1)=2.*(i-1)*Grain_length*sqrt(2.)+&
|
||||
&sqrt(2.)*Grain_length
|
||||
cell_centroid(icount,3)=2.*(k-1)*Grain_length*sqrt(2.)+&
|
||||
&Grain_length*sqrt(2.)
|
||||
else
|
||||
cell_centroid(icount,1)=2.*(i-1)*Grain_length*sqrt(2.)
|
||||
cell_centroid(icount,3)=2.*(k-1)*Grain_length*sqrt(2.)
|
||||
endif
|
||||
cell_centroid(icount,2)=2.*(j-1)*Grain_length
|
||||
endif
|
||||
icount=icount+1
|
||||
enddo
|
||||
enddo
|
||||
enddo
|
||||
endif
|
||||
!
|
||||
allocate(ele_centroid(max_elements,3))
|
||||
! Get element centroids
|
||||
call elem_centroids(num_elements,ele_centroid,mesh_type)
|
||||
!
|
||||
! Get neighbouring elements
|
||||
allocate(nbr_dist(max_elements,max_neighbours))
|
||||
do i=1,num_elements
|
||||
icount=1
|
||||
do j=1,num_elements
|
||||
if(icount>max_neighbours)then
|
||||
rmaxdist=0.
|
||||
do k=1,max_neighbours
|
||||
if(nbr_dist(i,k)>rmaxdist)then
|
||||
rmaxdist=nbr_dist(i,k)
|
||||
index_max_dist=k
|
||||
endif
|
||||
enddo
|
||||
endif
|
||||
cent1x=ele_centroid(i,1)
|
||||
cent1y=ele_centroid(i,2)
|
||||
cent1z=ele_centroid(i,3)
|
||||
cent2x=ele_centroid(j,1)
|
||||
cent2y=ele_centroid(j,2)
|
||||
cent2z=ele_centroid(j,3)
|
||||
dist=sqrt((cent1x-cent2x)*(cent1x-cent2x)+(cent1y-cent2y)*(cent1y-cent2y)&
|
||||
&+(cent1z-cent2z)*(cent1z-cent2z))
|
||||
if(icount>max_neighbours)then
|
||||
if(dist<rmaxdist)then
|
||||
nbr_dist(i,index_max_dist)=dist
|
||||
neighbour(i,index_max_dist)=j
|
||||
endif
|
||||
else
|
||||
nbr_dist(i,j)=dist
|
||||
neighbour(i,j)=j
|
||||
endif
|
||||
icount=icount+1
|
||||
enddo
|
||||
print *,float(i)/float(num_elements)
|
||||
enddo
|
||||
deallocate(nbr_dist)
|
||||
!
|
||||
! Get corrosion surface distances
|
||||
open(unit=22,file='CorSurf.dat',status='unknown')
|
||||
allocate(cor_faces(max_faces,3))
|
||||
ierr=0
|
||||
inum_faces=1
|
||||
do while (ierr==0)
|
||||
read(22,*,iostat=ierr)cor_faces(inum_faces,1),cor_faces(inum_faces,2),&
|
||||
&cor_faces(inum_faces,3)
|
||||
if(ierr==0)inum_faces=inum_faces+1
|
||||
enddo
|
||||
close(unit=22)
|
||||
do i=1,num_elements
|
||||
centx=ele_centroid(i,1)
|
||||
centy=ele_centroid(i,2)
|
||||
centz=ele_centroid(i,3)
|
||||
distmin=1000.
|
||||
do j=1,inum_faces-1
|
||||
facex=cor_faces(j,1)
|
||||
facey=cor_faces(j,2)
|
||||
facez=cor_faces(j,3)
|
||||
dist=sqrt((centx-facex)*(centx-facex)+(centy-facey)*(centy-facey)&
|
||||
&+(centz-facez)*(centz-facez))
|
||||
if(dist<distmin)distmin=dist
|
||||
enddo
|
||||
cor_dist(i)=distmin
|
||||
enddo
|
||||
deallocate(cor_faces)
|
||||
!
|
||||
! Find closest cell to element centroid
|
||||
allocate(closest(max_elements))
|
||||
if(mask_type==5)then
|
||||
do i=1,num_elements
|
||||
centx=ele_centroid(i,1)
|
||||
centy=ele_centroid(i,2)
|
||||
centz=ele_centroid(i,3)
|
||||
do j=1,num_cells
|
||||
if(num_faces(j)<3)then
|
||||
print *,'warning',i,j,num_faces(j)
|
||||
cycle
|
||||
endif
|
||||
if(cell_stat(j)==1)cycle
|
||||
icheck=0
|
||||
do k=1,num_faces(j)
|
||||
rnorx=face(j,k,1)
|
||||
rnory=face(j,k,2)
|
||||
rnorz=face(j,k,3)
|
||||
roff=face(j,k,4)
|
||||
dotprod=centx*rnorx+centy*rnory+centz*rnorz+roff
|
||||
if(dotprod<0.)then
|
||||
icheck=1
|
||||
exit
|
||||
endif
|
||||
enddo
|
||||
if(icheck==0)then
|
||||
closest(i)=j
|
||||
endif
|
||||
enddo
|
||||
enddo
|
||||
else
|
||||
do i=1,num_elements
|
||||
centx=ele_centroid(i,1)
|
||||
centy=ele_centroid(i,2)
|
||||
do j=1,num_cells
|
||||
if(cell_stat(j)==1)cycle
|
||||
cellx=cell_centroid(j,1)
|
||||
celly=cell_centroid(j,2)
|
||||
icheck=0
|
||||
do k=1,num_faces(j)
|
||||
fx1=face(j,k,1)
|
||||
fx2=face(j,k,2)
|
||||
fy1=face(j,k,3)
|
||||
fy2=face(j,k,4)
|
||||
dcell=(fx2-fx1)*(celly-fy1)-(fy2-fy1)*(cellx-fx1)
|
||||
dele=(fx2-fx1)*(centy-fy1)-(fy2-fy1)*(centx-fx1)
|
||||
if(dcell<0.)then
|
||||
if(dele>=0.)icheck=1
|
||||
else
|
||||
if(dele<0.)icheck=1
|
||||
endif
|
||||
if(icheck==1)exit
|
||||
enddo
|
||||
if(icheck==0)then
|
||||
closest(i)=j
|
||||
endif
|
||||
enddo
|
||||
enddo
|
||||
endif
|
||||
!
|
||||
allocate(num_ele_cell(num_cells),cell_ele(num_cells,max_elem_in_cell))
|
||||
! Find each element in a cell
|
||||
do i=1,num_cells
|
||||
num_ele_cell(i)=0
|
||||
do j=1,num_elements
|
||||
if(closest(j)==i)then
|
||||
num_ele_cell(i)=num_ele_cell(i)+1
|
||||
cell_ele(i,num_ele_cell(i))=j
|
||||
endif
|
||||
enddo
|
||||
enddo
|
||||
!
|
||||
!
|
||||
allocate(distance(num_cells,num_elements))
|
||||
! Find min distance between element centroid and cell faces/hyperplanes
|
||||
do i=1,num_cells
|
||||
if(i==1406) print *,num_faces(i)
|
||||
do j=1,num_ele_cell(i)
|
||||
centx=ele_centroid(cell_ele(i,j),1)
|
||||
centy=ele_centroid(cell_ele(i,j),2)
|
||||
centz=ele_centroid(cell_ele(i,j),3)
|
||||
distmin=1000.
|
||||
if(mask_type==5)then
|
||||
do k=1,num_faces(i)
|
||||
rnorx=face(i,k,1)
|
||||
rnory=face(i,k,2)
|
||||
rnorz=face(i,k,3)
|
||||
roff=face(i,k,4)
|
||||
dotprod=abs(centx*rnorx+centy*rnory+centz*rnorz+roff)
|
||||
if(dotprod<distmin)distmin=dotprod
|
||||
enddo
|
||||
else
|
||||
do k=1,num_faces(i)
|
||||
x1=face(i,k,1)
|
||||
x2=face(i,k,2)
|
||||
y1=face(i,k,3)
|
||||
y2=face(i,k,4)
|
||||
dotprod=abs((x2-x1)*(y1-centy)-(x1-centx)*(y2-y1))
|
||||
dotprod=dotprod/(sqrt((x2-x1)*(x2-x1)+(y2-y1)*(y2-y1)))
|
||||
if(dotprod<distmin)distmin=dotprod
|
||||
enddo
|
||||
endif
|
||||
distance(i,j)=distmin
|
||||
enddo
|
||||
enddo
|
||||
!
|
||||
! Write Element Sets
|
||||
rewind(10)
|
||||
open(unit=13,file='GeomGenINP.inp',status='unknown')
|
||||
input2(1)='**'
|
||||
do while (index(input2(1),'*End Part')==0)
|
||||
read(10,'(a)')input2(2)
|
||||
write(13,'(a)')input2(1)
|
||||
input2(1)=input2(2)
|
||||
enddo
|
||||
do i=1,num_cells
|
||||
if(num_ele_cell(i)==0)cycle
|
||||
write(13,*)'*Elset,elset=ele',i
|
||||
icheck=1
|
||||
do j=1,num_ele_cell(i)
|
||||
if(icheck==1)then
|
||||
if(num_ele_cell(i)>1)then
|
||||
write(13,'(i6)',advance='no')cell_ele(i,j)
|
||||
else
|
||||
write(13,'(i6)')cell_ele(i,j)
|
||||
endif
|
||||
elseif(icheck==num_ele_cell(i))then
|
||||
write(13,'(a1,i6)')',',cell_ele(i,j)
|
||||
else
|
||||
if(mod(icheck,15)==0)then
|
||||
write(13,'(a1,i6)')',',cell_ele(i,j)
|
||||
else
|
||||
write(13,'(a1,i6)',advance='no')',',cell_ele(i,j)
|
||||
endif
|
||||
endif
|
||||
icheck=icheck+1
|
||||
enddo
|
||||
if(iana_type==1)write(19,*)'*Solid Section,elset=ele',i,'Boundary,material=Mat',i
|
||||
enddo
|
||||
write(13,*)'**'
|
||||
do while (index(input2(1),'*End Assembly')==0)
|
||||
read(10,'(a)')input2(2)
|
||||
write(13,'(a)')input2(1)
|
||||
input2(1)=input2(2)
|
||||
enddo
|
||||
write(13,'(a)')'*End Assembly'
|
||||
write(13,*)'*INITIAL CONDITIONS,TYPE=SOLUTION'
|
||||
do i=1,num_cells
|
||||
if(num_ele_cell(i)==0)cycle
|
||||
do j=1,num_ele_cell(i)
|
||||
write(13,'(3(a,i6),2(a,f18.6),3(i6,a))')'Assembly.CorPart.',cell_ele(i,j),',' &
|
||||
& ,cell_ele(i,j),',',max_neighbours,',',distance(i,j),',',cor_dist(cell_ele(i,j)) &
|
||||
& ,0,',',0,',',0,','
|
||||
write(13,'(8(i6,a))')0,',',0,',',0,',',0,',',0,',',0,',',0,',',1,','
|
||||
do k=1, max_neighbours
|
||||
if(mod(k,8)/=0)then
|
||||
if(k/=max_neighbours)then
|
||||
write(13,'(i6,a)',advance='no')neighbour(cell_ele(i,j),k),','
|
||||
else
|
||||
write(13,'(i6)')neighbour(cell_ele(i,j),k)
|
||||
endif
|
||||
else
|
||||
if(k/=max_neighbours)then
|
||||
write(13,'(i6,a)')neighbour(cell_ele(i,j),k),','
|
||||
else
|
||||
write(13,'(i6)')neighbour(cell_ele(i,j),k)
|
||||
endif
|
||||
endif
|
||||
enddo
|
||||
enddo
|
||||
enddo
|
||||
ierr=0
|
||||
do while (ierr==0)
|
||||
read(10,'(a)',iostat=ierr)input2(1)
|
||||
if(ierr==0)write(13,'(a)')input2(1)
|
||||
enddo
|
||||
end program
|
||||
!~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
|
||||
! Generate Voronoi Tesselation Using QHULL
|
||||
!~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
|
||||
subroutine make_voronoi(mask_type,mesh_type,num_grains,num_x,rad_hard,grain_length)
|
||||
integer mesh_type,mask_type,num_grains
|
||||
integer seed(1)
|
||||
double precision grain_length,rad_hard,rscale
|
||||
if(mesh_type==2)mask_type=4
|
||||
! Write QHull input file
|
||||
open(unit=20,file='qhullin.dat',status='unknown')
|
||||
write(20,*)mask_type-2
|
||||
if(mask_type==5)write(20,*)num_grains*27
|
||||
if(mask_type==4)write(20,*)num_grains*9
|
||||
seed=1557
|
||||
rscale=float(num_x)*Grain_Length
|
||||
call random_seed(put=seed)
|
||||
do i=1,num_grains
|
||||
call random_number(xcor)
|
||||
call random_number(ycor)
|
||||
if(mask_type==5)call random_number(zcor)
|
||||
xcor=xcor*rscale
|
||||
ycor=ycor*rscale
|
||||
if(mask_type==5)zcor=zcor*rscale
|
||||
if(mask_type==4)then
|
||||
write(20,*)xcor,ycor
|
||||
write(20,*)xcor,ycor+rscale
|
||||
write(20,*)xcor,ycor-rscale
|
||||
write(20,*)xcor+rscale,ycor
|
||||
write(20,*)xcor-rscale,ycor
|
||||
write(20,*)xcor+rscale,ycor+rscale
|
||||
write(20,*)xcor-rscale,ycor-rscale
|
||||
write(20,*)xcor+rscale,ycor-rscale
|
||||
write(20,*)xcor-rscale,ycor+rscale
|
||||
elseif(mask_type==5)then
|
||||
write(20,*)xcor,ycor,zcor
|
||||
write(20,*)xcor+rscale,ycor,zcor
|
||||
write(20,*)xcor-rscale,ycor,zcor
|
||||
write(20,*)xcor,ycor+rscale,zcor
|
||||
write(20,*)xcor,ycor-rscale,zcor
|
||||
write(20,*)xcor+rscale,ycor+rscale,zcor
|
||||
write(20,*)xcor-rscale,ycor-rscale,zcor
|
||||
write(20,*)xcor+rscale,ycor-rscale,zcor
|
||||
write(20,*)xcor-rscale,ycor+rscale,zcor
|
||||
write(20,*)xcor,ycor,zcor+rscale
|
||||
write(20,*)xcor+rscale,ycor,zcor+rscale
|
||||
write(20,*)xcor-rscale,ycor,zcor+rscale
|
||||
write(20,*)xcor,ycor+rscale,zcor+rscale
|
||||
write(20,*)xcor,ycor-rscale,zcor+rscale
|
||||
write(20,*)xcor+rscale,ycor+rscale,zcor+rscale
|
||||
write(20,*)xcor-rscale,ycor-rscale,zcor+rscale
|
||||
write(20,*)xcor+rscale,ycor-rscale,zcor+rscale
|
||||
write(20,*)xcor-rscale,ycor+rscale,zcor+rscale
|
||||
write(20,*)xcor,ycor,zcor-rscale
|
||||
write(20,*)xcor+rscale,ycor,zcor-rscale
|
||||
write(20,*)xcor-rscale,ycor,zcor-rscale
|
||||
write(20,*)xcor,ycor+rscale,zcor-rscale
|
||||
write(20,*)xcor,ycor-rscale,zcor-rscale
|
||||
write(20,*)xcor+rscale,ycor+rscale,zcor-rscale
|
||||
write(20,*)xcor-rscale,ycor-rscale,zcor-rscale
|
||||
write(20,*)xcor+rscale,ycor-rscale,zcor-rscale
|
||||
write(20,*)xcor-rscale,ycor+rscale,zcor-rscale
|
||||
endif
|
||||
enddo
|
||||
close(20)
|
||||
call system('qvoronoi.exe TI qhullin.dat o Fi TO qhullout.dat')
|
||||
end subroutine
|
||||
!~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
|
||||
! Process Voronoi Tesselation - Return Arrays of Cell Faces and Centroids
|
||||
!~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
|
||||
subroutine process_voronoi(face_sub,num_faces_sub,cell_centroid,num_cells,cell_stat)
|
||||
!
|
||||
! Variables
|
||||
character(len=320)full_line
|
||||
character(len=320)test_string
|
||||
character(len=256)input
|
||||
character(len=256)input2(2)
|
||||
integer seed (1)
|
||||
integer cell_stat(20000)
|
||||
integer,allocatable,dimension(:)::num_verts
|
||||
integer,allocatable,dimension(:)::num_cell_hyp
|
||||
integer,allocatable,dimension(:)::numverts
|
||||
integer,dimension(20000)::num_faces_sub
|
||||
integer,allocatable,dimension(:,:)::num_hyp_verts
|
||||
integer,allocatable,dimension(:,:)::vert_list
|
||||
integer,allocatable,dimension(:,:)::hyp_list
|
||||
integer,allocatable,dimension(:,:)::facet
|
||||
integer max_vc,max_hc,max_vh
|
||||
double precision,allocatable,dimension(:)::xv_cor
|
||||
double precision,allocatable,dimension(:)::yv_cor
|
||||
double precision,allocatable,dimension(:)::zv_cor
|
||||
double precision,allocatable,dimension(:)::offset
|
||||
double precision,allocatable,dimension(:,:)::cor
|
||||
double precision,allocatable,dimension(:,:)::ele_centroid
|
||||
double precision,dimension(20000,3)::cell_centroid
|
||||
double precision,dimension(20000,100,4)::face_sub
|
||||
!
|
||||
! Parameters
|
||||
parameter(max_vc=100,max_hc=100,max_vh=50)
|
||||
!
|
||||
open(unit=21,file='qhullout.dat',status='unknown')
|
||||
!
|
||||
! Allocate Arrays
|
||||
read(21,*)idimension
|
||||
read(21,*)num_total_verts,num_cells
|
||||
allocate(num_verts(num_cells))
|
||||
allocate(xv_cor(num_total_verts),yv_cor(num_total_verts))
|
||||
if(idimension==3)allocate(zv_cor(num_total_verts))
|
||||
allocate(vert_list(num_cells,max_vc))
|
||||
!
|
||||
! Read in all vertice co-ordinates
|
||||
do i=1,num_total_verts
|
||||
if(idimension==2)read(21,*)xv_cor(i),yv_cor(i)
|
||||
if(idimension==3)read(21,*)xv_cor(i),yv_cor(i),zv_cor(i)
|
||||
enddo
|
||||
!
|
||||
! Read in vertice labels for each voronoi cell
|
||||
do i=1,num_cells
|
||||
read(21,*)num_verts(i)
|
||||
backspace(21)
|
||||
if(num_verts(i)>9)then
|
||||
read(21,'(i3,a320)')idummy,full_line
|
||||
else
|
||||
read(21,'(i2,a320)')idummy,full_line
|
||||
endif
|
||||
ileft=1
|
||||
num_points=1
|
||||
do iright=1,320
|
||||
test_string=full_line(iright:iright)
|
||||
if((test_string==' ').or.(iright==320))then
|
||||
read(full_line(ileft:iright-1),'(i6)')vert_list(i,num_points)
|
||||
if(num_points==num_verts(i))exit
|
||||
ileft=iright+1
|
||||
num_points=num_points+1
|
||||
endif
|
||||
enddo
|
||||
do j=1,num_points-1
|
||||
if(vert_list(i,j)==0)cell_stat(i)=1
|
||||
enddo
|
||||
enddo
|
||||
if(idimension==3)then
|
||||
!
|
||||
! Read in bounded hyperplane cell labels and co-ordinates
|
||||
read(21,*)num_hyp
|
||||
allocate(facet(2,num_hyp),cor(3,num_hyp),offset(num_hyp))
|
||||
allocate(hyp_list(num_cells,num_hyp),num_cell_hyp(num_cells))
|
||||
!
|
||||
do i=1,num_hyp
|
||||
read(21,*)dummy,facet(1,i),facet(2,i),cor(1,i),cor(2,i),cor(3,i),offset(i)
|
||||
enddo
|
||||
!
|
||||
! Determine hyperplanes of each cell
|
||||
do i=1,num_cells
|
||||
num_hy=1
|
||||
do j=1,num_hyp
|
||||
if((facet(1,j)==i-1).or.(facet(2,j)==i-1))then
|
||||
hyp_list(i,num_hy)=j
|
||||
num_cell_hyp(i)=num_hy
|
||||
num_hy=num_hy+1
|
||||
endif
|
||||
enddo
|
||||
enddo
|
||||
!
|
||||
! Store hyperplane info in convenient format
|
||||
do i=1,num_cells
|
||||
num_faces_sub(i)=num_cell_hyp(i)
|
||||
do j=1,num_cell_hyp(i)
|
||||
face_sub(i,j,1)=cor(1,hyp_list(i,j))
|
||||
face_sub(i,j,2)=cor(2,hyp_list(i,j))
|
||||
face_sub(i,j,3)=cor(3,hyp_list(i,j))
|
||||
face_sub(i,j,4)=offset(hyp_list(i,j))
|
||||
enddo
|
||||
enddo
|
||||
else
|
||||
do i=1,num_cells
|
||||
num_faces_sub(i)=num_verts(i)
|
||||
do j=1,num_verts(i)
|
||||
x2=xv_cor(vert_list(i,j)+1)
|
||||
y2=yv_cor(vert_list(i,j)+1)
|
||||
if(j==1)then
|
||||
x1=xv_cor(vert_list(i,num_verts(i))+1)
|
||||
y1=yv_cor(vert_list(i,num_verts(i))+1)
|
||||
else
|
||||
x1=xv_cor(vert_list(i,j-1)+1)
|
||||
y1=yv_cor(vert_list(i,j-1)+1)
|
||||
endif
|
||||
face_sub(i,j,1)=x1
|
||||
face_sub(i,j,2)=x2
|
||||
face_sub(i,j,3)=y1
|
||||
face_sub(i,j,4)=y2
|
||||
enddo
|
||||
enddo
|
||||
endif
|
||||
!
|
||||
! Get cell centroid
|
||||
do i=1,num_cells
|
||||
centroidx=0.
|
||||
centroidy=0.
|
||||
centroidz=0.
|
||||
do j=1,num_verts(i)
|
||||
centroidx=centroidx+xv_cor(vert_list(i,j)+1)
|
||||
centroidy=centroidy+yv_cor(vert_list(i,j)+1)
|
||||
if(idimension==3)centroidz=centroidz+zv_cor(vert_list(i,j)+1)
|
||||
enddo
|
||||
cell_centroid(i,1)=centroidx/float(num_verts(i))
|
||||
cell_centroid(i,2)=centroidy/float(num_verts(i))
|
||||
if(idimension==3)then
|
||||
cell_centroid(i,3)=centroidz/float(num_verts(i))
|
||||
else
|
||||
cell_centroid(i,3)=0.d0
|
||||
endif
|
||||
enddo
|
||||
if(idimension==3)then
|
||||
! Flip hyperplane normal if it points away from cell centroid
|
||||
do i=1,num_cells
|
||||
centx=cell_centroid(i,1)
|
||||
centy=cell_centroid(i,2)
|
||||
centz=cell_centroid(i,3)
|
||||
distmin=1000.
|
||||
do k=1,num_faces_sub(i)
|
||||
rnorx=face_sub(i,k,1)
|
||||
rnory=face_sub(i,k,2)
|
||||
rnorz=face_sub(i,k,3)
|
||||
roff=face_sub(i,k,4)
|
||||
dotprod=centx*rnorx+centy*rnory+centz*rnorz+roff
|
||||
if(dotprod<0.)then
|
||||
face_sub(i,k,1)=-face_sub(i,k,1)
|
||||
face_sub(i,k,2)=-face_sub(i,k,2)
|
||||
face_sub(i,k,3)=-face_sub(i,k,3)
|
||||
face_sub(i,k,4)=-face_sub(i,k,4)
|
||||
endif
|
||||
enddo
|
||||
enddo
|
||||
endif
|
||||
close(unit=21)
|
||||
deallocate(num_verts,xv_cor,yv_cor)
|
||||
if(idimension==3)deallocate(zv_cor,facet,cor,offset,hyp_list,num_cell_hyp)
|
||||
end subroutine
|
||||
!~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
|
||||
! Make Squares - Return Arrays of Cell Faces and Centroids
|
||||
!~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
|
||||
subroutine make_square(i,j,k,grain_length,num_faces,face,cell_centroid,mesh_type)
|
||||
!
|
||||
integer num_faces,m
|
||||
double precision grain_length,centrex,centrey,centrez,rsign,xnor,ynor,znor
|
||||
double precision rdist
|
||||
double precision,dimension(3)::cell_centroid
|
||||
double precision,dimension(6,4)::face
|
||||
!
|
||||
!
|
||||
num_faces=4
|
||||
centrex=(i-1)*Grain_length+Grain_length/2.d0
|
||||
centrey=(j-1)*Grain_length+Grain_length/2.d0
|
||||
if(mesh_type==3)then
|
||||
centrez=(k-1)*Grain_length+Grain_length/2.d0
|
||||
else
|
||||
centrez=0.d0
|
||||
endif
|
||||
!
|
||||
! Centroid
|
||||
cell_centroid(1)=centrex
|
||||
cell_centroid(2)=centrey
|
||||
cell_centroid(3)=centrez
|
||||
!
|
||||
! Faces
|
||||
do m=1,num_faces
|
||||
rsign=1.d0
|
||||
xnor=0.d0
|
||||
ynor=0.d0
|
||||
znor=0.d0
|
||||
unitx=grain_length/2.d0
|
||||
unity=grain_length/2.d0
|
||||
if(mod(m,2)==0)rsign=-1.d0
|
||||
if(m<=2)then
|
||||
x1=centrex+rsign*unitx
|
||||
x2=centrex+rsign*unitx
|
||||
y1=centrey+unity
|
||||
y2=centrey-unity
|
||||
else
|
||||
x1=centrex+unitx
|
||||
x2=centrex-unitx
|
||||
y1=centrey+rsign*unity
|
||||
y2=centrey+rsign*unity
|
||||
endif
|
||||
face(m,1)=x1
|
||||
face(m,2)=x2
|
||||
face(m,3)=y1
|
||||
face(m,4)=y2
|
||||
enddo
|
||||
end Subroutine
|
||||
!~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
|
||||
! Make Hexagons - Return Arrays of Cell Faces and Centroids
|
||||
!~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
|
||||
subroutine make_hexagon(i,j,k,grain_length,num_faces,face,cell_centroid,mesh_type)
|
||||
integer num_faces,m
|
||||
double precision grain_length,centrex,centrey,centrez,rsign,xnor,ynor,znor
|
||||
double precision rdist
|
||||
double precision,dimension(3)::cell_centroid
|
||||
double precision,dimension(6,4)::face
|
||||
!
|
||||
!
|
||||
num_faces=6
|
||||
if(mod(j,2)==0)then
|
||||
centrex=(i-1)*sqrt(3.d0)*Grain_length+sqrt(3.d0)*Grain_length/2.d0
|
||||
else
|
||||
centrex=(i-1)*sqrt(3.)*Grain_length
|
||||
endif
|
||||
centrey=(j-1)*1.5d0*Grain_length
|
||||
if(mesh_type==3)then
|
||||
centrez=(k-1)*Grain_length
|
||||
else
|
||||
centrez=0.d0
|
||||
endif
|
||||
!
|
||||
! Centroid
|
||||
cell_centroid(1)=centrex
|
||||
cell_centroid(2)=centrey
|
||||
cell_centroid(3)=centrez
|
||||
!
|
||||
! Faces
|
||||
do m=1,num_faces
|
||||
rsign=1.d0
|
||||
rsign2=1.d0
|
||||
xnor=0.d0
|
||||
ynor=0.d0
|
||||
znor=0.d0
|
||||
unity=0.5d0*grain_length
|
||||
unitx=(sqrt(3.d0)/2.d0)*grain_length
|
||||
if(mod(m,2)==0)rsign=-1.d0
|
||||
if(m<=2)then
|
||||
x1=centrex+rsign*unitx
|
||||
x2=centrex+rsign*unitx
|
||||
y1=centrey+unity
|
||||
y2=centrey-unity
|
||||
elseif(m>2.and.m<=4)then
|
||||
x1=centrex
|
||||
x2=centrex+unitx
|
||||
y1=centrey+rsign*unity*2.d0
|
||||
y2=centrey+rsign*unity
|
||||
else
|
||||
x1=centrex
|
||||
x2=centrex-unitx
|
||||
y1=centrey+rsign*unity*2.d0
|
||||
y2=centrey+rsign*unity
|
||||
endif
|
||||
face(m,1)=x1
|
||||
face(m,2)=x2
|
||||
face(m,3)=y1
|
||||
face(m,4)=y2
|
||||
enddo
|
||||
end Subroutine
|
||||
!~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
|
||||
! Get Element Centroids
|
||||
!~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
|
||||
subroutine elem_centroids(ne,ele_centroid,mesh_type)
|
||||
!
|
||||
! Parameters
|
||||
parameter(max_nodes=1000000,max_elements=100000,max_node_in_elem=8)
|
||||
!
|
||||
! Variables
|
||||
character(len=256)input
|
||||
integer,dimension(max_elements,max_node_in_elem)::elements
|
||||
double precision,dimension(max_nodes,3)::nodes
|
||||
double precision,dimension(max_elements,3)::ele_centroid
|
||||
!
|
||||
! Open Input File and read node and element co-ordinates
|
||||
open(unit=10,file='GeomGenTemp.inp',status='unknown')
|
||||
do while (index(input,'*Node')==0)
|
||||
read(10,'(a)')input
|
||||
end do
|
||||
nn=0
|
||||
do while(1==1)
|
||||
read(10,'(a)')input
|
||||
if(index(input,'*')==0)then
|
||||
backspace(10)
|
||||
nn=nn+1
|
||||
if(mesh_type==3)then
|
||||
read(10,*)dummy,nodes(nn,1),nodes(nn,2),nodes(nn,3)
|
||||
else
|
||||
read(10,*)dummy,nodes(nn,1),nodes(nn,2)
|
||||
endif
|
||||
else
|
||||
if(mesh_type==2)then
|
||||
nele_type=4
|
||||
else
|
||||
if(index(input,'C3D8')/=0)nele_type=8
|
||||
if(index(input,'C3D4')/=0)nele_type=4
|
||||
endif
|
||||
exit
|
||||
endif
|
||||
end do
|
||||
ne=0
|
||||
do while(1==1)
|
||||
read(10,'(a)')input
|
||||
if(index(input,'*')==0)then
|
||||
backspace(10)
|
||||
ne=ne+1
|
||||
if(nele_type==8)then
|
||||
read(10,*)dummy,elements(ne,1),elements(ne,2),elements(ne,3),elements(ne,4)&
|
||||
& ,elements(ne,5),elements(ne,6),elements(ne,7),elements(ne,8)
|
||||
elseif(nele_type==4)then
|
||||
read(10,*)dummy,elements(ne,1),elements(ne,2),elements(ne,3),elements(ne,4)
|
||||
endif
|
||||
else
|
||||
exit
|
||||
endif
|
||||
end do
|
||||
!
|
||||
! Get element centroid
|
||||
do i=1,ne
|
||||
centroidx=0.d0
|
||||
centroidy=0.d0
|
||||
centroidz=0.d0
|
||||
do j=1,nele_type
|
||||
centroidx=centroidx+nodes(elements(i,j),1)
|
||||
centroidy=centroidy+nodes(elements(i,j),2)
|
||||
if(mesh_type==3)centroidz=centroidz+nodes(elements(i,j),3)
|
||||
enddo
|
||||
ele_centroid(i,1)=centroidx/float(nele_type)
|
||||
ele_centroid(i,2)=centroidy/float(nele_type)
|
||||
if(mesh_type==3)ele_centroid(i,3)=centroidz/float(nele_type)
|
||||
enddo
|
||||
end subroutine
|
||||
200
Unpublished/3D_Voxel_Assign/GrainMask_VUSD.f90
Normal file
200
Unpublished/3D_Voxel_Assign/GrainMask_VUSD.f90
Normal file
|
|
@ -0,0 +1,200 @@
|
|||
! This program generates a micro-strucutre mask and applies it to
|
||||
! an existing mesh.
|
||||
! J.Grogan 05/08/11
|
||||
program Corrosion_Preprocessor
|
||||
!
|
||||
! Parameters
|
||||
parameter(max_elements=100000,max_cells=20000,max_fc=100,max_faces=10000)
|
||||
parameter(max_elem_in_cell=50000,max_neigh_per_elem=6,max_neighbours=50)
|
||||
!
|
||||
! Variables
|
||||
character(len=256)input
|
||||
character(len=256)input2(2)
|
||||
integer,allocatable,dimension(:)::num_faces
|
||||
integer,dimension(max_elements,max_neighbours)::neighbour
|
||||
integer mesh_type
|
||||
double precision,allocatable,dimension(:,:)::distance
|
||||
double precision,allocatable,dimension(:,:)::nbr_dist
|
||||
double precision,allocatable,dimension(:,:)::cor_faces
|
||||
double precision,dimension(max_elements)::cor_dist
|
||||
double precision,allocatable,dimension(:,:)::ele_centroid
|
||||
!
|
||||
! Mesh Type: 2 = 2D, 3 = 3D
|
||||
mesh_type=3
|
||||
!
|
||||
allocate(ele_centroid(max_elements,3))
|
||||
! Get element centroids
|
||||
call elem_centroids(num_elements,ele_centroid,mesh_type)
|
||||
!
|
||||
! Get neighbouring elements
|
||||
allocate(nbr_dist(max_elements,max_neighbours))
|
||||
do i=1,num_elements
|
||||
icount=1
|
||||
do j=1,num_elements
|
||||
if(icount>max_neighbours)then
|
||||
rmaxdist=0.
|
||||
do k=1,max_neighbours
|
||||
if(nbr_dist(i,k)>rmaxdist)then
|
||||
rmaxdist=nbr_dist(i,k)
|
||||
index_max_dist=k
|
||||
endif
|
||||
enddo
|
||||
endif
|
||||
cent1x=ele_centroid(i,1)
|
||||
cent1y=ele_centroid(i,2)
|
||||
cent1z=ele_centroid(i,3)
|
||||
cent2x=ele_centroid(j,1)
|
||||
cent2y=ele_centroid(j,2)
|
||||
cent2z=ele_centroid(j,3)
|
||||
dist=sqrt((cent1x-cent2x)*(cent1x-cent2x)+(cent1y-cent2y)*(cent1y-cent2y)&
|
||||
&+(cent1z-cent2z)*(cent1z-cent2z))
|
||||
if(icount>max_neighbours)then
|
||||
if(dist<rmaxdist)then
|
||||
nbr_dist(i,index_max_dist)=dist
|
||||
neighbour(i,index_max_dist)=j
|
||||
endif
|
||||
else
|
||||
nbr_dist(i,j)=dist
|
||||
neighbour(i,j)=j
|
||||
endif
|
||||
icount=icount+1
|
||||
enddo
|
||||
print *,float(i)/float(num_elements)
|
||||
enddo
|
||||
deallocate(nbr_dist)
|
||||
!
|
||||
! Get corrosion surface distances
|
||||
open(unit=22,file='CorSurf.dat',status='unknown')
|
||||
allocate(cor_faces(max_faces,3))
|
||||
ierr=0
|
||||
inum_faces=1
|
||||
do while (ierr==0)
|
||||
read(22,*,iostat=ierr)cor_faces(inum_faces,1),cor_faces(inum_faces,2),&
|
||||
&cor_faces(inum_faces,3)
|
||||
if(ierr==0)inum_faces=inum_faces+1
|
||||
enddo
|
||||
close(unit=22)
|
||||
do i=1,num_elements
|
||||
centx=ele_centroid(i,1)
|
||||
centy=ele_centroid(i,2)
|
||||
centz=ele_centroid(i,3)
|
||||
distmin=1000.
|
||||
do j=1,inum_faces-1
|
||||
facex=cor_faces(j,1)
|
||||
facey=cor_faces(j,2)
|
||||
facez=cor_faces(j,3)
|
||||
dist=sqrt((centx-facex)*(centx-facex)+(centy-facey)*(centy-facey)&
|
||||
&+(centz-facez)*(centz-facez))
|
||||
if(dist<distmin)distmin=dist
|
||||
enddo
|
||||
cor_dist(i)=distmin
|
||||
enddo
|
||||
deallocate(cor_faces)
|
||||
!
|
||||
rewind(10)
|
||||
open(unit=13,file='GeomGenINP.inp',status='unknown')
|
||||
input2(1)='**'
|
||||
do while (index(input2(1),'*End Assembly')==0)
|
||||
read(10,'(a)')input2(2)
|
||||
write(13,'(a)')input2(1)
|
||||
input2(1)=input2(2)
|
||||
enddo
|
||||
write(13,'(a)')'*End Assembly'
|
||||
write(13,*)'*INITIAL CONDITIONS,TYPE=SOLUTION'
|
||||
do i=1,num_elements
|
||||
write(13,'(3(a,i6),2(a,f18.6),3(i6,a))')'Assembly.CorPart.',i,',' &
|
||||
& ,i,',',max_neighbours,',',0.,',',cor_dist(i,j),0,',',1.,',',0,','
|
||||
do k=1, max_neighbours
|
||||
if(mod(k,8)/=0)then
|
||||
if(k/=max_neighbours)then
|
||||
write(13,'(i6,a)',advance='no')neighbour(i,k),','
|
||||
else
|
||||
write(13,'(i6)')neighbour(i,k)
|
||||
endif
|
||||
else
|
||||
if(k/=max_neighbours)then
|
||||
write(13,'(i6,a)')neighbour(i,k),','
|
||||
else
|
||||
write(13,'(i6)')neighbour(i,k)
|
||||
endif
|
||||
endif
|
||||
enddo
|
||||
enddo
|
||||
ierr=0
|
||||
do while (ierr==0)
|
||||
read(10,'(a)',iostat=ierr)input2(1)
|
||||
if(ierr==0)write(13,'(a)')input2(1)
|
||||
enddo
|
||||
end program
|
||||
!~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
|
||||
! Get Element Centroids
|
||||
!~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
|
||||
subroutine elem_centroids(ne,ele_centroid,mesh_type)
|
||||
!
|
||||
! Parameters
|
||||
parameter(max_nodes=1000000,max_elements=100000,max_node_in_elem=8)
|
||||
!
|
||||
! Variables
|
||||
character(len=256)input
|
||||
integer,dimension(max_elements,max_node_in_elem)::elements
|
||||
double precision,dimension(max_nodes,3)::nodes
|
||||
double precision,dimension(max_elements,3)::ele_centroid
|
||||
!
|
||||
! Open Input File and read node and element co-ordinates
|
||||
open(unit=10,file='GeomGenTemp.inp',status='unknown')
|
||||
do while (index(input,'*Node')==0)
|
||||
read(10,'(a)')input
|
||||
end do
|
||||
nn=0
|
||||
do while(1==1)
|
||||
read(10,'(a)')input
|
||||
if(index(input,'*')==0)then
|
||||
backspace(10)
|
||||
nn=nn+1
|
||||
if(mesh_type==3)then
|
||||
read(10,*)dummy,nodes(nn,1),nodes(nn,2),nodes(nn,3)
|
||||
else
|
||||
read(10,*)dummy,nodes(nn,1),nodes(nn,2)
|
||||
endif
|
||||
else
|
||||
if(mesh_type==2)then
|
||||
nele_type=4
|
||||
else
|
||||
if(index(input,'C3D8')/=0)nele_type=8
|
||||
if(index(input,'C3D4')/=0)nele_type=4
|
||||
endif
|
||||
exit
|
||||
endif
|
||||
end do
|
||||
ne=0
|
||||
do while(1==1)
|
||||
read(10,'(a)')input
|
||||
if(index(input,'*')==0)then
|
||||
backspace(10)
|
||||
ne=ne+1
|
||||
if(nele_type==8)then
|
||||
read(10,*)dummy,elements(ne,1),elements(ne,2),elements(ne,3),elements(ne,4)&
|
||||
& ,elements(ne,5),elements(ne,6),elements(ne,7),elements(ne,8)
|
||||
elseif(nele_type==4)then
|
||||
read(10,*)dummy,elements(ne,1),elements(ne,2),elements(ne,3),elements(ne,4)
|
||||
endif
|
||||
else
|
||||
exit
|
||||
endif
|
||||
end do
|
||||
!
|
||||
! Get element centroid
|
||||
do i=1,ne
|
||||
centroidx=0.d0
|
||||
centroidy=0.d0
|
||||
centroidz=0.d0
|
||||
do j=1,nele_type
|
||||
centroidx=centroidx+nodes(elements(i,j),1)
|
||||
centroidy=centroidy+nodes(elements(i,j),2)
|
||||
if(mesh_type==3)centroidz=centroidz+nodes(elements(i,j),3)
|
||||
enddo
|
||||
ele_centroid(i,1)=centroidx/float(nele_type)
|
||||
ele_centroid(i,2)=centroidy/float(nele_type)
|
||||
if(mesh_type==3)ele_centroid(i,3)=centroidz/float(nele_type)
|
||||
enddo
|
||||
end subroutine
|
||||
750
Unpublished/3D_Voxel_Assign/GrainMask_VUSD.for
Normal file
750
Unpublished/3D_Voxel_Assign/GrainMask_VUSD.for
Normal file
|
|
@ -0,0 +1,750 @@
|
|||
! This program generates a micro-strucutre mask and applies it to
|
||||
! an existing mesh.
|
||||
! J.Grogan 05/08/11
|
||||
program Voronoi3DPost
|
||||
!
|
||||
! Parameters
|
||||
parameter(max_elements=100000,max_cells=20000,max_fc=100,max_faces=10000)
|
||||
parameter(max_elem_in_cell=50000,max_neigh_per_elem=6,max_neighbours=50)
|
||||
!
|
||||
! Variables
|
||||
character(len=256)input
|
||||
character(len=256)input2(2)
|
||||
integer cell_stat(20000)
|
||||
integer,allocatable,dimension(:)::closest
|
||||
integer,allocatable,dimension(:)::num_ele_cell
|
||||
integer,allocatable,dimension(:)::num_faces
|
||||
integer,allocatable,dimension(:)::cell_status
|
||||
integer,allocatable,dimension(:,:)::cell_ele
|
||||
integer,dimension(max_elements)::num_neighbours
|
||||
integer,dimension(max_elements,max_neighbours)::neighbour
|
||||
integer mesh_type,mask_type,num_x,num_y,num_z,num_grains
|
||||
double precision grain_length,rad_hard,rscale
|
||||
double precision,allocatable,dimension(:,:)::distance
|
||||
double precision,allocatable,dimension(:,:)::nbr_dist
|
||||
double precision,allocatable,dimension(:,:)::cor_faces
|
||||
double precision,dimension(max_elements)::cor_dist
|
||||
double precision,allocatable,dimension(:,:)::ele_centroid
|
||||
double precision,allocatable,dimension(:,:)::cell_centroid
|
||||
double precision,allocatable,dimension(:,:,:)::face
|
||||
!
|
||||
! Mesh Type: 2 = 2D, 3 = 3D
|
||||
mesh_type=3
|
||||
! Mask Type: 1= Square, 2= Hexagon, 3= Dodec, 4=2D Voronoi, 5=3D Voronoi
|
||||
mask_type=5
|
||||
! Grain Length
|
||||
Grain_length=0.025
|
||||
! Num grains x
|
||||
num_x=10
|
||||
! Num grains y
|
||||
num_y=10
|
||||
! Num grains z
|
||||
num_z=1
|
||||
! Hardcore Voronoi Radius
|
||||
rad_hard=0.00
|
||||
num_grains=num_x*num_y*num_z
|
||||
if(mask_type>3)then
|
||||
! Create Tessellation
|
||||
allocate(face(max_cells,max_fc,4),num_faces(max_cells),cell_centroid(max_cells,3))
|
||||
call make_voronoi(mask_type,mesh_type,num_grains,num_x,rad_hard,grain_length)
|
||||
call process_voronoi(face,num_faces,cell_centroid,num_cells,cell_stat)
|
||||
else
|
||||
! Generate Centroids and faces for other geometries
|
||||
icount=1
|
||||
num_cells=num_grains
|
||||
allocate(face(num_cells,6,4),num_faces(num_cells),cell_centroid(num_cells,3))
|
||||
do i=1,num_x
|
||||
do j=1,num_y
|
||||
do k=1,num_z
|
||||
if(mask_type==1)then
|
||||
call make_square(i,j,k,grain_length,num_faces(icount), &
|
||||
& face(icount,:,:),cell_centroid(icount,:),mesh_type)
|
||||
elseif(mask_type==2)then
|
||||
call make_hexagon(i,j,k,grain_length,num_faces(icount), &
|
||||
& face(icount,:,:),cell_centroid(icount,:),mesh_type)
|
||||
else
|
||||
if(mod(j,2)==0)then
|
||||
cell_centroid(icount,1)=2.*(i-1)*Grain_length*sqrt(2.)+&
|
||||
&sqrt(2.)*Grain_length
|
||||
cell_centroid(icount,3)=2.*(k-1)*Grain_length*sqrt(2.)+&
|
||||
&Grain_length*sqrt(2.)
|
||||
else
|
||||
cell_centroid(icount,1)=2.*(i-1)*Grain_length*sqrt(2.)
|
||||
cell_centroid(icount,3)=2.*(k-1)*Grain_length*sqrt(2.)
|
||||
endif
|
||||
cell_centroid(icount,2)=2.*(j-1)*Grain_length
|
||||
endif
|
||||
icount=icount+1
|
||||
enddo
|
||||
enddo
|
||||
enddo
|
||||
endif
|
||||
!
|
||||
allocate(ele_centroid(max_elements,3))
|
||||
! Get element centroids
|
||||
call elem_centroids(num_elements,ele_centroid,mesh_type)
|
||||
!
|
||||
! Get neighbouring elements
|
||||
allocate(nbr_dist(max_elements,max_neighbours))
|
||||
do i=1,num_elements
|
||||
icount=1
|
||||
do j=1,num_elements
|
||||
if(icount>max_neighbours)then
|
||||
rmaxdist=0.
|
||||
do k=1,max_neighbours
|
||||
if(nbr_dist(i,k)>rmaxdist)then
|
||||
rmaxdist=nbr_dist(i,k)
|
||||
index_max_dist=k
|
||||
endif
|
||||
enddo
|
||||
endif
|
||||
cent1x=ele_centroid(i,1)
|
||||
cent1y=ele_centroid(i,2)
|
||||
cent1z=ele_centroid(i,3)
|
||||
cent2x=ele_centroid(j,1)
|
||||
cent2y=ele_centroid(j,2)
|
||||
cent2z=ele_centroid(j,3)
|
||||
dist=sqrt((cent1x-cent2x)*(cent1x-cent2x)+(cent1y-cent2y)*(cent1y-cent2y)&
|
||||
&+(cent1z-cent2z)*(cent1z-cent2z))
|
||||
if(icount>max_neighbours)then
|
||||
if(dist<rmaxdist)then
|
||||
nbr_dist(i,index_max_dist)=dist
|
||||
neighbour(i,index_max_dist)=j
|
||||
endif
|
||||
else
|
||||
nbr_dist(i,j)=dist
|
||||
neighbour(i,j)=j
|
||||
endif
|
||||
icount=icount+1
|
||||
enddo
|
||||
print *,float(i)/float(num_elements)
|
||||
enddo
|
||||
deallocate(nbr_dist)
|
||||
!
|
||||
! Get corrosion surface distances
|
||||
open(unit=22,file='CorSurf.dat',status='unknown')
|
||||
allocate(cor_faces(max_faces,3))
|
||||
ierr=0
|
||||
inum_faces=1
|
||||
do while (ierr==0)
|
||||
read(22,*,iostat=ierr)cor_faces(inum_faces,1),cor_faces(inum_faces,2),&
|
||||
&cor_faces(inum_faces,3)
|
||||
if(ierr==0)inum_faces=inum_faces+1
|
||||
enddo
|
||||
close(unit=22)
|
||||
do i=1,num_elements
|
||||
centx=ele_centroid(i,1)
|
||||
centy=ele_centroid(i,2)
|
||||
centz=ele_centroid(i,3)
|
||||
distmin=1000.
|
||||
do j=1,inum_faces-1
|
||||
facex=cor_faces(j,1)
|
||||
facey=cor_faces(j,2)
|
||||
facez=cor_faces(j,3)
|
||||
dist=sqrt((centx-facex)*(centx-facex)+(centy-facey)*(centy-facey)&
|
||||
&+(centz-facez)*(centz-facez))
|
||||
if(dist<distmin)distmin=dist
|
||||
enddo
|
||||
cor_dist(i)=distmin
|
||||
enddo
|
||||
deallocate(cor_faces)
|
||||
!
|
||||
! Find closest cell to element centroid
|
||||
allocate(closest(max_elements))
|
||||
if(mask_type==5)then
|
||||
do i=1,num_elements
|
||||
centx=ele_centroid(i,1)
|
||||
centy=ele_centroid(i,2)
|
||||
centz=ele_centroid(i,3)
|
||||
do j=1,num_cells
|
||||
if(num_faces(j)<3)then
|
||||
print *,'warning',i,j,num_faces(j)
|
||||
cycle
|
||||
endif
|
||||
if(cell_stat(j)==1)cycle
|
||||
icheck=0
|
||||
do k=1,num_faces(j)
|
||||
rnorx=face(j,k,1)
|
||||
rnory=face(j,k,2)
|
||||
rnorz=face(j,k,3)
|
||||
roff=face(j,k,4)
|
||||
dotprod=centx*rnorx+centy*rnory+centz*rnorz+roff
|
||||
if(dotprod<0.)then
|
||||
icheck=1
|
||||
exit
|
||||
endif
|
||||
enddo
|
||||
if(icheck==0)then
|
||||
closest(i)=j
|
||||
endif
|
||||
enddo
|
||||
enddo
|
||||
else
|
||||
do i=1,num_elements
|
||||
centx=ele_centroid(i,1)
|
||||
centy=ele_centroid(i,2)
|
||||
do j=1,num_cells
|
||||
if(cell_stat(j)==1)cycle
|
||||
cellx=cell_centroid(j,1)
|
||||
celly=cell_centroid(j,2)
|
||||
icheck=0
|
||||
do k=1,num_faces(j)
|
||||
fx1=face(j,k,1)
|
||||
fx2=face(j,k,2)
|
||||
fy1=face(j,k,3)
|
||||
fy2=face(j,k,4)
|
||||
dcell=(fx2-fx1)*(celly-fy1)-(fy2-fy1)*(cellx-fx1)
|
||||
dele=(fx2-fx1)*(centy-fy1)-(fy2-fy1)*(centx-fx1)
|
||||
if(dcell<0.)then
|
||||
if(dele>=0.)icheck=1
|
||||
else
|
||||
if(dele<0.)icheck=1
|
||||
endif
|
||||
if(icheck==1)exit
|
||||
enddo
|
||||
if(icheck==0)then
|
||||
closest(i)=j
|
||||
endif
|
||||
enddo
|
||||
enddo
|
||||
endif
|
||||
!
|
||||
allocate(num_ele_cell(num_cells),cell_ele(num_cells,max_elem_in_cell))
|
||||
! Find each element in a cell
|
||||
do i=1,num_cells
|
||||
num_ele_cell(i)=0
|
||||
do j=1,num_elements
|
||||
if(closest(j)==i)then
|
||||
num_ele_cell(i)=num_ele_cell(i)+1
|
||||
cell_ele(i,num_ele_cell(i))=j
|
||||
endif
|
||||
enddo
|
||||
enddo
|
||||
!
|
||||
!
|
||||
allocate(distance(num_cells,num_elements))
|
||||
! Find min distance between element centroid and cell faces/hyperplanes
|
||||
do i=1,num_cells
|
||||
if(i==1406) print *,num_faces(i)
|
||||
do j=1,num_ele_cell(i)
|
||||
centx=ele_centroid(cell_ele(i,j),1)
|
||||
centy=ele_centroid(cell_ele(i,j),2)
|
||||
centz=ele_centroid(cell_ele(i,j),3)
|
||||
distmin=1000.
|
||||
if(mask_type==5)then
|
||||
do k=1,num_faces(i)
|
||||
rnorx=face(i,k,1)
|
||||
rnory=face(i,k,2)
|
||||
rnorz=face(i,k,3)
|
||||
roff=face(i,k,4)
|
||||
dotprod=abs(centx*rnorx+centy*rnory+centz*rnorz+roff)
|
||||
if(dotprod<distmin)distmin=dotprod
|
||||
enddo
|
||||
else
|
||||
do k=1,num_faces(i)
|
||||
x1=face(i,k,1)
|
||||
x2=face(i,k,2)
|
||||
y1=face(i,k,3)
|
||||
y2=face(i,k,4)
|
||||
dotprod=abs((x2-x1)*(y1-centy)-(x1-centx)*(y2-y1))
|
||||
dotprod=dotprod/(sqrt((x2-x1)*(x2-x1)+(y2-y1)*(y2-y1)))
|
||||
if(dotprod<distmin)distmin=dotprod
|
||||
enddo
|
||||
endif
|
||||
distance(i,j)=distmin
|
||||
enddo
|
||||
enddo
|
||||
!
|
||||
! Write Element Sets
|
||||
rewind(10)
|
||||
open(unit=13,file='GeomGenINP.inp',status='unknown')
|
||||
input2(1)='**'
|
||||
do while (index(input2(1),'*End Part')==0)
|
||||
read(10,'(a)')input2(2)
|
||||
write(13,'(a)')input2(1)
|
||||
input2(1)=input2(2)
|
||||
enddo
|
||||
do i=1,num_cells
|
||||
if(num_ele_cell(i)==0)cycle
|
||||
write(13,*)'*Elset,elset=ele',i
|
||||
icheck=1
|
||||
do j=1,num_ele_cell(i)
|
||||
if(icheck==1)then
|
||||
if(num_ele_cell(i)>1)then
|
||||
write(13,'(i6)',advance='no')cell_ele(i,j)
|
||||
else
|
||||
write(13,'(i6)')cell_ele(i,j)
|
||||
endif
|
||||
elseif(icheck==num_ele_cell(i))then
|
||||
write(13,'(a1,i6)')',',cell_ele(i,j)
|
||||
else
|
||||
if(mod(icheck,15)==0)then
|
||||
write(13,'(a1,i6)')',',cell_ele(i,j)
|
||||
else
|
||||
write(13,'(a1,i6)',advance='no')',',cell_ele(i,j)
|
||||
endif
|
||||
endif
|
||||
icheck=icheck+1
|
||||
enddo
|
||||
if(iana_type==1)write(19,*)'*Solid Section,elset=ele',i,'Boundary,material=Mat',i
|
||||
enddo
|
||||
write(13,*)'**'
|
||||
do while (index(input2(1),'*End Assembly')==0)
|
||||
read(10,'(a)')input2(2)
|
||||
write(13,'(a)')input2(1)
|
||||
input2(1)=input2(2)
|
||||
enddo
|
||||
write(13,'(a)')'*End Assembly'
|
||||
write(13,*)'*INITIAL CONDITIONS,TYPE=SOLUTION'
|
||||
do i=1,num_cells
|
||||
if(num_ele_cell(i)==0)cycle
|
||||
do j=1,num_ele_cell(i)
|
||||
write(13,'(3(a,i6),2(a,f18.6),3(i6,a))')'Assembly.CorPart.',cell_ele(i,j),',' &
|
||||
& ,cell_ele(i,j),',',max_neighbours,',',distance(i,j),',',cor_dist(cell_ele(i,j)) &
|
||||
& ,0,',',0,',',0,','
|
||||
write(13,'(8(i6,a))')0,',',0,',',0,',',0,',',0,',',0,',',0,',',1,','
|
||||
do k=1, max_neighbours
|
||||
if(mod(k,8)/=0)then
|
||||
if(k/=max_neighbours)then
|
||||
write(13,'(i6,a)',advance='no')neighbour(cell_ele(i,j),k),','
|
||||
else
|
||||
write(13,'(i6)')neighbour(cell_ele(i,j),k)
|
||||
endif
|
||||
else
|
||||
if(k/=max_neighbours)then
|
||||
write(13,'(i6,a)')neighbour(cell_ele(i,j),k),','
|
||||
else
|
||||
write(13,'(i6)')neighbour(cell_ele(i,j),k)
|
||||
endif
|
||||
endif
|
||||
enddo
|
||||
enddo
|
||||
enddo
|
||||
ierr=0
|
||||
do while (ierr==0)
|
||||
read(10,'(a)',iostat=ierr)input2(1)
|
||||
if(ierr==0)write(13,'(a)')input2(1)
|
||||
enddo
|
||||
end program
|
||||
!~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
|
||||
! Generate Voronoi Tesselation Using QHULL
|
||||
!~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
|
||||
subroutine make_voronoi(mask_type,mesh_type,num_grains,num_x,rad_hard,grain_length)
|
||||
integer mesh_type,mask_type,num_grains
|
||||
integer seed(1)
|
||||
double precision grain_length,rad_hard,rscale
|
||||
if(mesh_type==2)mask_type=4
|
||||
! Write QHull input file
|
||||
open(unit=20,file='qhullin.dat',status='unknown')
|
||||
write(20,*)mask_type-2
|
||||
if(mask_type==5)write(20,*)num_grains*27
|
||||
if(mask_type==4)write(20,*)num_grains*9
|
||||
seed=1557
|
||||
rscale=float(num_x)*Grain_Length
|
||||
call random_seed(put=seed)
|
||||
do i=1,num_grains
|
||||
call random_number(xcor)
|
||||
call random_number(ycor)
|
||||
if(mask_type==5)call random_number(zcor)
|
||||
xcor=xcor*rscale
|
||||
ycor=ycor*rscale
|
||||
if(mask_type==5)zcor=zcor*rscale
|
||||
if(mask_type==4)then
|
||||
write(20,*)xcor,ycor
|
||||
write(20,*)xcor,ycor+rscale
|
||||
write(20,*)xcor,ycor-rscale
|
||||
write(20,*)xcor+rscale,ycor
|
||||
write(20,*)xcor-rscale,ycor
|
||||
write(20,*)xcor+rscale,ycor+rscale
|
||||
write(20,*)xcor-rscale,ycor-rscale
|
||||
write(20,*)xcor+rscale,ycor-rscale
|
||||
write(20,*)xcor-rscale,ycor+rscale
|
||||
elseif(mask_type==5)then
|
||||
write(20,*)xcor,ycor,zcor
|
||||
write(20,*)xcor+rscale,ycor,zcor
|
||||
write(20,*)xcor-rscale,ycor,zcor
|
||||
write(20,*)xcor,ycor+rscale,zcor
|
||||
write(20,*)xcor,ycor-rscale,zcor
|
||||
write(20,*)xcor+rscale,ycor+rscale,zcor
|
||||
write(20,*)xcor-rscale,ycor-rscale,zcor
|
||||
write(20,*)xcor+rscale,ycor-rscale,zcor
|
||||
write(20,*)xcor-rscale,ycor+rscale,zcor
|
||||
write(20,*)xcor,ycor,zcor+rscale
|
||||
write(20,*)xcor+rscale,ycor,zcor+rscale
|
||||
write(20,*)xcor-rscale,ycor,zcor+rscale
|
||||
write(20,*)xcor,ycor+rscale,zcor+rscale
|
||||
write(20,*)xcor,ycor-rscale,zcor+rscale
|
||||
write(20,*)xcor+rscale,ycor+rscale,zcor+rscale
|
||||
write(20,*)xcor-rscale,ycor-rscale,zcor+rscale
|
||||
write(20,*)xcor+rscale,ycor-rscale,zcor+rscale
|
||||
write(20,*)xcor-rscale,ycor+rscale,zcor+rscale
|
||||
write(20,*)xcor,ycor,zcor-rscale
|
||||
write(20,*)xcor+rscale,ycor,zcor-rscale
|
||||
write(20,*)xcor-rscale,ycor,zcor-rscale
|
||||
write(20,*)xcor,ycor+rscale,zcor-rscale
|
||||
write(20,*)xcor,ycor-rscale,zcor-rscale
|
||||
write(20,*)xcor+rscale,ycor+rscale,zcor-rscale
|
||||
write(20,*)xcor-rscale,ycor-rscale,zcor-rscale
|
||||
write(20,*)xcor+rscale,ycor-rscale,zcor-rscale
|
||||
write(20,*)xcor-rscale,ycor+rscale,zcor-rscale
|
||||
endif
|
||||
enddo
|
||||
close(20)
|
||||
call system('qvoronoi.exe TI qhullin.dat o Fi TO qhullout.dat')
|
||||
end subroutine
|
||||
!~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
|
||||
! Process Voronoi Tesselation - Return Arrays of Cell Faces and Centroids
|
||||
!~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
|
||||
subroutine process_voronoi(face_sub,num_faces_sub,cell_centroid,num_cells,cell_stat)
|
||||
!
|
||||
! Variables
|
||||
character(len=320)full_line
|
||||
character(len=320)test_string
|
||||
character(len=256)input
|
||||
character(len=256)input2(2)
|
||||
integer seed (1)
|
||||
integer cell_stat(20000)
|
||||
integer,allocatable,dimension(:)::num_verts
|
||||
integer,allocatable,dimension(:)::num_cell_hyp
|
||||
integer,allocatable,dimension(:)::numverts
|
||||
integer,dimension(20000)::num_faces_sub
|
||||
integer,allocatable,dimension(:,:)::num_hyp_verts
|
||||
integer,allocatable,dimension(:,:)::vert_list
|
||||
integer,allocatable,dimension(:,:)::hyp_list
|
||||
integer,allocatable,dimension(:,:)::facet
|
||||
integer max_vc,max_hc,max_vh
|
||||
double precision,allocatable,dimension(:)::xv_cor
|
||||
double precision,allocatable,dimension(:)::yv_cor
|
||||
double precision,allocatable,dimension(:)::zv_cor
|
||||
double precision,allocatable,dimension(:)::offset
|
||||
double precision,allocatable,dimension(:,:)::cor
|
||||
double precision,allocatable,dimension(:,:)::ele_centroid
|
||||
double precision,dimension(20000,3)::cell_centroid
|
||||
double precision,dimension(20000,100,4)::face_sub
|
||||
!
|
||||
! Parameters
|
||||
parameter(max_vc=100,max_hc=100,max_vh=50)
|
||||
!
|
||||
open(unit=21,file='qhullout.dat',status='unknown')
|
||||
!
|
||||
! Allocate Arrays
|
||||
read(21,*)idimension
|
||||
read(21,*)num_total_verts,num_cells
|
||||
allocate(num_verts(num_cells))
|
||||
allocate(xv_cor(num_total_verts),yv_cor(num_total_verts))
|
||||
if(idimension==3)allocate(zv_cor(num_total_verts))
|
||||
allocate(vert_list(num_cells,max_vc))
|
||||
!
|
||||
! Read in all vertice co-ordinates
|
||||
do i=1,num_total_verts
|
||||
if(idimension==2)read(21,*)xv_cor(i),yv_cor(i)
|
||||
if(idimension==3)read(21,*)xv_cor(i),yv_cor(i),zv_cor(i)
|
||||
enddo
|
||||
!
|
||||
! Read in vertice labels for each voronoi cell
|
||||
do i=1,num_cells
|
||||
read(21,*)num_verts(i)
|
||||
backspace(21)
|
||||
if(num_verts(i)>9)then
|
||||
read(21,'(i3,a320)')idummy,full_line
|
||||
else
|
||||
read(21,'(i2,a320)')idummy,full_line
|
||||
endif
|
||||
ileft=1
|
||||
num_points=1
|
||||
do iright=1,320
|
||||
test_string=full_line(iright:iright)
|
||||
if((test_string==' ').or.(iright==320))then
|
||||
read(full_line(ileft:iright-1),'(i6)')vert_list(i,num_points)
|
||||
if(num_points==num_verts(i))exit
|
||||
ileft=iright+1
|
||||
num_points=num_points+1
|
||||
endif
|
||||
enddo
|
||||
do j=1,num_points-1
|
||||
if(vert_list(i,j)==0)cell_stat(i)=1
|
||||
enddo
|
||||
enddo
|
||||
if(idimension==3)then
|
||||
!
|
||||
! Read in bounded hyperplane cell labels and co-ordinates
|
||||
read(21,*)num_hyp
|
||||
allocate(facet(2,num_hyp),cor(3,num_hyp),offset(num_hyp))
|
||||
allocate(hyp_list(num_cells,num_hyp),num_cell_hyp(num_cells))
|
||||
!
|
||||
do i=1,num_hyp
|
||||
read(21,*)dummy,facet(1,i),facet(2,i),cor(1,i),cor(2,i),cor(3,i),offset(i)
|
||||
enddo
|
||||
!
|
||||
! Determine hyperplanes of each cell
|
||||
do i=1,num_cells
|
||||
num_hy=1
|
||||
do j=1,num_hyp
|
||||
if((facet(1,j)==i-1).or.(facet(2,j)==i-1))then
|
||||
hyp_list(i,num_hy)=j
|
||||
num_cell_hyp(i)=num_hy
|
||||
num_hy=num_hy+1
|
||||
endif
|
||||
enddo
|
||||
enddo
|
||||
!
|
||||
! Store hyperplane info in convenient format
|
||||
do i=1,num_cells
|
||||
num_faces_sub(i)=num_cell_hyp(i)
|
||||
do j=1,num_cell_hyp(i)
|
||||
face_sub(i,j,1)=cor(1,hyp_list(i,j))
|
||||
face_sub(i,j,2)=cor(2,hyp_list(i,j))
|
||||
face_sub(i,j,3)=cor(3,hyp_list(i,j))
|
||||
face_sub(i,j,4)=offset(hyp_list(i,j))
|
||||
enddo
|
||||
enddo
|
||||
else
|
||||
do i=1,num_cells
|
||||
num_faces_sub(i)=num_verts(i)
|
||||
do j=1,num_verts(i)
|
||||
x2=xv_cor(vert_list(i,j)+1)
|
||||
y2=yv_cor(vert_list(i,j)+1)
|
||||
if(j==1)then
|
||||
x1=xv_cor(vert_list(i,num_verts(i))+1)
|
||||
y1=yv_cor(vert_list(i,num_verts(i))+1)
|
||||
else
|
||||
x1=xv_cor(vert_list(i,j-1)+1)
|
||||
y1=yv_cor(vert_list(i,j-1)+1)
|
||||
endif
|
||||
face_sub(i,j,1)=x1
|
||||
face_sub(i,j,2)=x2
|
||||
face_sub(i,j,3)=y1
|
||||
face_sub(i,j,4)=y2
|
||||
enddo
|
||||
enddo
|
||||
endif
|
||||
!
|
||||
! Get cell centroid
|
||||
do i=1,num_cells
|
||||
centroidx=0.
|
||||
centroidy=0.
|
||||
centroidz=0.
|
||||
do j=1,num_verts(i)
|
||||
centroidx=centroidx+xv_cor(vert_list(i,j)+1)
|
||||
centroidy=centroidy+yv_cor(vert_list(i,j)+1)
|
||||
if(idimension==3)centroidz=centroidz+zv_cor(vert_list(i,j)+1)
|
||||
enddo
|
||||
cell_centroid(i,1)=centroidx/float(num_verts(i))
|
||||
cell_centroid(i,2)=centroidy/float(num_verts(i))
|
||||
if(idimension==3)then
|
||||
cell_centroid(i,3)=centroidz/float(num_verts(i))
|
||||
else
|
||||
cell_centroid(i,3)=0.d0
|
||||
endif
|
||||
enddo
|
||||
if(idimension==3)then
|
||||
! Flip hyperplane normal if it points away from cell centroid
|
||||
do i=1,num_cells
|
||||
centx=cell_centroid(i,1)
|
||||
centy=cell_centroid(i,2)
|
||||
centz=cell_centroid(i,3)
|
||||
distmin=1000.
|
||||
do k=1,num_faces_sub(i)
|
||||
rnorx=face_sub(i,k,1)
|
||||
rnory=face_sub(i,k,2)
|
||||
rnorz=face_sub(i,k,3)
|
||||
roff=face_sub(i,k,4)
|
||||
dotprod=centx*rnorx+centy*rnory+centz*rnorz+roff
|
||||
if(dotprod<0.)then
|
||||
face_sub(i,k,1)=-face_sub(i,k,1)
|
||||
face_sub(i,k,2)=-face_sub(i,k,2)
|
||||
face_sub(i,k,3)=-face_sub(i,k,3)
|
||||
face_sub(i,k,4)=-face_sub(i,k,4)
|
||||
endif
|
||||
enddo
|
||||
enddo
|
||||
endif
|
||||
close(unit=21)
|
||||
deallocate(num_verts,xv_cor,yv_cor)
|
||||
if(idimension==3)deallocate(zv_cor,facet,cor,offset,hyp_list,num_cell_hyp)
|
||||
end subroutine
|
||||
!~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
|
||||
! Make Squares - Return Arrays of Cell Faces and Centroids
|
||||
!~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
|
||||
subroutine make_square(i,j,k,grain_length,num_faces,face,cell_centroid,mesh_type)
|
||||
!
|
||||
integer num_faces,m
|
||||
double precision grain_length,centrex,centrey,centrez,rsign,xnor,ynor,znor
|
||||
double precision rdist
|
||||
double precision,dimension(3)::cell_centroid
|
||||
double precision,dimension(6,4)::face
|
||||
!
|
||||
!
|
||||
num_faces=4
|
||||
centrex=(i-1)*Grain_length+Grain_length/2.d0
|
||||
centrey=(j-1)*Grain_length+Grain_length/2.d0
|
||||
if(mesh_type==3)then
|
||||
centrez=(k-1)*Grain_length+Grain_length/2.d0
|
||||
else
|
||||
centrez=0.d0
|
||||
endif
|
||||
!
|
||||
! Centroid
|
||||
cell_centroid(1)=centrex
|
||||
cell_centroid(2)=centrey
|
||||
cell_centroid(3)=centrez
|
||||
!
|
||||
! Faces
|
||||
do m=1,num_faces
|
||||
rsign=1.d0
|
||||
xnor=0.d0
|
||||
ynor=0.d0
|
||||
znor=0.d0
|
||||
unitx=grain_length/2.d0
|
||||
unity=grain_length/2.d0
|
||||
if(mod(m,2)==0)rsign=-1.d0
|
||||
if(m<=2)then
|
||||
x1=centrex+rsign*unitx
|
||||
x2=centrex+rsign*unitx
|
||||
y1=centrey+unity
|
||||
y2=centrey-unity
|
||||
else
|
||||
x1=centrex+unitx
|
||||
x2=centrex-unitx
|
||||
y1=centrey+rsign*unity
|
||||
y2=centrey+rsign*unity
|
||||
endif
|
||||
face(m,1)=x1
|
||||
face(m,2)=x2
|
||||
face(m,3)=y1
|
||||
face(m,4)=y2
|
||||
enddo
|
||||
end Subroutine
|
||||
!~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
|
||||
! Make Hexagons - Return Arrays of Cell Faces and Centroids
|
||||
!~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
|
||||
subroutine make_hexagon(i,j,k,grain_length,num_faces,face,cell_centroid,mesh_type)
|
||||
integer num_faces,m
|
||||
double precision grain_length,centrex,centrey,centrez,rsign,xnor,ynor,znor
|
||||
double precision rdist
|
||||
double precision,dimension(3)::cell_centroid
|
||||
double precision,dimension(6,4)::face
|
||||
!
|
||||
!
|
||||
num_faces=6
|
||||
if(mod(j,2)==0)then
|
||||
centrex=(i-1)*sqrt(3.d0)*Grain_length+sqrt(3.d0)*Grain_length/2.d0
|
||||
else
|
||||
centrex=(i-1)*sqrt(3.)*Grain_length
|
||||
endif
|
||||
centrey=(j-1)*1.5d0*Grain_length
|
||||
if(mesh_type==3)then
|
||||
centrez=(k-1)*Grain_length
|
||||
else
|
||||
centrez=0.d0
|
||||
endif
|
||||
!
|
||||
! Centroid
|
||||
cell_centroid(1)=centrex
|
||||
cell_centroid(2)=centrey
|
||||
cell_centroid(3)=centrez
|
||||
!
|
||||
! Faces
|
||||
do m=1,num_faces
|
||||
rsign=1.d0
|
||||
rsign2=1.d0
|
||||
xnor=0.d0
|
||||
ynor=0.d0
|
||||
znor=0.d0
|
||||
unity=0.5d0*grain_length
|
||||
unitx=(sqrt(3.d0)/2.d0)*grain_length
|
||||
if(mod(m,2)==0)rsign=-1.d0
|
||||
if(m<=2)then
|
||||
x1=centrex+rsign*unitx
|
||||
x2=centrex+rsign*unitx
|
||||
y1=centrey+unity
|
||||
y2=centrey-unity
|
||||
elseif(m>2.and.m<=4)then
|
||||
x1=centrex
|
||||
x2=centrex+unitx
|
||||
y1=centrey+rsign*unity*2.d0
|
||||
y2=centrey+rsign*unity
|
||||
else
|
||||
x1=centrex
|
||||
x2=centrex-unitx
|
||||
y1=centrey+rsign*unity*2.d0
|
||||
y2=centrey+rsign*unity
|
||||
endif
|
||||
face(m,1)=x1
|
||||
face(m,2)=x2
|
||||
face(m,3)=y1
|
||||
face(m,4)=y2
|
||||
enddo
|
||||
end Subroutine
|
||||
!~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
|
||||
! Get Element Centroids
|
||||
!~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
|
||||
subroutine elem_centroids(ne,ele_centroid,mesh_type)
|
||||
!
|
||||
! Parameters
|
||||
parameter(max_nodes=1000000,max_elements=100000,max_node_in_elem=8)
|
||||
!
|
||||
! Variables
|
||||
character(len=256)input
|
||||
integer,dimension(max_elements,max_node_in_elem)::elements
|
||||
double precision,dimension(max_nodes,3)::nodes
|
||||
double precision,dimension(max_elements,3)::ele_centroid
|
||||
!
|
||||
! Open Input File and read node and element co-ordinates
|
||||
open(unit=10,file='GeomGenTemp.inp',status='unknown')
|
||||
do while (index(input,'*Node')==0)
|
||||
read(10,'(a)')input
|
||||
end do
|
||||
nn=0
|
||||
do while(1==1)
|
||||
read(10,'(a)')input
|
||||
if(index(input,'*')==0)then
|
||||
backspace(10)
|
||||
nn=nn+1
|
||||
if(mesh_type==3)then
|
||||
read(10,*)dummy,nodes(nn,1),nodes(nn,2),nodes(nn,3)
|
||||
else
|
||||
read(10,*)dummy,nodes(nn,1),nodes(nn,2)
|
||||
endif
|
||||
else
|
||||
if(mesh_type==2)then
|
||||
nele_type=4
|
||||
else
|
||||
if(index(input,'C3D8')/=0)nele_type=8
|
||||
if(index(input,'C3D4')/=0)nele_type=4
|
||||
endif
|
||||
exit
|
||||
endif
|
||||
end do
|
||||
ne=0
|
||||
do while(1==1)
|
||||
read(10,'(a)')input
|
||||
if(index(input,'*')==0)then
|
||||
backspace(10)
|
||||
ne=ne+1
|
||||
if(nele_type==8)then
|
||||
read(10,*)dummy,elements(ne,1),elements(ne,2),elements(ne,3),elements(ne,4)&
|
||||
& ,elements(ne,5),elements(ne,6),elements(ne,7),elements(ne,8)
|
||||
elseif(nele_type==4)then
|
||||
read(10,*)dummy,elements(ne,1),elements(ne,2),elements(ne,3),elements(ne,4)
|
||||
endif
|
||||
else
|
||||
exit
|
||||
endif
|
||||
end do
|
||||
!
|
||||
! Get element centroid
|
||||
do i=1,ne
|
||||
centroidx=0.d0
|
||||
centroidy=0.d0
|
||||
centroidz=0.d0
|
||||
do j=1,nele_type
|
||||
centroidx=centroidx+nodes(elements(i,j),1)
|
||||
centroidy=centroidy+nodes(elements(i,j),2)
|
||||
if(mesh_type==3)centroidz=centroidz+nodes(elements(i,j),3)
|
||||
enddo
|
||||
ele_centroid(i,1)=centroidx/float(nele_type)
|
||||
ele_centroid(i,2)=centroidy/float(nele_type)
|
||||
if(mesh_type==3)ele_centroid(i,3)=centroidz/float(nele_type)
|
||||
enddo
|
||||
end subroutine
|
||||
205
Unpublished/3D_Voxel_Assign/GrainMask_VUSD_Nodes.for
Normal file
205
Unpublished/3D_Voxel_Assign/GrainMask_VUSD_Nodes.for
Normal file
|
|
@ -0,0 +1,205 @@
|
|||
! This program generates a micro-strucutre mask and applies it to
|
||||
! an existing mesh.
|
||||
! J.Grogan 05/08/11
|
||||
program Corrosion_Preprocessor
|
||||
!
|
||||
! Parameters
|
||||
parameter(max_elements=600000,max_cells=20000,max_fc=100,max_faces=10000)
|
||||
parameter(max_elem_in_cell=50000,max_neigh_per_elem=6,max_neighbours=50)
|
||||
!
|
||||
! Variables
|
||||
character(len=256)input
|
||||
character(len=256)input2(2)
|
||||
integer,allocatable,dimension(:)::num_faces
|
||||
integer,dimension(max_elements,max_neighbours)::neighbour
|
||||
integer mesh_type
|
||||
integer(1) iseed
|
||||
double precision,allocatable,dimension(:,:)::distance
|
||||
double precision,allocatable,dimension(:,:)::nbr_dist
|
||||
double precision,allocatable,dimension(:,:)::cor_faces
|
||||
double precision,dimension(max_elements)::cor_dist
|
||||
double precision,allocatable,dimension(:,:)::ele_centroid
|
||||
!
|
||||
! Mesh Type: 2 = 2D, 3 = 3D
|
||||
mesh_type=3
|
||||
iseed=3
|
||||
call random_seed(iseed)
|
||||
!
|
||||
allocate(ele_centroid(max_elements,3))
|
||||
! Get element centroids
|
||||
call elem_centroids(num_elements,ele_centroid,mesh_type)
|
||||
!
|
||||
! Get neighbouring elements
|
||||
allocate(nbr_dist(max_elements,max_neighbours))
|
||||
do i=1,num_elements
|
||||
icount=1
|
||||
do j=1,num_elements
|
||||
if(icount>max_neighbours)then
|
||||
rmaxdist=0.
|
||||
do k=1,max_neighbours
|
||||
if(nbr_dist(i,k)>rmaxdist)then
|
||||
rmaxdist=nbr_dist(i,k)
|
||||
index_max_dist=k
|
||||
endif
|
||||
enddo
|
||||
endif
|
||||
cent1x=ele_centroid(i,1)
|
||||
cent1y=ele_centroid(i,2)
|
||||
cent1z=ele_centroid(i,3)
|
||||
cent2x=ele_centroid(j,1)
|
||||
cent2y=ele_centroid(j,2)
|
||||
cent2z=ele_centroid(j,3)
|
||||
dist=sqrt((cent1x-cent2x)*(cent1x-cent2x)+(cent1y-cent2y)*(cent1y-cent2y)&
|
||||
&+(cent1z-cent2z)*(cent1z-cent2z))
|
||||
if(icount>max_neighbours)then
|
||||
if(dist<rmaxdist)then
|
||||
nbr_dist(i,index_max_dist)=dist
|
||||
neighbour(i,index_max_dist)=j
|
||||
endif
|
||||
else
|
||||
nbr_dist(i,j)=dist
|
||||
neighbour(i,j)=j
|
||||
endif
|
||||
icount=icount+1
|
||||
enddo
|
||||
print *,float(i)/float(num_elements)
|
||||
enddo
|
||||
deallocate(nbr_dist)
|
||||
!
|
||||
! Get corrosion surface distances
|
||||
open(unit=22,file='CorSurf.dat',status='unknown')
|
||||
allocate(cor_faces(max_faces,3))
|
||||
ierr=0
|
||||
inum_faces=1
|
||||
do while (ierr==0)
|
||||
read(22,*,iostat=ierr)cor_faces(inum_faces,1),cor_faces(inum_faces,2),&
|
||||
&cor_faces(inum_faces,3)
|
||||
if(ierr==0)inum_faces=inum_faces+1
|
||||
enddo
|
||||
close(unit=22)
|
||||
do i=1,num_elements
|
||||
centx=ele_centroid(i,1)
|
||||
centy=ele_centroid(i,2)
|
||||
centz=ele_centroid(i,3)
|
||||
distmin=1000.
|
||||
do j=1,inum_faces-1
|
||||
facex=cor_faces(j,1)
|
||||
facey=cor_faces(j,2)
|
||||
facez=cor_faces(j,3)
|
||||
dist=sqrt((centx-facex)*(centx-facex)+(centy-facey)*(centy-facey)&
|
||||
&+(centz-facez)*(centz-facez))
|
||||
if(dist<distmin)distmin=dist
|
||||
enddo
|
||||
cor_dist(i)=distmin
|
||||
enddo
|
||||
deallocate(cor_faces)
|
||||
!
|
||||
rewind(10)
|
||||
open(unit=13,file='GeomGenINP.inp',status='unknown')
|
||||
input2(1)='**'
|
||||
do while (index(input2(1),'*End Assembly')==0)
|
||||
read(10,'(a)')input2(2)
|
||||
write(13,'(a)')input2(1)
|
||||
input2(1)=input2(2)
|
||||
enddo
|
||||
write(13,'(a)')'*End Assembly'
|
||||
write(13,*)'*INITIAL CONDITIONS,TYPE=SOLUTION'
|
||||
do i=1,num_elements
|
||||
call random_number(randnum)
|
||||
randnum=0
|
||||
write(13,'(3(a,i6),2(a,f18.6),a,2(i6,a),f18.6,a)')'Assembly.CorPart.',i,',' &
|
||||
& ,i,',',max_neighbours,',',0.,',',cor_dist(i),',',0,',',1,',',randnum,','
|
||||
do k=1, max_neighbours
|
||||
if(mod(k,8)/=0)then
|
||||
if(k/=max_neighbours)then
|
||||
write(13,'(i6,a)',advance='no')neighbour(i,k),','
|
||||
else
|
||||
write(13,'(i6,a,f18.6,a,i6,a,i6,a,i6)')neighbour(i,k),',',cor_dist(i),',',0,',',0,',',0
|
||||
endif
|
||||
else
|
||||
if(k/=max_neighbours)then
|
||||
write(13,'(i6,a)')neighbour(i,k),','
|
||||
else
|
||||
write(13,'(i6,a,f18.6,a,i6,a,i6,a,i6)')neighbour(i,k),',',cor_dist(i),',',0,',',0,',',0
|
||||
endif
|
||||
endif
|
||||
enddo
|
||||
enddo
|
||||
ierr=0
|
||||
do while (ierr==0)
|
||||
read(10,'(a)',iostat=ierr)input2(1)
|
||||
if(ierr==0)write(13,'(a)')input2(1)
|
||||
enddo
|
||||
end program
|
||||
!~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
|
||||
! Get Element Centroids
|
||||
!~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
|
||||
subroutine elem_centroids(ne,ele_centroid,mesh_type)
|
||||
!
|
||||
! Parameters
|
||||
parameter(max_nodes=6000000,max_elements=600000,max_node_in_elem=8)
|
||||
!
|
||||
! Variables
|
||||
character(len=256)input
|
||||
integer,dimension(max_elements,max_node_in_elem)::elements
|
||||
double precision,dimension(max_nodes,3)::nodes
|
||||
double precision,dimension(max_elements,3)::ele_centroid
|
||||
!
|
||||
! Open Input File and read node and element co-ordinates
|
||||
open(unit=10,file='GeomGenTemp.inp',status='unknown')
|
||||
do while (index(input,'*Node')==0)
|
||||
read(10,'(a)')input
|
||||
end do
|
||||
nn=0
|
||||
do while(1==1)
|
||||
read(10,'(a)')input
|
||||
if(index(input,'*')==0)then
|
||||
backspace(10)
|
||||
nn=nn+1
|
||||
if(mesh_type==3)then
|
||||
read(10,*)dummy,nodes(nn,1),nodes(nn,2),nodes(nn,3)
|
||||
else
|
||||
read(10,*)dummy,nodes(nn,1),nodes(nn,2)
|
||||
endif
|
||||
else
|
||||
if(mesh_type==2)then
|
||||
nele_type=4
|
||||
else
|
||||
if(index(input,'C3D8')/=0)nele_type=8
|
||||
if(index(input,'C3D4')/=0)nele_type=4
|
||||
endif
|
||||
exit
|
||||
endif
|
||||
end do
|
||||
ne=0
|
||||
do while(1==1)
|
||||
read(10,'(a)')input
|
||||
if(index(input,'*')==0)then
|
||||
backspace(10)
|
||||
ne=ne+1
|
||||
if(nele_type==8)then
|
||||
read(10,*)dummy,elements(ne,1),elements(ne,2),elements(ne,3),elements(ne,4)&
|
||||
& ,elements(ne,5),elements(ne,6),elements(ne,7),elements(ne,8)
|
||||
elseif(nele_type==4)then
|
||||
read(10,*)dummy,elements(ne,1),elements(ne,2),elements(ne,3),elements(ne,4)
|
||||
endif
|
||||
else
|
||||
exit
|
||||
endif
|
||||
end do
|
||||
!
|
||||
! Get element centroid
|
||||
do i=1,ne
|
||||
centroidx=0.d0
|
||||
centroidy=0.d0
|
||||
centroidz=0.d0
|
||||
do j=1,nele_type
|
||||
centroidx=centroidx+nodes(elements(i,j),1)
|
||||
centroidy=centroidy+nodes(elements(i,j),2)
|
||||
if(mesh_type==3)centroidz=centroidz+nodes(elements(i,j),3)
|
||||
enddo
|
||||
ele_centroid(i,1)=centroidx/float(nele_type)
|
||||
ele_centroid(i,2)=centroidy/float(nele_type)
|
||||
if(mesh_type==3)ele_centroid(i,3)=centroidz/float(nele_type)
|
||||
enddo
|
||||
end subroutine
|
||||
88
Unpublished/3D_Voxel_Assign/Voronoi2DPost.f90
Normal file
88
Unpublished/3D_Voxel_Assign/Voronoi2DPost.f90
Normal file
|
|
@ -0,0 +1,88 @@
|
|||
! This program takes output from the QHULL package and converts it into
|
||||
! a format suitable for use with the GeomGen script
|
||||
! J.Grogan 05/08/11
|
||||
program Voronoi2DPost
|
||||
!
|
||||
! Parameters
|
||||
parameter(max_verts=1000000,max_cells=100000,max_verts_in_cell=100)
|
||||
!
|
||||
! Variables
|
||||
character(len=256)full_line,test_string
|
||||
integer vnum(max_cells,max_verts_in_cell),num_verts(max_cells)
|
||||
integer in_tol(max_cells)
|
||||
real xv_cor(max_verts)
|
||||
real yv_cor(max_verts)
|
||||
logical xtrue
|
||||
logical ytrue
|
||||
!
|
||||
! Read Scales
|
||||
open(unit=15,file='scales.dat',status='unknown')
|
||||
read(15,*)rmaxscale
|
||||
!
|
||||
! Read in vertex co-ordinates
|
||||
open(unit=11,file='qhullout.dat',status='unknown')
|
||||
read(11,*)
|
||||
read(11,*)num_verts_tot,num_cells,dummy
|
||||
do i=1,num_verts_tot
|
||||
read(11,*)xv_cor(i),yv_cor(i)
|
||||
enddo
|
||||
!
|
||||
! Read in vertices on each cell
|
||||
do i=1,num_cells
|
||||
read(11,*)num_verts(i)
|
||||
backspace(11)
|
||||
read(11,'(i2,a256)')idummy,full_line
|
||||
ileft=1
|
||||
num_points=1
|
||||
do iright=1,256
|
||||
test_string=full_line(iright:iright)
|
||||
if((test_string==' ').or.(iright==256))then
|
||||
read(full_line(ileft:iright-1),'(i6)')vnum(i,num_points)
|
||||
if(num_points==num_verts(i))exit
|
||||
ileft=iright+1
|
||||
num_points=num_points+1
|
||||
endif
|
||||
enddo
|
||||
enddo
|
||||
!
|
||||
! Check if cells are within specified region
|
||||
open(unit=12,file='fortranout.dat',status='unknown')
|
||||
num_inside_cells=num_cells
|
||||
do i=1,num_cells
|
||||
icheck=0
|
||||
do j=1,num_verts(i)
|
||||
xcor=xv_cor(vnum(i,j)+1)
|
||||
ycor=yv_cor(vnum(i,j)+1)
|
||||
if(abs(xcor)==10.101)then
|
||||
icheck=0
|
||||
exit
|
||||
endif
|
||||
rmax=1.1*rmaxscale
|
||||
rmin=-0.1
|
||||
xtrue=(xcor<rmax).and.(xcor>rmin)
|
||||
ytrue=(ycor<rmax).and.(ycor>rmin)
|
||||
if(xtrue.and.ytrue)icheck=icheck+1
|
||||
enddo
|
||||
if(icheck<1)then
|
||||
in_tol(i)=2
|
||||
num_inside_cells=num_inside_cells-1
|
||||
else
|
||||
in_tol(i)=1
|
||||
endif
|
||||
enddo
|
||||
!
|
||||
! Write vertex coordinates for each cell
|
||||
write(12,*)num_inside_cells
|
||||
do i=1,num_cells
|
||||
if(in_tol(i)==1)then
|
||||
write(12,*)num_verts(i)
|
||||
do j=1,num_verts(i)
|
||||
write(12,*)xv_cor(vnum(i,j)+1),',',yv_cor(vnum(i,j)+1)
|
||||
enddo
|
||||
else
|
||||
cycle
|
||||
endif
|
||||
enddo
|
||||
close(unit=11)
|
||||
close(unit=12)
|
||||
end program
|
||||
141
Unpublished/3D_Voxel_Assign/Voronoi3DPost.f90
Normal file
141
Unpublished/3D_Voxel_Assign/Voronoi3DPost.f90
Normal file
|
|
@ -0,0 +1,141 @@
|
|||
! This program takes output from the QHULL package and converts it into
|
||||
! a format suitable for use with the GeomGen script
|
||||
! J.Grogan 05/08/11
|
||||
program Voronoi3DPost
|
||||
!
|
||||
! Parameters
|
||||
parameter(max_verts=500000,max_cells=50000,max_verts_in_cell=100)
|
||||
parameter(max_hyps=500000,max_hyp_in_cell=100,max_verts_on_hyp=50)
|
||||
!
|
||||
! Variables
|
||||
character(len=256)full_line,test_string
|
||||
integer num_verts(max_cells)
|
||||
integer vert_list(max_cells,max_verts_in_cell)
|
||||
integer facet(2,max_hyps)
|
||||
integer hyp_list(max_cells,max_hyp_in_cell)
|
||||
integer num_cell_hyp(max_cells)
|
||||
integer cell_status(max_cells)
|
||||
integer num_hyp_verts(max_cells,max_hyp_in_cell)
|
||||
integer hyp_vert_list(max_cells,max_hyp_in_cell,max_verts_on_hyp)
|
||||
double precision xv_cor(max_verts)
|
||||
double precision yv_cor(max_verts)
|
||||
double precision zv_cor(max_verts)
|
||||
double precision cor(3,max_hyps)
|
||||
double precision offset(max_hyps)
|
||||
double precision xcor,ycor,zcor
|
||||
double precision dotrprod,distance,tol
|
||||
logical xtrue,ytrue,ztrue
|
||||
!
|
||||
! Open output files
|
||||
open(unit=12,file='fortranout.dat',status='unknown')
|
||||
!
|
||||
! Open scales file
|
||||
open(unit=15,file='scales.dat',status='unknown')
|
||||
read(15,*)rmaxscale
|
||||
!
|
||||
! Read tessellation results from QHULL
|
||||
open(unit=11,file='qhullout.dat',status='unknown')
|
||||
read(11,*)
|
||||
read(11,*)num_total_verts,num_cells
|
||||
!
|
||||
! Read in all vertice co-ordinates
|
||||
do i=1,num_total_verts
|
||||
read(11,*)xv_cor(i),yv_cor(i),zv_cor(i)
|
||||
enddo
|
||||
!
|
||||
! Read in vertice labels for each voronoi cell
|
||||
do i=1,num_cells
|
||||
read(11,*)num_verts(i)
|
||||
backspace(11)
|
||||
if(num_verts(i)>9)then
|
||||
read(11,'(i3,a256)')idummy,full_line
|
||||
else
|
||||
read(11,'(i2,a256)')idummy,full_line
|
||||
endif
|
||||
ileft=1
|
||||
num_points=1
|
||||
do iright=1,256
|
||||
test_string=full_line(iright:iright)
|
||||
if((test_string==' ').or.(iright==256))then
|
||||
read(full_line(ileft:iright-1),'(i6)')vert_list(i,num_points)
|
||||
if(num_points==num_verts(i))exit
|
||||
ileft=iright+1
|
||||
num_points=num_points+1
|
||||
endif
|
||||
enddo
|
||||
enddo
|
||||
!
|
||||
! Read in bounded hyperplane cell labels and co-ordinates
|
||||
read(11,*)num_hyp
|
||||
do i=1,num_hyp
|
||||
read(11,*)dummy,facet(1,i),facet(2,i),cor(1,i),cor(2,i),cor(3,i),offset(i)
|
||||
enddo
|
||||
!
|
||||
! Determine hyperplanes of each cell
|
||||
do i=1,num_cells
|
||||
num_hy=1
|
||||
do j=1,num_hyp
|
||||
if((facet(1,j)==i-1).or.(facet(2,j)==i-1))then
|
||||
hyp_list(i,num_hy)=j
|
||||
num_cell_hyp(i)=num_hy
|
||||
num_hy=num_hy+1
|
||||
endif
|
||||
enddo
|
||||
enddo
|
||||
!
|
||||
! Check if any cell vertices are outside the chosen tolerance
|
||||
do i=1,num_cells
|
||||
cell_status(i)=1
|
||||
do j=1,num_verts(i)
|
||||
xcor=xv_cor(vert_list(i,j)+1)
|
||||
ycor=yv_cor(vert_list(i,j)+1)
|
||||
zcor=zv_cor(vert_list(i,j)+1)
|
||||
rmax=1.1*rmaxscale
|
||||
rmin=-0.1
|
||||
xtrue=(xcor<rmax).and.(xcor>rmin)
|
||||
ytrue=(ycor<rmax).and.(ycor>rmin)
|
||||
ztrue=(zcor<rmax).and.(zcor>rmin)
|
||||
if(xtrue.and.ytrue.and.ztrue)cell_status(i)=0
|
||||
enddo
|
||||
enddo
|
||||
!
|
||||
! For all cells within tolerance determine vertices on each hyperplane
|
||||
num_skipped=0
|
||||
tol=1.e-5*rmaxscale
|
||||
do i=1,num_cells
|
||||
if(cell_status(i)/=0)then
|
||||
num_skipped=num_skipped+1
|
||||
cycle
|
||||
endif
|
||||
do j=1,num_cell_hyp(i)
|
||||
nverts_on_hyp=1
|
||||
do k=1,num_verts(i)
|
||||
dotprod1=cor(1,hyp_list(i,j))*xv_cor(vert_list(i,k)+1)
|
||||
dotprod2=cor(2,hyp_list(i,j))*yv_cor(vert_list(i,k)+1)
|
||||
dotprod3=cor(3,hyp_list(i,j))*zv_cor(vert_list(i,k)+1)
|
||||
distance=dotprod1+dotprod2+dotprod3+offset(hyp_list(i,j))
|
||||
if(abs(distance)<tol)then
|
||||
hyp_vert_list(i,j,nverts_on_hyp)=vert_list(i,k)
|
||||
num_hyp_verts(i,j)=nverts_on_hyp
|
||||
nverts_on_hyp=nverts_on_hyp+1
|
||||
endif
|
||||
enddo
|
||||
enddo
|
||||
enddo
|
||||
! Write output for the of co-orindates of vertices on each hyperplane
|
||||
! that make up a cell.
|
||||
write(12,*)num_cells-num_skipped
|
||||
do i=1,num_cells
|
||||
if(cell_status(i)/=0)cycle
|
||||
write(12,*)num_cell_hyp(i)
|
||||
do j=1,num_cell_hyp(i)
|
||||
write(12,*)num_hyp_verts(i,j)
|
||||
do k=1,num_hyp_verts(i,j)
|
||||
xcor=xv_cor(hyp_vert_list(i,j,k)+1)
|
||||
ycor=yv_cor(hyp_vert_list(i,j,k)+1)
|
||||
zcor=zv_cor(hyp_vert_list(i,j,k)+1)
|
||||
write(12,'(2(f20.15,a),f20.15)')xcor,',',ycor,',',zcor
|
||||
enddo
|
||||
enddo
|
||||
enddo
|
||||
end program
|
||||
215
Unpublished/PeriodicBoundary/3d_PBC_Pre.py
Normal file
215
Unpublished/PeriodicBoundary/3d_PBC_Pre.py
Normal file
|
|
@ -0,0 +1,215 @@
|
|||
# 3D PCBs - JGrogan - V1.0
|
||||
# V1.0 - Ceated: 18-02-12
|
||||
from abaqus import *
|
||||
from abaqusConstants import *
|
||||
#
|
||||
zModel=mdb.models['Model-1']
|
||||
zAssembly=zModel.rootAssembly
|
||||
zInstance=zAssembly.instances['Part-1-1']
|
||||
#
|
||||
# Enter Node Selection Tolerance and a 'Big' Number
|
||||
Toler=1.e-6
|
||||
BigNum=1.e6
|
||||
# Characterize Part
|
||||
XMax=-BigNum
|
||||
YMax=-BigNum
|
||||
ZMax=-BigNum
|
||||
XMin=BigNum
|
||||
YMin=BigNum
|
||||
ZMin=BigNum
|
||||
for eachNode in zInstance.nodes:
|
||||
XCor=eachNode.coordinates[0]
|
||||
YCor=eachNode.coordinates[1]
|
||||
ZCor=eachNode.coordinates[2]
|
||||
if XCor>XMax:
|
||||
XMax=XCor
|
||||
elif XCor<XMin:
|
||||
XMin=XCor
|
||||
if YCor>YMax:
|
||||
YMax=YCor
|
||||
elif YCor<YMin:
|
||||
YMin=YCor
|
||||
if ZCor>ZMax:
|
||||
ZMax=ZCor
|
||||
elif ZCor<ZMin:
|
||||
ZMin=ZCor
|
||||
#
|
||||
# Distribute Nodes into Sets
|
||||
for eachNode in zInstance.nodes:
|
||||
XCor=eachNode.coordinates[0]
|
||||
YCor=eachNode.coordinates[1]
|
||||
ZCor=eachNode.coordinates[2]
|
||||
# Front Face, Edges and Nodes
|
||||
if(XCor<XMax+Toler)and(XCor>XMax-Toler):
|
||||
if(YCor<YMax+Toler)and(YCor>YMax-Toler):
|
||||
if(ZCor<ZMax+Toler)and(ZCor>ZMax-Toler):
|
||||
Node=zInstance.nodes.sequenceFromLabels(labels=(eachNode.label,))
|
||||
zAssembly.Set(name='B',nodes=Node)
|
||||
elif(ZCor<ZMin+Toler)and(ZCor>ZMin-Toler):
|
||||
Node=zInstance.nodes.sequenceFromLabels(labels=(eachNode.label,))
|
||||
zAssembly.Set(name='C',nodes=Node)
|
||||
else:
|
||||
Node=zInstance.nodes.sequenceFromLabels(labels=(eachNode.label,))
|
||||
zAssembly.Set(name='Temp',nodes=Node)
|
||||
try:
|
||||
zAssembly.SetByMerge(name='EdgeBC', sets=(zAssembly.sets['EdgeBC'],zAssembly.sets['Temp']))
|
||||
except:
|
||||
zAssembly.Set(name='EdgeBC',nodes=Node)
|
||||
elif(YCor<YMin+Toler)and(YCor>YMin-Toler):
|
||||
if(ZCor<ZMax+Toler)and(ZCor>ZMax-Toler):
|
||||
Node=zInstance.nodes.sequenceFromLabels(labels=(eachNode.label,))
|
||||
zAssembly.Set(name='B1',nodes=Node)
|
||||
elif(ZCor<ZMin+Toler)and(ZCor>ZMin-Toler):
|
||||
Node=zInstance.nodes.sequenceFromLabels(labels=(eachNode.label,))
|
||||
zAssembly.Set(name='C1',nodes=Node)
|
||||
else:
|
||||
Node=zInstance.nodes.sequenceFromLabels(labels=(eachNode.label,))
|
||||
zAssembly.Set(name='Temp',nodes=Node)
|
||||
try:
|
||||
zAssembly.SetByMerge(name='EdgeB1C1', sets=(zAssembly.sets['EdgeB1C1'],zAssembly.sets['Temp']))
|
||||
except:
|
||||
zAssembly.Set(name='EdgeB1C1',nodes=Node)
|
||||
elif(ZCor<ZMax+Toler)and(ZCor>ZMax-Toler):
|
||||
if(YCor<YMax-Toler)and(YCor>YMin+Toler):
|
||||
Node=zInstance.nodes.sequenceFromLabels(labels=(eachNode.label,))
|
||||
zAssembly.Set(name='Temp',nodes=Node)
|
||||
try:
|
||||
zAssembly.SetByMerge(name='EdgeBB1', sets=(zAssembly.sets['EdgeBB1'],zAssembly.sets['Temp']))
|
||||
except:
|
||||
zAssembly.Set(name='EdgeBB1',nodes=Node)
|
||||
elif(ZCor<ZMin+Toler)and(ZCor>ZMin-Toler):
|
||||
if(YCor<YMax-Toler)and(YCor>YMin+Toler):
|
||||
Node=zInstance.nodes.sequenceFromLabels(labels=(eachNode.label,))
|
||||
zAssembly.Set(name='Temp',nodes=Node)
|
||||
try:
|
||||
zAssembly.SetByMerge(name='EdgeCC1', sets=(zAssembly.sets['EdgeCC1'],zAssembly.sets['Temp']))
|
||||
except:
|
||||
zAssembly.Set(name='EdgeCC1',nodes=Node)
|
||||
else:
|
||||
Node=zInstance.nodes.sequenceFromLabels(labels=(eachNode.label,))
|
||||
zAssembly.Set(name='Temp',nodes=Node)
|
||||
try:
|
||||
zAssembly.SetByMerge(name='FaceFront', sets=(zAssembly.sets['FaceFront'],zAssembly.sets['Temp']))
|
||||
except:
|
||||
zAssembly.Set(name='FaceFront',nodes=Node)
|
||||
# Back Face, Edges and Nodes
|
||||
elif(XCor<XMin+Toler)and(XCor>XMin-Toler):
|
||||
if(YCor<YMax+Toler)and(YCor>YMax-Toler):
|
||||
if(ZCor<ZMax+Toler)and(ZCor>ZMax-Toler):
|
||||
Node=zInstance.nodes.sequenceFromLabels(labels=(eachNode.label,))
|
||||
zAssembly.Set(name='A',nodes=Node)
|
||||
elif(ZCor<ZMin+Toler)and(ZCor>ZMin-Toler):
|
||||
Node=zInstance.nodes.sequenceFromLabels(labels=(eachNode.label,))
|
||||
zAssembly.Set(name='D',nodes=Node)
|
||||
else:
|
||||
Node=zInstance.nodes.sequenceFromLabels(labels=(eachNode.label,))
|
||||
zAssembly.Set(name='Temp',nodes=Node)
|
||||
try:
|
||||
zAssembly.SetByMerge(name='EdgeAD', sets=(zAssembly.sets['EdgeAD'],zAssembly.sets['Temp']))
|
||||
except:
|
||||
zAssembly.Set(name='EdgeAD',nodes=Node)
|
||||
elif(YCor<YMin+Toler)and(YCor>YMin-Toler):
|
||||
if(ZCor<ZMax+Toler)and(ZCor>ZMax-Toler):
|
||||
Node=zInstance.nodes.sequenceFromLabels(labels=(eachNode.label,))
|
||||
zAssembly.Set(name='A1',nodes=Node)
|
||||
elif(ZCor<ZMin+Toler)and(ZCor>ZMin-Toler):
|
||||
Node=zInstance.nodes.sequenceFromLabels(labels=(eachNode.label,))
|
||||
zAssembly.Set(name='D1',nodes=Node)
|
||||
else:
|
||||
Node=zInstance.nodes.sequenceFromLabels(labels=(eachNode.label,))
|
||||
zAssembly.Set(name='Temp',nodes=Node)
|
||||
try:
|
||||
zAssembly.SetByMerge(name='EdgeA1D1', sets=(zAssembly.sets['EdgeA1D1'],zAssembly.sets['Temp']))
|
||||
except:
|
||||
zAssembly.Set(name='EdgeA1D1',nodes=Node)
|
||||
elif(ZCor<ZMax+Toler)and(ZCor>ZMax-Toler):
|
||||
if(YCor<YMax-Toler)and(YCor>YMin+Toler):
|
||||
Node=zInstance.nodes.sequenceFromLabels(labels=(eachNode.label,))
|
||||
zAssembly.Set(name='Temp',nodes=Node)
|
||||
try:
|
||||
zAssembly.SetByMerge(name='EdgeAA1', sets=(zAssembly.sets['EdgeAA1'],zAssembly.sets['Temp']))
|
||||
except:
|
||||
zAssembly.Set(name='EdgeAA1',nodes=Node)
|
||||
elif(ZCor<ZMin+Toler)and(ZCor>ZMin-Toler):
|
||||
if(YCor<YMax-Toler)and(YCor>YMin+Toler):
|
||||
Node=zInstance.nodes.sequenceFromLabels(labels=(eachNode.label,))
|
||||
zAssembly.Set(name='Temp',nodes=Node)
|
||||
try:
|
||||
zAssembly.SetByMerge(name='EdgeDD1', sets=(zAssembly.sets['EdgeDD1'],zAssembly.sets['Temp']))
|
||||
except:
|
||||
zAssembly.Set(name='EdgeDD1',nodes=Node)
|
||||
else:
|
||||
Node=zInstance.nodes.sequenceFromLabels(labels=(eachNode.label,))
|
||||
zAssembly.Set(name='Temp',nodes=Node)
|
||||
try:
|
||||
zAssembly.SetByMerge(name='FaceRear', sets=(zAssembly.sets['FaceRear'],zAssembly.sets['Temp']))
|
||||
except:
|
||||
zAssembly.Set(name='FaceRear',nodes=Node)
|
||||
# Top Face and Edges
|
||||
elif(YCor<YMax+Toler)and(YCor>YMax-Toler):
|
||||
if(XCor<XMax-Toler)and(XCor>XMin+Toler):
|
||||
if(ZCor<ZMax+Toler)and(ZCor>ZMax-Toler):
|
||||
Node=zInstance.nodes.sequenceFromLabels(labels=(eachNode.label,))
|
||||
zAssembly.Set(name='Temp',nodes=Node)
|
||||
try:
|
||||
zAssembly.SetByMerge(name='EdgeAB', sets=(zAssembly.sets['EdgeAB'],zAssembly.sets['Temp']))
|
||||
except:
|
||||
zAssembly.Set(name='EdgeAB',nodes=Node)
|
||||
elif(ZCor<ZMin+Toler)and(ZCor>ZMin-Toler):
|
||||
Node=zInstance.nodes.sequenceFromLabels(labels=(eachNode.label,))
|
||||
zAssembly.Set(name='Temp',nodes=Node)
|
||||
try:
|
||||
zAssembly.SetByMerge(name='EdgeCD', sets=(zAssembly.sets['EdgeCD'],zAssembly.sets['Temp']))
|
||||
except:
|
||||
zAssembly.Set(name='EdgeCD',nodes=Node)
|
||||
else:
|
||||
Node=zInstance.nodes.sequenceFromLabels(labels=(eachNode.label,))
|
||||
zAssembly.Set(name='Temp',nodes=Node)
|
||||
try:
|
||||
zAssembly.SetByMerge(name='FaceTop', sets=(zAssembly.sets['FaceTop'],zAssembly.sets['Temp']))
|
||||
except:
|
||||
zAssembly.Set(name='FaceTop',nodes=Node)
|
||||
# Bottom Face and Edges
|
||||
elif(YCor<YMin+Toler)and(YCor>YMin-Toler):
|
||||
if(XCor<XMax-Toler)and(XCor>XMin+Toler):
|
||||
if(ZCor<ZMax+Toler)and(ZCor>ZMax-Toler):
|
||||
Node=zInstance.nodes.sequenceFromLabels(labels=(eachNode.label,))
|
||||
zAssembly.Set(name='Temp',nodes=Node)
|
||||
try:
|
||||
zAssembly.SetByMerge(name='EdgeA1B1', sets=(zAssembly.sets['EdgeA1B1'],zAssembly.sets['Temp']))
|
||||
except:
|
||||
zAssembly.Set(name='EdgeA1B1',nodes=Node)
|
||||
elif(ZCor<ZMin+Toler)and(ZCor>ZMin-Toler):
|
||||
Node=zInstance.nodes.sequenceFromLabels(labels=(eachNode.label,))
|
||||
zAssembly.Set(name='Temp',nodes=Node)
|
||||
try:
|
||||
zAssembly.SetByMerge(name='EdgeC1D1', sets=(zAssembly.sets['EdgeC1D1'],zAssembly.sets['Temp']))
|
||||
except:
|
||||
zAssembly.Set(name='EdgeC1D1',nodes=Node)
|
||||
else:
|
||||
Node=zInstance.nodes.sequenceFromLabels(labels=(eachNode.label,))
|
||||
zAssembly.Set(name='Temp',nodes=Node)
|
||||
try:
|
||||
zAssembly.SetByMerge(name='FaceBottom', sets=(zAssembly.sets['FaceBottom'],zAssembly.sets['Temp']))
|
||||
except:
|
||||
zAssembly.Set(name='FaceBottom',nodes=Node)
|
||||
# Left Face
|
||||
elif(ZCor<ZMax+Toler)and(ZCor>ZMax-Toler):
|
||||
if(XCor<XMax-Toler)and(XCor>XMin+Toler)and(YCor>YMin+Toler)and(YCor>YMin+Toler):
|
||||
Node=zInstance.nodes.sequenceFromLabels(labels=(eachNode.label,))
|
||||
zAssembly.Set(name='Temp',nodes=Node)
|
||||
try:
|
||||
zAssembly.SetByMerge(name='FaceLeft', sets=(zAssembly.sets['FaceLeft'],zAssembly.sets['Temp']))
|
||||
except:
|
||||
zAssembly.Set(name='FaceLeft',nodes=Node)
|
||||
elif(ZCor<ZMin+Toler)and(ZCor>ZMin-Toler):
|
||||
if(XCor<XMax-Toler)and(XCor>XMin+Toler)and(YCor>YMin+Toler)and(YCor>YMin+Toler):
|
||||
Node=zInstance.nodes.sequenceFromLabels(labels=(eachNode.label,))
|
||||
zAssembly.Set(name='Temp',nodes=Node)
|
||||
try:
|
||||
zAssembly.SetByMerge(name='FaceRight', sets=(zAssembly.sets['FaceRight'],zAssembly.sets['Temp']))
|
||||
except:
|
||||
zAssembly.Set(name='FaceRight',nodes=Node)
|
||||
# Clean Up
|
||||
del zAssembly.sets['Temp']
|
||||
|
||||
261
Unpublished/PeriodicBoundary/PBC3D.py
Normal file
261
Unpublished/PeriodicBoundary/PBC3D.py
Normal file
|
|
@ -0,0 +1,261 @@
|
|||
# 3D PCBs - JGrogan - V1.0
|
||||
# V1.0 - Ceated: 18-02-12
|
||||
from abaqus import *
|
||||
from abaqusConstants import *
|
||||
#
|
||||
# Define Tolerance for Node Matching:
|
||||
Toler = 0.0001
|
||||
#
|
||||
zModel=mdb.models['Model-1']
|
||||
zAssembly=zModel.rootAssembly
|
||||
#
|
||||
# Constraints
|
||||
for j in range(0,3):
|
||||
if j == 0:
|
||||
Name1='FaceBottom'
|
||||
Name2='FaceTop'
|
||||
Coeff11=1.
|
||||
Coeff12=-1.
|
||||
Coeff13=0.
|
||||
Coeff21=1. #
|
||||
Coeff22=-1.
|
||||
Coeff23=-1.
|
||||
Coeff31=1. #
|
||||
Coeff32=-1.
|
||||
Coeff33=0.
|
||||
elif j == 1:
|
||||
Name1='FaceFront'
|
||||
Name2='FaceRear'
|
||||
Coeff11=1.
|
||||
Coeff12=-1.
|
||||
Coeff13=-1.
|
||||
Coeff21=1. #
|
||||
Coeff22=-1.
|
||||
Coeff23=0.
|
||||
Coeff31=1. #
|
||||
Coeff32=-1.
|
||||
Coeff33=0.
|
||||
elif j == 2:
|
||||
Name1='FaceLeft'
|
||||
Name2='FaceRight'
|
||||
Coeff11=1.
|
||||
Coeff12=-1.
|
||||
Coeff13=0.
|
||||
Coeff21=1. #
|
||||
Coeff22=-1.
|
||||
Coeff23=0.
|
||||
Coeff31=1. #
|
||||
Coeff32=-1.
|
||||
Coeff33=-1.
|
||||
elif j == 3:
|
||||
Name1='EdgeCC1'
|
||||
Name2='EdgeBB1'
|
||||
Coeff11=1.
|
||||
Coeff12=-1.
|
||||
Coeff13=0.
|
||||
Coeff21=1. #
|
||||
Coeff22=-1.
|
||||
Coeff23=0.
|
||||
Coeff31=1. #
|
||||
Coeff32=-1.
|
||||
Coeff33=1.
|
||||
elif j == 4:
|
||||
Name1='EdgeBB1'
|
||||
Name2='EdgeAA1'
|
||||
Coeff11=1.
|
||||
Coeff12=-1.
|
||||
Coeff13=-1.
|
||||
Coeff21=1. #
|
||||
Coeff22=-1.
|
||||
Coeff23=0.
|
||||
Coeff31=1. #
|
||||
Coeff32=-1.
|
||||
Coeff33=0.
|
||||
elif j == 5:
|
||||
Name1='EdgeAA1'
|
||||
Name2='EdgeDD1'
|
||||
Coeff11=1.
|
||||
Coeff12=-1.
|
||||
Coeff13=0.
|
||||
Coeff21=1. #
|
||||
Coeff22=-1.
|
||||
Coeff23=0.
|
||||
Coeff31=1. #
|
||||
Coeff32=-1.
|
||||
Coeff33=-1.
|
||||
elif j == 6:
|
||||
Name1='EdgeCD'
|
||||
Name2='EdgeAB'
|
||||
Coeff11=1.
|
||||
Coeff12=-1.
|
||||
Coeff13=0.
|
||||
Coeff21=1. #
|
||||
Coeff22=-1.
|
||||
Coeff23=0.
|
||||
Coeff31=1. #
|
||||
Coeff32=-1.
|
||||
Coeff33=1.
|
||||
elif j == 6:
|
||||
Name1='EdgeAB'
|
||||
Name2='EdgeA1B1'
|
||||
Coeff11=-1.
|
||||
Coeff12=1.
|
||||
Coeff13=0.
|
||||
Coeff21=-1. #
|
||||
Coeff22=1.
|
||||
Coeff23=-1.
|
||||
Coeff31=-1. #
|
||||
Coeff32=-1.
|
||||
Coeff33=0.
|
||||
elif j == 7:
|
||||
Name1='EdgeA1B1'
|
||||
Name2='EdgeC1D1'
|
||||
Coeff11=1.
|
||||
Coeff12=-1.
|
||||
Coeff13=0.
|
||||
Coeff21=1. #
|
||||
Coeff22=-1.
|
||||
Coeff23=0.
|
||||
Coeff31=1. #
|
||||
Coeff32=-1.
|
||||
Coeff33=-1.
|
||||
elif j == 7:
|
||||
Name1='EdgeAD'
|
||||
Name2='EdgeBC'
|
||||
Coeff11=-1.
|
||||
Coeff12=1.
|
||||
Coeff13=-1.
|
||||
Coeff21=-1. #
|
||||
Coeff22=1.
|
||||
Coeff23=0.
|
||||
Coeff31=1. #
|
||||
Coeff32=-1.
|
||||
Coeff33=0.
|
||||
elif j == 8:
|
||||
Name1='EdgeBC'
|
||||
Name2='EdgeB1C1'
|
||||
Coeff11=-1.
|
||||
Coeff12=1.
|
||||
Coeff13=0.
|
||||
Coeff21=-1. #
|
||||
Coeff22=1.
|
||||
Coeff23=-1.
|
||||
Coeff31=1. #
|
||||
Coeff32=-1.
|
||||
Coeff33=0.
|
||||
elif j == 8:
|
||||
Name1='EdgeB1C1'
|
||||
Name2='EdgeA1D1'
|
||||
Coeff11=1.
|
||||
Coeff12=-1.
|
||||
Coeff13=-1.
|
||||
Coeff21=1. #
|
||||
Coeff22=-1.
|
||||
Coeff23=0.
|
||||
Coeff31=1. #
|
||||
Coeff32=-1.
|
||||
Coeff33=0.
|
||||
elif j == 9:
|
||||
Name1='B'
|
||||
Name2='C'
|
||||
Coeff11=1.
|
||||
Coeff12=-1.
|
||||
Coeff13=0.
|
||||
Coeff21=1. #
|
||||
Coeff22=-1.
|
||||
Coeff23=0.
|
||||
Coeff31=1. #
|
||||
Coeff32=-1.
|
||||
Coeff33=-1.
|
||||
elif j == 10:
|
||||
Name1='A'
|
||||
Name2='D'
|
||||
Coeff11=1.
|
||||
Coeff12=-1.
|
||||
Coeff13=0.
|
||||
Coeff21=-1. #
|
||||
Coeff22=1.
|
||||
Coeff23=0.
|
||||
Coeff31=1. #
|
||||
Coeff32=-1.
|
||||
Coeff33=-1.
|
||||
elif j == 11:
|
||||
Name1='C'
|
||||
Name2='C1'
|
||||
Coeff11=1.
|
||||
Coeff12=-1.
|
||||
Coeff13=0.
|
||||
Coeff21=1. #
|
||||
Coeff22=-1.
|
||||
Coeff23=1.
|
||||
Coeff31=1. #
|
||||
Coeff32=-1.
|
||||
Coeff33=-0.
|
||||
elif j == 12:
|
||||
Name1='D'
|
||||
Name2='D1'
|
||||
Coeff11=1.
|
||||
Coeff12=-1.
|
||||
Coeff13=0.
|
||||
Coeff21=1. #
|
||||
Coeff22=-1.
|
||||
Coeff23=1.
|
||||
Coeff31=1. #
|
||||
Coeff32=-1.
|
||||
Coeff33=-0.
|
||||
elif j == 13:
|
||||
Name1='C1'
|
||||
Name2='B1'
|
||||
Coeff11=1.
|
||||
Coeff12=-1.
|
||||
Coeff13=0.
|
||||
Coeff21=1. #
|
||||
Coeff22=-1.
|
||||
Coeff23=0.
|
||||
Coeff31=1. #
|
||||
Coeff32=-1.
|
||||
Coeff33=1.
|
||||
elif j == 14:
|
||||
Name1='D1'
|
||||
Name2='A1'
|
||||
Coeff11=1.
|
||||
Coeff12=-1.
|
||||
Coeff13=0.
|
||||
Coeff21=1. #
|
||||
Coeff22=-1.
|
||||
Coeff23=0.
|
||||
Coeff31=1. #
|
||||
Coeff32=-1.
|
||||
Coeff33=1.
|
||||
elif j == 15:
|
||||
Name1='A1'
|
||||
Name2='B1'
|
||||
Coeff11=-1.
|
||||
Coeff12=1.
|
||||
Coeff13=-1.
|
||||
Coeff21=-1. #
|
||||
Coeff22=-1.
|
||||
Coeff23=0.
|
||||
Coeff31=1. #
|
||||
Coeff32=-1.
|
||||
Coeff33=0.
|
||||
i=1
|
||||
entity1=zAssembly.sets[Name1].nodes
|
||||
entity2=zAssembly.sets[Name2].nodes
|
||||
for eachNode1 in entity1:
|
||||
cor1x=eachNode1.coordinates[0]
|
||||
cor1y=eachNode1.coordinates[1]
|
||||
cor1z=eachNode1.coordinates[2]
|
||||
for eachNode2 in entity2:
|
||||
distx=abs(cor1x-eachNode2.coordinates[0])
|
||||
disty=abs(cor1y-eachNode2.coordinates[1])
|
||||
distz=abs(cor1z-eachNode2.coordinates[2])
|
||||
if (distx<Toler and disty<Toler)or(disty<Toler and distz<Toler)or(distx<Toler and distz<Toler) :
|
||||
Node1=entity1.sequenceFromLabels(labels=(eachNode1.label,))
|
||||
Node2=entity2.sequenceFromLabels(labels=(eachNode2.label,))
|
||||
ZAssembly.Set(name=Name1+str(i),nodes=Node1)
|
||||
ZAssembly.Set(name=Name2+str(i),nodes=Node2)
|
||||
ZModel.Equation(name=Name1+Name2+'1'+str(i),terms=((Coeff11,Name1+str(i),1),(Coeff12,Name2+str(i),1),(Coeff13,'Dummy',1)))
|
||||
ZModel.Equation(name=Name1+Name2+'2'+str(i),terms=((Coeff21,Name1+str(i),2),(Coeff22,Name2+str(i),2),(Coeff23,'Dummy',2)))
|
||||
ZModel.Equation(name=Name1+Name2+'3'+str(i),terms=((Coeff31,Name1+str(i),3),(Coeff32,Name2+str(i),3),(Coeff33,'Dummy',3)))
|
||||
i=i+1
|
||||
261
Unpublished/PeriodicBoundary/PBC3D_V1_0.py
Normal file
261
Unpublished/PeriodicBoundary/PBC3D_V1_0.py
Normal file
|
|
@ -0,0 +1,261 @@
|
|||
# 3D PCBs - JGrogan - V1.0
|
||||
# V1.0 - Ceated: 18-02-12
|
||||
from abaqus import *
|
||||
from abaqusConstants import *
|
||||
#
|
||||
# Define Tolerance for Node Matching:
|
||||
Toler = 0.0001
|
||||
#
|
||||
zModel=mdb.models['Model-1']
|
||||
zAssembly=zModel.rootAssembly
|
||||
#
|
||||
# Constraints
|
||||
for j in range(0,19):
|
||||
if j == 0:
|
||||
Name1='FaceBottom'
|
||||
Name2='FaceTop'
|
||||
Coeff11=1.
|
||||
Coeff12=-1.
|
||||
Coeff13=0.
|
||||
Coeff21=1. #
|
||||
Coeff22=-1.
|
||||
Coeff23=-1.
|
||||
Coeff31=1. #
|
||||
Coeff32=-1.
|
||||
Coeff33=0.
|
||||
elif j == 1:
|
||||
Name1='FaceFront'
|
||||
Name2='FaceRear'
|
||||
Coeff11=1.
|
||||
Coeff12=-1.
|
||||
Coeff13=-1.
|
||||
Coeff21=1. #
|
||||
Coeff22=-1.
|
||||
Coeff23=0.
|
||||
Coeff31=1. #
|
||||
Coeff32=-1.
|
||||
Coeff33=0.
|
||||
elif j == 2:
|
||||
Name1='FaceLeft'
|
||||
Name2='FaceRight'
|
||||
Coeff11=1.
|
||||
Coeff12=-1.
|
||||
Coeff13=0.
|
||||
Coeff21=1. #
|
||||
Coeff22=-1.
|
||||
Coeff23=0.
|
||||
Coeff31=1. #
|
||||
Coeff32=-1.
|
||||
Coeff33=-1.
|
||||
elif j == 3:
|
||||
Name1='EdgeCC1'
|
||||
Name2='EdgeBB1'
|
||||
Coeff11=1.
|
||||
Coeff12=-1.
|
||||
Coeff13=0.
|
||||
Coeff21=1. #
|
||||
Coeff22=-1.
|
||||
Coeff23=0.
|
||||
Coeff31=1. #
|
||||
Coeff32=-1.
|
||||
Coeff33=1.
|
||||
elif j == 4:
|
||||
Name1='EdgeBB1'
|
||||
Name2='EdgeAA1'
|
||||
Coeff11=1.
|
||||
Coeff12=-1.
|
||||
Coeff13=-1.
|
||||
Coeff21=1. #
|
||||
Coeff22=-1.
|
||||
Coeff23=0.
|
||||
Coeff31=1. #
|
||||
Coeff32=-1.
|
||||
Coeff33=0.
|
||||
elif j == 5:
|
||||
Name1='EdgeAA1'
|
||||
Name2='EdgeDD1'
|
||||
Coeff11=1.
|
||||
Coeff12=-1.
|
||||
Coeff13=0.
|
||||
Coeff21=1. #
|
||||
Coeff22=-1.
|
||||
Coeff23=0.
|
||||
Coeff31=1. #
|
||||
Coeff32=-1.
|
||||
Coeff33=-1.
|
||||
elif j == 6:
|
||||
Name1='EdgeCD'
|
||||
Name2='EdgeAB'
|
||||
Coeff11=1.
|
||||
Coeff12=-1.
|
||||
Coeff13=0.
|
||||
Coeff21=1. #
|
||||
Coeff22=-1.
|
||||
Coeff23=0.
|
||||
Coeff31=1. #
|
||||
Coeff32=-1.
|
||||
Coeff33=1.
|
||||
elif j == 7:
|
||||
Name1='EdgeAB'
|
||||
Name2='EdgeA1B1'
|
||||
Coeff11=-1.
|
||||
Coeff12=1.
|
||||
Coeff13=0.
|
||||
Coeff21=-1. #
|
||||
Coeff22=1.
|
||||
Coeff23=-1.
|
||||
Coeff31=-1. #
|
||||
Coeff32=1.
|
||||
Coeff33=0.
|
||||
elif j == 8:
|
||||
Name1='EdgeA1B1'
|
||||
Name2='EdgeC1D1'
|
||||
Coeff11=1.
|
||||
Coeff12=-1.
|
||||
Coeff13=0.
|
||||
Coeff21=1. #
|
||||
Coeff22=-1.
|
||||
Coeff23=0.
|
||||
Coeff31=1. #
|
||||
Coeff32=-1.
|
||||
Coeff33=-1.
|
||||
elif j == 9:
|
||||
Name1='EdgeAD'
|
||||
Name2='EdgeBC'
|
||||
Coeff11=-1.
|
||||
Coeff12=1.
|
||||
Coeff13=-1.
|
||||
Coeff21=-1. #
|
||||
Coeff22=1.
|
||||
Coeff23=0.
|
||||
Coeff31=1. #
|
||||
Coeff32=-1.
|
||||
Coeff33=0.
|
||||
elif j == 10:
|
||||
Name1='EdgeBC'
|
||||
Name2='EdgeB1C1'
|
||||
Coeff11=-1.
|
||||
Coeff12=1.
|
||||
Coeff13=0.
|
||||
Coeff21=-1. #
|
||||
Coeff22=1.
|
||||
Coeff23=-1.
|
||||
Coeff31=1. #
|
||||
Coeff32=-1.
|
||||
Coeff33=0.
|
||||
elif j == 11:
|
||||
Name1='EdgeB1C1'
|
||||
Name2='EdgeA1D1'
|
||||
Coeff11=1.
|
||||
Coeff12=-1.
|
||||
Coeff13=-1.
|
||||
Coeff21=1. #
|
||||
Coeff22=-1.
|
||||
Coeff23=0.
|
||||
Coeff31=1. #
|
||||
Coeff32=-1.
|
||||
Coeff33=0.
|
||||
elif j == 12:
|
||||
Name1='B'
|
||||
Name2='C'
|
||||
Coeff11=1.
|
||||
Coeff12=-1.
|
||||
Coeff13=0.
|
||||
Coeff21=1. #
|
||||
Coeff22=-1.
|
||||
Coeff23=0.
|
||||
Coeff31=1. #
|
||||
Coeff32=-1.
|
||||
Coeff33=-1.
|
||||
elif j == 13:
|
||||
Name1='A'
|
||||
Name2='D'
|
||||
Coeff11=1.
|
||||
Coeff12=-1.
|
||||
Coeff13=0.
|
||||
Coeff21=-1. #
|
||||
Coeff22=1.
|
||||
Coeff23=0.
|
||||
Coeff31=1. #
|
||||
Coeff32=-1.
|
||||
Coeff33=-1.
|
||||
elif j == 14:
|
||||
Name1='C'
|
||||
Name2='C1'
|
||||
Coeff11=1.
|
||||
Coeff12=-1.
|
||||
Coeff13=0.
|
||||
Coeff21=1. #
|
||||
Coeff22=-1.
|
||||
Coeff23=1.
|
||||
Coeff31=1. #
|
||||
Coeff32=-1.
|
||||
Coeff33=-0.
|
||||
elif j == 15:
|
||||
Name1='D'
|
||||
Name2='D1'
|
||||
Coeff11=1.
|
||||
Coeff12=-1.
|
||||
Coeff13=0.
|
||||
Coeff21=1. #
|
||||
Coeff22=-1.
|
||||
Coeff23=1.
|
||||
Coeff31=1. #
|
||||
Coeff32=-1.
|
||||
Coeff33=-0.
|
||||
elif j == 16:
|
||||
Name1='C1'
|
||||
Name2='B1'
|
||||
Coeff11=1.
|
||||
Coeff12=-1.
|
||||
Coeff13=0.
|
||||
Coeff21=1. #
|
||||
Coeff22=-1.
|
||||
Coeff23=0.
|
||||
Coeff31=1. #
|
||||
Coeff32=-1.
|
||||
Coeff33=1.
|
||||
elif j == 17:
|
||||
Name1='D1'
|
||||
Name2='A1'
|
||||
Coeff11=1.
|
||||
Coeff12=-1.
|
||||
Coeff13=0.
|
||||
Coeff21=1. #
|
||||
Coeff22=-1.
|
||||
Coeff23=0.
|
||||
Coeff31=1. #
|
||||
Coeff32=-1.
|
||||
Coeff33=1.
|
||||
elif j == 18:
|
||||
Name1='A1'
|
||||
Name2='B1'
|
||||
Coeff11=-1.
|
||||
Coeff12=1.
|
||||
Coeff13=-1.
|
||||
Coeff21=-1. #
|
||||
Coeff22=1.
|
||||
Coeff23=0.
|
||||
Coeff31=1. #
|
||||
Coeff32=-1.
|
||||
Coeff33=0.
|
||||
i=1
|
||||
entity1=zAssembly.sets[Name1].nodes
|
||||
entity2=zAssembly.sets[Name2].nodes
|
||||
for eachNode1 in entity1:
|
||||
cor1x=eachNode1.coordinates[0]
|
||||
cor1y=eachNode1.coordinates[1]
|
||||
cor1z=eachNode1.coordinates[2]
|
||||
for eachNode2 in entity2:
|
||||
distx=abs(cor1x-eachNode2.coordinates[0])
|
||||
disty=abs(cor1y-eachNode2.coordinates[1])
|
||||
distz=abs(cor1z-eachNode2.coordinates[2])
|
||||
if (distx<Toler and disty<Toler)or(disty<Toler and distz<Toler)or(distx<Toler and distz<Toler):
|
||||
Node1=entity1.sequenceFromLabels(labels=(eachNode1.label,))
|
||||
Node2=entity2.sequenceFromLabels(labels=(eachNode2.label,))
|
||||
zAssembly.Set(name='S'+Name1+str(i),nodes=Node1)
|
||||
zAssembly.Set(name='S'+Name2+str(i),nodes=Node2)
|
||||
zModel.Equation(name=Name1+Name2+'1'+str(i),terms=((Coeff11,'S'+Name1+str(i),1),(Coeff12,'S'+Name2+str(i),1),(Coeff13,'Dummy',1)))
|
||||
zModel.Equation(name=Name1+Name2+'2'+str(i),terms=((Coeff21,'S'+Name1+str(i),2),(Coeff22,'S'+Name2+str(i),2),(Coeff23,'Dummy',2)))
|
||||
zModel.Equation(name=Name1+Name2+'3'+str(i),terms=((Coeff31,'S'+Name1+str(i),3),(Coeff32,'S'+Name2+str(i),3),(Coeff33,'Dummy',3)))
|
||||
i=i+1
|
||||
14
Unpublished/PeriodicBoundary/periodic.py
Normal file
14
Unpublished/PeriodicBoundary/periodic.py
Normal file
|
|
@ -0,0 +1,14 @@
|
|||
from abaqusConstants import *
|
||||
from abaqus import *
|
||||
aModel=mdb.models['3D_Rad']
|
||||
aAss=aMode.rootAsembly
|
||||
aPart=aModel.parts['Mesh']
|
||||
aSet=aAss.sets['Set-1']
|
||||
aInst=aAss.instances['Mesh-1']
|
||||
for eachnode in aSet.nodes:
|
||||
theta=eachnode.coordinates[1]/Radius
|
||||
newcoord1=eachnode.coordinates[0]
|
||||
newcoord2=(Radius-eachnode.coordinates[2])*cos(theta)
|
||||
newcoord3=(Radius-eachnode.coordinates[2])*sin(theta)
|
||||
aPart.editNode(nodes=eachnode,coordinate1=newcoord1,coordinate2=newcoord2,
|
||||
coordinate3=newcoord3)
|
||||
0
Unpublished/README.md
Normal file
0
Unpublished/README.md
Normal file
64
Unpublished/RigidSurface/rsurfu.for
Normal file
64
Unpublished/RigidSurface/rsurfu.for
Normal file
|
|
@ -0,0 +1,64 @@
|
|||
subroutine rsurfu(h,p,tgt,dnds,x1,time,u,ciname,slname,msname,
|
||||
1 noel,node,lclose)
|
||||
include 'aba_param.inc'
|
||||
c
|
||||
character*80 ciname,slname,msname
|
||||
dimension p(3),tgt(3,2),dnds(3,2),x1(3,2),time(2)
|
||||
parameter(zero=0.d0,one=1.d0)
|
||||
c get cylinder radius
|
||||
stime=time(2)
|
||||
if(msname(1:5)=='INNER')then
|
||||
ri=0.4d0
|
||||
drdt=one
|
||||
if(stime<=one)then
|
||||
radius=ri+drdt*stime
|
||||
elseif(stime<=2.d0)then
|
||||
radius=ri+drdt*(2.d0-stime)
|
||||
else
|
||||
radius=ri
|
||||
endif
|
||||
else
|
||||
ri=1.8d0
|
||||
drdt=-one
|
||||
if(stime>=2.0d0)then
|
||||
radius=ri+drdt*(stime-2.0d0)
|
||||
else
|
||||
radius=ri
|
||||
endif
|
||||
endif
|
||||
c initialize variables
|
||||
do k1=1,2
|
||||
do k2=1,3
|
||||
tgt(k2,k1) = zero
|
||||
dnds(k2,k1) = zero
|
||||
p(k2) = zero
|
||||
enddo
|
||||
enddo
|
||||
c coordinates of point on deforming body
|
||||
x = x1(1,1)
|
||||
y = x1(2,1)
|
||||
z = x1(3,1)
|
||||
c project point onto unit radius cylinder
|
||||
r = ( x*x + y*y )**(0.5d0)
|
||||
x = x / r
|
||||
y = y / r
|
||||
c get point on rigid cylinder
|
||||
p(1) = radius*x
|
||||
p(2) = radius*y
|
||||
p(3) = z
|
||||
c get unit tangents
|
||||
tgt(1,1) = -y
|
||||
tgt(2,1) = x
|
||||
tgt(3,2) = one
|
||||
c get local curvatures
|
||||
dnds(1,1) = -y / radius
|
||||
dnds(2,1) = x / radius
|
||||
c get surface penetration depth
|
||||
if(msname(1:5)=='INNER')then
|
||||
h = radius - r
|
||||
else
|
||||
h = r - radius
|
||||
endif
|
||||
print *,radius,stime,msname(1:5),h
|
||||
return
|
||||
end
|
||||
102
Unpublished/RigidSurface/rsurfu_surf.for
Normal file
102
Unpublished/RigidSurface/rsurfu_surf.for
Normal file
|
|
@ -0,0 +1,102 @@
|
|||
subroutine rsurfu(h,p,tgt,dnds,x1,time,u,ciname,slname,msname,
|
||||
1 noel,node,lclose)
|
||||
include 'aba_param.inc'
|
||||
c
|
||||
character*80 ciname,slname,msname
|
||||
dimension p(3),tgt(3,2),dnds(3,2),x1(3,2),time(2)
|
||||
parameter(zero=0.d0,one=1.d0)
|
||||
c get cylinder radius
|
||||
stime=time(2)
|
||||
if(msname(1:5)=='INNER')then
|
||||
ri=0.4d0
|
||||
drdt=one
|
||||
if(stime<=one)then
|
||||
radius=ri+drdt*stime
|
||||
elseif(stime<=2.d0)then
|
||||
radius=ri+drdt*(2.d0-stime)
|
||||
else
|
||||
radius=ri
|
||||
endif
|
||||
else
|
||||
ri=1.8d0
|
||||
drdt=-one
|
||||
if(stime>=3.05d0)then
|
||||
radius=ri+drdt*(stime-3.05d0)
|
||||
else
|
||||
radius=ri
|
||||
endif
|
||||
endif
|
||||
c initialize variables
|
||||
do k1=1,2
|
||||
do k2=1,3
|
||||
tgt(k2,k1) = zero
|
||||
dnds(k2,k1) = zero
|
||||
p(k2) = zero
|
||||
enddo
|
||||
enddo
|
||||
c coordinates of point on deforming body
|
||||
x = x1(1,1)
|
||||
y = x1(2,1)
|
||||
z = x1(3,1)
|
||||
c get point on rigid cylinder
|
||||
x2=x1(1,1)+x1(1,3)
|
||||
y2=x1(2,1)+x1(2,3)
|
||||
z2=x1(3,1)+x1(3,3)
|
||||
dx=x2-x
|
||||
dy=y2-y
|
||||
dr=sqrt(dx*dx+dy*dy)
|
||||
D=x*y2-x2*y
|
||||
disc=radius*radius*dr*dr-D*D
|
||||
if(disc==zero)then
|
||||
xcor=D*dy/(dr*dr)
|
||||
ycor=-D*dx/(dr*dr)
|
||||
elseif(disc<zero)then
|
||||
xcor=1.e6
|
||||
ycor=1.e6
|
||||
print *,'warning - perpendicular slave master normals'
|
||||
else
|
||||
x1cor=(d*dy+sign(one,dy)*dx*disc)/(dr*dr)
|
||||
x2cor=(d*dy-sign(one,dy)*dx*disc)/(dr*dr)
|
||||
y1cor=(-d*dx+abs(dy)*disc)/(dr*dr)
|
||||
y2cor=(-d*dx-abs(dy)*disc)/(dr*dr)
|
||||
dx1=x1cor-x
|
||||
dx2=x2cor-x2
|
||||
dy1=y1cor-y
|
||||
dy2=y2cor-y2
|
||||
d1=sqrt(dx1*dx1+dy1*dy1)
|
||||
d2=sqrt(dx2*dx2+dy2*dy2)
|
||||
z1cor=x1(3,3)*d1+z
|
||||
z2cor=x1(3,3)*d2+z
|
||||
dz1=z1cor-z
|
||||
dz2=z2cor-z2
|
||||
dist1=sqrt(dx1*dx1+dy1*dy1+dz1*dz1)
|
||||
dist2=sqrt(dx2*dx2+dy2*dy2+dz2*dz2)
|
||||
if(dist1<dist2)then
|
||||
p(1) = x1cor
|
||||
p(2) = y1cor
|
||||
p(3) = z1cor
|
||||
else
|
||||
p(1) = x2cor
|
||||
p(2) = y2cor
|
||||
p(3) = z2cor
|
||||
endif
|
||||
endif
|
||||
c project point onto unit radius cylinder
|
||||
r = ( x*x + y*y )**(0.5d0)
|
||||
x = p(1)/radius
|
||||
y = p(2)/radius
|
||||
c get unit tangents
|
||||
tgt(1,1) = -y
|
||||
tgt(2,1) = x
|
||||
tgt(3,2) = one
|
||||
c get local curvatures
|
||||
dnds(1,1) = -y / radius
|
||||
dnds(2,1) = x / radius
|
||||
c get surface penetration depth
|
||||
if(msname(1:5)=='INNER')then
|
||||
h = radius - r
|
||||
else
|
||||
h = r - radius
|
||||
endif
|
||||
return
|
||||
end
|
||||
234
Unpublished/XFEM/1D_Solver/2DLevelSet.m
Normal file
234
Unpublished/XFEM/1D_Solver/2DLevelSet.m
Normal file
|
|
@ -0,0 +1,234 @@
|
|||
function [] = 2DLevelSet()
|
||||
clear all
|
||||
% Define Main Solution Mesh
|
||||
NumX=8;
|
||||
NumY=8;
|
||||
delX=1.;
|
||||
delY=1.;
|
||||
for j=1:NumY+1
|
||||
for i=1:NumX+1
|
||||
index=i+(NumX+1)*(j-1);
|
||||
Node(index,1)=single((i-1.))*delX;
|
||||
Node(index,2)=single((j-1.))*delY;
|
||||
end
|
||||
end
|
||||
numNodes=(NumX+1)*(NumY+1);
|
||||
for j=1:NumY
|
||||
for i=1:NumX
|
||||
index=i+NumX*(j-1);
|
||||
Element(index,1)=i+(NumX+1)*(j-1);
|
||||
Element(index,2)=i+(NumX+1)*(j-1)+1;
|
||||
Element(index,3)=i+(NumX+1)*(j)+1;
|
||||
Element(index,4)=i+(NumX+1)*(j);
|
||||
end
|
||||
end
|
||||
numElem=(NumX)*(NumY);
|
||||
% Define Initial Level Set
|
||||
centx=4.;
|
||||
centy=4.;
|
||||
rad=2.1;
|
||||
for i=1:numNodes;
|
||||
dist=sqrt((Node(i,1)-centx)*(Node(i,1)-centx)+(Node(i,2)-centy)*(Node(i,2)-centy));
|
||||
lSet(i)=dist-rad;
|
||||
end
|
||||
%for i=1:numNodes;
|
||||
% dist=Node(i,1)-0.1;
|
||||
% lSet(i)=dist;
|
||||
%end
|
||||
% Plot initial level set
|
||||
[X Y]=meshgrid(0:1.:8);
|
||||
Z=zeros(9);
|
||||
for i=1:81
|
||||
Z(i)=lSet(i);
|
||||
end
|
||||
surf(X,Y,Z)
|
||||
% LS Algorithm Parameters
|
||||
lSet'
|
||||
bandwidth=10.;
|
||||
% Loop through timesteps
|
||||
for tstep=1:100
|
||||
% Identify Narrow Band Elements
|
||||
NBindex=0;
|
||||
for i=1:numElem
|
||||
check=0;
|
||||
for iNd=1:4
|
||||
if abs(lSet(Element(i,iNd)))<=bandwidth*delX
|
||||
check=1;
|
||||
end
|
||||
end
|
||||
% If an element is in the narrow band split it into triangles
|
||||
if check==1
|
||||
NBindex=NBindex+1;
|
||||
NBelem(NBindex,1)=Element(i,1);
|
||||
NBelem(NBindex,2)=Element(i,2);
|
||||
NBelem(NBindex,3)=Element(i,3);
|
||||
NBindex=NBindex+1;
|
||||
NBelem(NBindex,1)=Element(i,1);
|
||||
NBelem(NBindex,2)=Element(i,3);
|
||||
NBelem(NBindex,3)=Element(i,4);
|
||||
end
|
||||
end
|
||||
% Velocity BC
|
||||
F=zeros(numNodes,1);
|
||||
for i=1:NBindex
|
||||
if sign(lSet(NBelem(i,1)))~=sign(lSet(NBelem(i,2)))||sign(lSet(NBelem(i,1)))~=sign(lSet(NBelem(i,3)))
|
||||
F(NBelem(i,1))= 1.;
|
||||
F(NBelem(i,2))= 1.;
|
||||
F(NBelem(i,3))= 1.;
|
||||
end
|
||||
end
|
||||
% Assemble 'Stiffness' Matrices
|
||||
A=zeros(numNodes);
|
||||
for i=1:NBindex
|
||||
gx(1)=2./3.;
|
||||
gx(2)=1./6.;
|
||||
gx(3)=1./6.;
|
||||
hx(1)=1./6.;
|
||||
hx(2)=1./6.;
|
||||
hx(3)=2./3.;
|
||||
AfL=zeros(3);
|
||||
AfLGLS=zeros(3);
|
||||
x1=Node(NBelem(i,1),1);
|
||||
y1=Node(NBelem(i,1),2);
|
||||
x2=Node(NBelem(i,2),1);
|
||||
y2=Node(NBelem(i,2),2);
|
||||
x3=Node(NBelem(i,3),1);
|
||||
y3=Node(NBelem(i,3),2);
|
||||
for j=1:3
|
||||
g=gx(j);
|
||||
h=hx(j);
|
||||
phi(1)=1.-g-h;
|
||||
phi(2)=g;
|
||||
phi(3)=h;
|
||||
phig(1)=-1.;
|
||||
phig(2)=1.;
|
||||
phig(3)=0.;
|
||||
phih(1)=-1.;
|
||||
phih(2)=0.;
|
||||
phih(3)=1.;
|
||||
djac=2*abs(x1*(y2-y3)+x2*(y3-y1)+x3*(y1-y2));
|
||||
for k=1:3
|
||||
phix(k)=(1./djac)*((-y1+y3)*phig(k)+(y1-y2)*phih(k));
|
||||
phiy(k)=(1./djac)*((x1-x3)*phig(k)+(-x1+x2)*phih(k));
|
||||
end
|
||||
delphi=[phix;phiy];
|
||||
nodalLset=[lSet(NBelem(i,1));lSet(NBelem(i,2));lSet(NBelem(i,3))];
|
||||
set=phi*nodalLset;
|
||||
delset=delphi*nodalLset;
|
||||
AfL=AfL+(phi'*sign(set))*(delset'*delphi)/3.;
|
||||
AfLGLS=AfLGLS+(delphi'*delset)*(1./norm(delset))*(delset'*delphi)/3.;
|
||||
end
|
||||
sum=AfL+AfLGLS;
|
||||
for k=1:3;
|
||||
for j=1:3;
|
||||
A(NBelem(i,j),NBelem(i,k))=A(NBelem(i,j),NBelem(i,k))+sum(j,k);
|
||||
end
|
||||
end
|
||||
end
|
||||
% Apply BCs
|
||||
RHS=zeros(numNodes,1);
|
||||
Sub=A*F;
|
||||
iindex=0;
|
||||
for i=1:numNodes
|
||||
if F(i)==0.
|
||||
iindex=iindex+1;
|
||||
RHSred(iindex)=RHS(i)-Sub(i);
|
||||
Fred=0.;
|
||||
jindex=0;
|
||||
for j=1:numNodes
|
||||
if F(j)==0.
|
||||
jindex=jindex+1;
|
||||
Ared(iindex,jindex)=A(i,j);
|
||||
end
|
||||
end
|
||||
end
|
||||
end
|
||||
% Solve for Fred
|
||||
Fred=(Ared^-1)*RHSred';
|
||||
% Get F
|
||||
iindex=0;
|
||||
for i=1:numNodes
|
||||
if F(i)==0.
|
||||
iindex=iindex+1;
|
||||
F(i)=Fred(iindex);
|
||||
end
|
||||
end
|
||||
% Update level set
|
||||
mMat=zeros(numNodes);
|
||||
mMatGLS=zeros(numNodes);
|
||||
f1=zeros(numNodes,1);
|
||||
f2=zeros(numNodes,1);
|
||||
f3=zeros(numNodes,1);
|
||||
h2=0.00001;
|
||||
visc=0.0005;
|
||||
for i=1:NBindex
|
||||
mMatL=zeros(3);
|
||||
mMatGLSL=zeros(3);
|
||||
f1L=zeros(3,1);
|
||||
f2L=zeros(3,1);
|
||||
f3L=zeros(3,1);
|
||||
gx(1)=2./3.;
|
||||
gx(2)=1./6.;
|
||||
gx(3)=1./6.;
|
||||
hx(1)=1./6.;
|
||||
hx(2)=1./6.;
|
||||
hx(3)=2./3.;
|
||||
x1=Node(NBelem(i,1),1);
|
||||
y1=Node(NBelem(i,1),2);
|
||||
x2=Node(NBelem(i,2),1);
|
||||
y2=Node(NBelem(i,2),2);
|
||||
x3=Node(NBelem(i,3),1);
|
||||
y3=Node(NBelem(i,3),2);
|
||||
for j=1:3
|
||||
g=gx(j);
|
||||
h=hx(j);
|
||||
phi(1)=1.-g-h;
|
||||
phi(2)=g;
|
||||
phi(3)=h;
|
||||
phig(1)=-1.;
|
||||
phig(2)=1.;
|
||||
phig(3)=0.;
|
||||
phih(1)=-1.;
|
||||
phih(2)=0.;
|
||||
phih(3)=1.;
|
||||
djac=abs(x1*(y2-y3)+x2*(y3-y1)+x3*(y1-y2));
|
||||
for k=1:3
|
||||
phix(k)=(1./djac)*((-y1+y3)*phig(k)+(y1-y2)*phih(k));
|
||||
phiy(k)=(1./djac)*((x1-x3)*phig(k)+(-x1+x2)*phih(k));
|
||||
end
|
||||
delphi=[phix;phiy];
|
||||
nodalLset=[lSet(NBelem(i,1));lSet(NBelem(i,2));lSet(NBelem(i,3))];
|
||||
nodalF=[F(NBelem(i,1));F(NBelem(i,2));F(NBelem(i,3))];
|
||||
delset=delphi*nodalLset;
|
||||
Floc=phi*nodalF;
|
||||
mMatL=mMatL+(phi'*phi)/3.;
|
||||
mMatGLSL=mMatGLSL+((delphi'*(delset/norm(delset)))*Floc*(h2/abs(Floc)))*phi/3.;
|
||||
f1L=f1L+phi'*Floc*norm(delset)/3.;
|
||||
f2L=f2L+(delphi'*(delset/norm(delset))*Floc)*(h2/abs(Floc))*Floc*norm(delset)/3.;
|
||||
vs=h2*((abs(visc+Floc*norm(delset)))/(norm(Floc*delset)+h2));
|
||||
f3L=f3L+vs*delphi'*delset/3.;
|
||||
end
|
||||
for k=1:3;
|
||||
for j=1:3;
|
||||
mMat(NBelem(i,j),NBelem(i,k))=mMat(NBelem(i,j),NBelem(i,k))+mMatL(j,k);
|
||||
mMatGLS(NBelem(i,j),NBelem(i,k))=mMatGLS(NBelem(i,j),NBelem(i,k))+mMatGLSL(j,k);
|
||||
end
|
||||
f1(NBelem(i,k))=f1(NBelem(i,k))+f1L(k);
|
||||
f2(NBelem(i,k))=f2(NBelem(i,k))+f2L(k);
|
||||
f3(NBelem(i,k))=f3(NBelem(i,k))+f3L(k);
|
||||
end
|
||||
end
|
||||
dt=0.01;
|
||||
lSet=lSet-((((mMat+mMatGLS)^-1)*dt)*(f1+f2+f3))';
|
||||
end
|
||||
lSet'
|
||||
%[X Y]=meshgrid(0:1.:8);
|
||||
%Z=zeros(9);
|
||||
%for i=1:81
|
||||
% Z(i)=lSet(i);
|
||||
%end
|
||||
%surf(X,Y,Z)
|
||||
|
||||
|
||||
|
||||
|
||||
234
Unpublished/XFEM/1D_Solver/2DLevelSetFMM.m
Normal file
234
Unpublished/XFEM/1D_Solver/2DLevelSetFMM.m
Normal file
|
|
@ -0,0 +1,234 @@
|
|||
function [] = 2DLevelSetFMM()
|
||||
clear all
|
||||
% Define Main Solution Mesh
|
||||
NumX=3;
|
||||
NumY=1;
|
||||
delX=1.;
|
||||
delY=1.;
|
||||
for j=1:NumY+1
|
||||
for i=1:NumX+1
|
||||
index=i+(NumX+1)*(j-1);
|
||||
Node(index,1)=single((i-1.))*delX;
|
||||
Node(index,2)=single((j-1.))*delY;
|
||||
end
|
||||
end
|
||||
numNodes=(NumX+1)*(NumY+1);
|
||||
for j=1:NumY
|
||||
for i=1:NumX
|
||||
index=i+NumX*(j-1);
|
||||
Element(index,1)=i+(NumX+1)*(j-1);
|
||||
Element(index,2)=i+(NumX+1)*(j-1)+1;
|
||||
Element(index,3)=i+(NumX+1)*(j)+1;
|
||||
Element(index,4)=i+(NumX+1)*(j);
|
||||
end
|
||||
end
|
||||
numElem=(NumX)*(NumY);
|
||||
% Define Initial Level Set
|
||||
%centx=4.;
|
||||
%centy=4.;
|
||||
%rad=2.1;
|
||||
%for i=1:numNodes;
|
||||
% dist=sqrt((Node(i,1)-centx)*(Node(i,1)-centx)+(Node(i,2)-centy)*(Node(i,2)-centy));
|
||||
% lSet(i)=dist-rad;
|
||||
%end
|
||||
for i=1:numNodes;
|
||||
dist=Node(i,1)-0.1;
|
||||
lSet(i)=dist;
|
||||
end
|
||||
% Plot initial level set
|
||||
%[X Y]=meshgrid(0:1.:8);
|
||||
%Z=zeros(9);
|
||||
%for i=1:81
|
||||
% Z(i)=lSet(i);
|
||||
%end
|
||||
%surf(X,Y,Z)
|
||||
% LS Algorithm Parameters
|
||||
lSet'
|
||||
bandwidth=10.;
|
||||
% Loop through timesteps
|
||||
for tstep=1:1
|
||||
% Identify Narrow Band Elements
|
||||
NBindex=0;
|
||||
for i=1:numElem
|
||||
check=0;
|
||||
for iNd=1:4
|
||||
if abs(lSet(Element(i,iNd)))<=bandwidth*delX
|
||||
check=1;
|
||||
end
|
||||
end
|
||||
% If an element is in the narrow band split it into triangles
|
||||
if check==1
|
||||
NBindex=NBindex+1;
|
||||
NBelem(NBindex,1)=Element(i,1);
|
||||
NBelem(NBindex,2)=Element(i,2);
|
||||
NBelem(NBindex,3)=Element(i,3);
|
||||
NBindex=NBindex+1;
|
||||
NBelem(NBindex,1)=Element(i,1);
|
||||
NBelem(NBindex,2)=Element(i,3);
|
||||
NBelem(NBindex,3)=Element(i,4);
|
||||
end
|
||||
end
|
||||
% Velocity BC
|
||||
F=zeros(numNodes,1);
|
||||
for i=1:NBindex
|
||||
if sign(lSet(NBelem(i,1)))~=sign(lSet(NBelem(i,2)))||sign(lSet(NBelem(i,1)))~=sign(lSet(NBelem(i,3)))
|
||||
F(NBelem(i,1))= 1.;
|
||||
F(NBelem(i,2))= 1.;
|
||||
F(NBelem(i,3))= 1.;
|
||||
end
|
||||
end
|
||||
% Assemble 'Stiffness' Matrices
|
||||
A=zeros(numNodes);
|
||||
for i=1:NBindex
|
||||
gx(1)=2./3.;
|
||||
gx(2)=1./6.;
|
||||
gx(3)=1./6.;
|
||||
hx(1)=1./6.;
|
||||
hx(2)=1./6.;
|
||||
hx(3)=2./3.;
|
||||
AfL=zeros(3);
|
||||
AfLGLS=zeros(3);
|
||||
x1=Node(NBelem(i,1),1);
|
||||
y1=Node(NBelem(i,1),2);
|
||||
x2=Node(NBelem(i,2),1);
|
||||
y2=Node(NBelem(i,2),2);
|
||||
x3=Node(NBelem(i,3),1);
|
||||
y3=Node(NBelem(i,3),2);
|
||||
for j=1:3
|
||||
g=gx(j);
|
||||
h=hx(j);
|
||||
phi(1)=1.-g-h;
|
||||
phi(2)=g;
|
||||
phi(3)=h;
|
||||
phig(1)=-1.;
|
||||
phig(2)=1.;
|
||||
phig(3)=0.;
|
||||
phih(1)=-1.;
|
||||
phih(2)=0.;
|
||||
phih(3)=1.;
|
||||
djac=2*abs(x1*(y2-y3)+x2*(y3-y1)+x3*(y1-y2));
|
||||
for k=1:3
|
||||
phix(k)=(1./djac)*((-y1+y3)*phig(k)+(y1-y2)*phih(k));
|
||||
phiy(k)=(1./djac)*((x1-x3)*phig(k)+(-x1+x2)*phih(k));
|
||||
end
|
||||
delphi=[phix;phiy];
|
||||
nodalLset=[lSet(NBelem(i,1));lSet(NBelem(i,2));lSet(NBelem(i,3))];
|
||||
set=phi*nodalLset;
|
||||
delset=delphi*nodalLset;
|
||||
AfL=AfL+(phi'*sign(set))*(delset'*delphi)/3.;
|
||||
AfLGLS=AfLGLS+(delphi'*delset)*(1./norm(delset))*(delset'*delphi)/3.;
|
||||
end
|
||||
sum=AfL+AfLGLS;
|
||||
for k=1:3;
|
||||
for j=1:3;
|
||||
A(NBelem(i,j),NBelem(i,k))=A(NBelem(i,j),NBelem(i,k))+sum(j,k);
|
||||
end
|
||||
end
|
||||
end
|
||||
% Apply BCs
|
||||
RHS=zeros(numNodes,1);
|
||||
Sub=A*F;
|
||||
iindex=0;
|
||||
for i=1:numNodes
|
||||
if F(i)==0.
|
||||
iindex=iindex+1;
|
||||
RHSred(iindex)=RHS(i)-Sub(i);
|
||||
Fred=0.;
|
||||
jindex=0;
|
||||
for j=1:numNodes
|
||||
if F(j)==0.
|
||||
jindex=jindex+1;
|
||||
Ared(iindex,jindex)=A(i,j);
|
||||
end
|
||||
end
|
||||
end
|
||||
end
|
||||
% Solve for Fred
|
||||
Fred=(Ared^-1)*RHSred';
|
||||
% Get F
|
||||
iindex=0;
|
||||
for i=1:numNodes
|
||||
if F(i)==0.
|
||||
iindex=iindex+1;
|
||||
F(i)=Fred(iindex);
|
||||
end
|
||||
end
|
||||
% Update level set
|
||||
mMat=zeros(numNodes);
|
||||
mMatGLS=zeros(numNodes);
|
||||
f1=zeros(numNodes,1);
|
||||
f2=zeros(numNodes,1);
|
||||
f3=zeros(numNodes,1);
|
||||
h2=0.00001;
|
||||
visc=0.0005;
|
||||
for i=1:NBindex
|
||||
mMatL=zeros(3);
|
||||
mMatGLSL=zeros(3);
|
||||
f1L=zeros(3,1);
|
||||
f2L=zeros(3,1);
|
||||
f3L=zeros(3,1);
|
||||
gx(1)=2./3.;
|
||||
gx(2)=1./6.;
|
||||
gx(3)=1./6.;
|
||||
hx(1)=1./6.;
|
||||
hx(2)=1./6.;
|
||||
hx(3)=2./3.;
|
||||
x1=Node(NBelem(i,1),1);
|
||||
y1=Node(NBelem(i,1),2);
|
||||
x2=Node(NBelem(i,2),1);
|
||||
y2=Node(NBelem(i,2),2);
|
||||
x3=Node(NBelem(i,3),1);
|
||||
y3=Node(NBelem(i,3),2);
|
||||
for j=1:3
|
||||
g=gx(j);
|
||||
h=hx(j);
|
||||
phi(1)=1.-g-h;
|
||||
phi(2)=g;
|
||||
phi(3)=h;
|
||||
phig(1)=-1.;
|
||||
phig(2)=1.;
|
||||
phig(3)=0.;
|
||||
phih(1)=-1.;
|
||||
phih(2)=0.;
|
||||
phih(3)=1.;
|
||||
djac=abs(x1*(y2-y3)+x2*(y3-y1)+x3*(y1-y2));
|
||||
for k=1:3
|
||||
phix(k)=(1./djac)*((-y1+y3)*phig(k)+(y1-y2)*phih(k));
|
||||
phiy(k)=(1./djac)*((x1-x3)*phig(k)+(-x1+x2)*phih(k));
|
||||
end
|
||||
delphi=[phix;phiy];
|
||||
nodalLset=[lSet(NBelem(i,1));lSet(NBelem(i,2));lSet(NBelem(i,3))];
|
||||
nodalF=[F(NBelem(i,1));F(NBelem(i,2));F(NBelem(i,3))];
|
||||
delset=delphi*nodalLset;
|
||||
Floc=phi*nodalF;
|
||||
mMatL=mMatL+(phi'*phi)/3.;
|
||||
mMatGLSL=mMatGLSL+((delphi'*(delset/norm(delset)))*Floc*(h2/abs(Floc)))*phi/3.;
|
||||
f1L=f1L+phi'*Floc*norm(delset)/3.;
|
||||
f2L=f2L+(delphi'*(delset/norm(delset))*Floc)*(h2/abs(Floc))*Floc*norm(delset)/3.;
|
||||
vs=h2*((abs(visc+Floc*norm(delset)))/(norm(Floc*delset)+h2));
|
||||
f3L=f3L+vs*delphi'*delset/3.;
|
||||
end
|
||||
for k=1:3;
|
||||
for j=1:3;
|
||||
mMat(NBelem(i,j),NBelem(i,k))=mMat(NBelem(i,j),NBelem(i,k))+mMatL(j,k);
|
||||
mMatGLS(NBelem(i,j),NBelem(i,k))=mMatGLS(NBelem(i,j),NBelem(i,k))+mMatGLSL(j,k);
|
||||
end
|
||||
f1(NBelem(i,k))=f1(NBelem(i,k))+f1L(k);
|
||||
f2(NBelem(i,k))=f2(NBelem(i,k))+f2L(k);
|
||||
f3(NBelem(i,k))=f3(NBelem(i,k))+f3L(k);
|
||||
end
|
||||
end
|
||||
dt=0.01;
|
||||
lSet=lSet-((((mMat+mMatGLS)^-1)*dt)*(f1+f2+f3))';
|
||||
end
|
||||
lSet'
|
||||
%[X Y]=meshgrid(0:1.:8);
|
||||
%Z=zeros(9);
|
||||
%for i=1:81
|
||||
% Z(i)=lSet(i);
|
||||
%end
|
||||
%surf(X,Y,Z)
|
||||
|
||||
|
||||
|
||||
|
||||
322
Unpublished/XFEM/1D_Solver/F2DLevelSetFMM.asv
Normal file
322
Unpublished/XFEM/1D_Solver/F2DLevelSetFMM.asv
Normal file
|
|
@ -0,0 +1,322 @@
|
|||
function [] = F2DLevelSetFMM()
|
||||
clear all
|
||||
% Define Main Solution Mesh
|
||||
NumX=5;
|
||||
NumY=1;
|
||||
delX=1.;
|
||||
delY=1.;
|
||||
for j=1:NumY+1
|
||||
for i=1:NumX+1
|
||||
index=i+(NumX+1)*(j-1);
|
||||
Node(index,1)=single((i-1.))*delX;
|
||||
Node(index,2)=single((j-1.))*delY;
|
||||
end
|
||||
end
|
||||
numNodes=(NumX+1)*(NumY+1);
|
||||
for j=1:NumY
|
||||
for i=1:NumX
|
||||
index=i+NumX*(j-1);
|
||||
Element(index,1)=i+(NumX+1)*(j-1);
|
||||
Element(index,2)=i+(NumX+1)*(j-1)+1;
|
||||
Element(index,3)=i+(NumX+1)*(j)+1;
|
||||
Element(index,4)=i+(NumX+1)*(j);
|
||||
end
|
||||
end
|
||||
numElem=(NumX)*(NumY);
|
||||
% Define Initial Level Set
|
||||
%centx=4.;
|
||||
%centy=4.;
|
||||
%rad=2.1;
|
||||
%for i=1:numNodes;
|
||||
% dist=sqrt((Node(i,1)-centx)*(Node(i,1)-centx)+(Node(i,2)-centy)*(Node(i,2)-centy));
|
||||
% lSet(i)=dist-rad;
|
||||
%end
|
||||
for i=1:numNodes;
|
||||
dist=Node(i,1)-0.1;
|
||||
lSet(i)=dist;
|
||||
end
|
||||
% Plot initial level set
|
||||
%[X Y]=meshgrid(0:1.:8);
|
||||
%Z=zeros(9);
|
||||
%for i=1:81
|
||||
% Z(i)=lSet(i);
|
||||
%end
|
||||
%surf(X,Y,Z)
|
||||
% LS Algorithm Parameters
|
||||
lSet'
|
||||
bandwidth=3.;
|
||||
% Loop through timesteps
|
||||
for tstep=1:1
|
||||
% Identify Narrow Band Elements
|
||||
NBElems=0;
|
||||
NBNodes=0;
|
||||
NGlobal=zeros(NumNodes);
|
||||
for i=1:numElem
|
||||
check=0;
|
||||
for iNd=1:4
|
||||
if abs(lSet(Element(i,iNd)))<=bandwidth*delX
|
||||
check=1;
|
||||
end
|
||||
end
|
||||
% If an element is in the narrow band split it into triangles
|
||||
if check==1
|
||||
for j=1:4
|
||||
if NewNums(Element(i,j))==0
|
||||
NBNodes=NBNodes+1
|
||||
NGlobal(Element(i,j))=NBNodes;
|
||||
NLocal(NBNodes)=Element(i,j);
|
||||
end
|
||||
end
|
||||
NBElems=NBElems+1;
|
||||
NBelem(NBElems,1)=NGlobal(Element(i,1));
|
||||
NBelem(NBElems,2)=NGlobal(Element(i,2));
|
||||
NBelem(NBElems,3)=NGlobal(Element(i,3));
|
||||
NBElems=NBElems+1;
|
||||
NBelem(NBElems,1)=NGlobal(Element(i,1));
|
||||
NBelem(NBElems,2)=NGlobal(Element(i,3));
|
||||
NBelem(NBElems,3)=NGlobal(Element(i,4));
|
||||
end
|
||||
end
|
||||
% Get local Level Set
|
||||
for i=1:NBNodes
|
||||
lSetLocal(i)=lSet(NLocal(i));
|
||||
end
|
||||
% Velocity BC
|
||||
F=zeros(NBNodes,1);
|
||||
for i=1:NBElems
|
||||
L1=sign(lSetLocal(NBelem(i,1)));
|
||||
L2=sign(lSetLocal(NBelem(i,2)));
|
||||
L3=sign(lSetLocal(NBelem(i,3)));
|
||||
if L1 ~= L2 || L1 ~= L3
|
||||
F(NBelem(i,1))= 1.;
|
||||
F(NBelem(i,2))= 1.;
|
||||
F(NBelem(i,3))= 1.;
|
||||
end
|
||||
end
|
||||
% Assemble 'Stiffness' Matrices
|
||||
A=zeros(NBNodes);
|
||||
for i=1:NBElems
|
||||
gx(1)=2./3.;
|
||||
gx(2)=1./6.;
|
||||
gx(3)=1./6.;
|
||||
hx(1)=1./6.;
|
||||
hx(2)=1./6.;
|
||||
hx(3)=2./3.;
|
||||
AfL=zeros(3);
|
||||
AfLGLS=zeros(3);
|
||||
x1=Node(NLocal(NBelem(i,1)),1);
|
||||
y1=Node(NLocal(NBelem(i,1)),2);
|
||||
x2=Node(NLocal(NBelem(i,2)),1);
|
||||
y2=Node(NLocal(NBelem(i,2)),2);
|
||||
x3=Node(NLocal(NBelem(i,3)),1);
|
||||
y3=Node(NLocal(NBelem(i,3)),2);
|
||||
for j=1:3
|
||||
g=gx(j);
|
||||
h=hx(j);
|
||||
phi(1)=1.-g-h;
|
||||
phi(2)=g;
|
||||
phi(3)=h;
|
||||
phig(1)=-1.;
|
||||
phig(2)=1.;
|
||||
phig(3)=0.;
|
||||
phih(1)=-1.;
|
||||
phih(2)=0.;
|
||||
phih(3)=1.;
|
||||
djac=2*abs(x1*(y2-y3)+x2*(y3-y1)+x3*(y1-y2));
|
||||
for k=1:3
|
||||
phix(k)=(1./djac)*((-y1+y3)*phig(k)+(y1-y2)*phih(k));
|
||||
phiy(k)=(1./djac)*((x1-x3)*phig(k)+(-x1+x2)*phih(k));
|
||||
end
|
||||
delphi=[phix;phiy];
|
||||
nodalLset=[lSetLocal(NBelem(i,1));lSetLocal(NBelem(i,2));lSetLocal(NBelem(i,3))];
|
||||
set=phi*nodalLset;
|
||||
delset=delphi*nodalLset;
|
||||
AfL=AfL+(phi'*sign(set))*(delset'*delphi)/3.;
|
||||
AfLGLS=AfLGLS+(delphi'*delset)*(1./norm(delset))*(delset'*delphi)/3.;
|
||||
end
|
||||
sum=AfL+AfLGLS;
|
||||
for k=1:3;
|
||||
for j=1:3;
|
||||
A(NBelem(i,j),NBelem(i,k))=A(NBelem(i,j),NBelem(i,k))+sum(j,k);
|
||||
end
|
||||
end
|
||||
end
|
||||
% Apply BCs
|
||||
RHS=zeros(NBNodes,1);
|
||||
Sub=A*F;
|
||||
iindex=0;
|
||||
for i=1:NBNodes
|
||||
if F(i)==0.
|
||||
iindex=iindex+1;
|
||||
RHSred(iindex)=RHS(i)-Sub(i);
|
||||
Fred=0.;
|
||||
jindex=0;
|
||||
for j=1:NBNodes
|
||||
if F(j)==0.
|
||||
jindex=jindex+1;
|
||||
Ared(iindex,jindex)=A(i,j);
|
||||
end
|
||||
end
|
||||
end
|
||||
end
|
||||
% Solve for Fred
|
||||
Fred=(Ared^-1)*RHSred';
|
||||
% Get F
|
||||
iindex=0;
|
||||
for i=1:NBNodes
|
||||
if F(i)==0.
|
||||
iindex=iindex+1;
|
||||
F(i)=Fred(iindex);
|
||||
end
|
||||
end
|
||||
% Update level set
|
||||
mMat=zeros(NBNodes);
|
||||
mMatGLS=zeros(NBNodes);
|
||||
f1=zeros(NBNodes,1);
|
||||
f2=zeros(NBNodes,1);
|
||||
f3=zeros(NBNodes,1);
|
||||
h2=0.00001;
|
||||
visc=0.0005;
|
||||
for i=1:NBElems
|
||||
mMatL=zeros(3);
|
||||
mMatGLSL=zeros(3);
|
||||
f1L=zeros(3,1);
|
||||
f2L=zeros(3,1);
|
||||
f3L=zeros(3,1);
|
||||
gx(1)=2./3.;
|
||||
gx(2)=1./6.;
|
||||
gx(3)=1./6.;
|
||||
hx(1)=1./6.;
|
||||
hx(2)=1./6.;
|
||||
hx(3)=2./3.;
|
||||
x1=Node(NLocal(NBelem(i,1)),1);
|
||||
y1=Node(NLocal(NBelem(i,1)),2);
|
||||
x2=Node(NLocal(NBelem(i,2)),1);
|
||||
y2=Node(NLocal(NBelem(i,2)),2);
|
||||
x3=Node(NLocal(NBelem(i,3)),1);
|
||||
y3=Node(NLocal(NBelem(i,3)),2);
|
||||
for j=1:3
|
||||
g=gx(j);
|
||||
h=hx(j);
|
||||
phi(1)=1.-g-h;
|
||||
phi(2)=g;
|
||||
phi(3)=h;
|
||||
phig(1)=-1.;
|
||||
phig(2)=1.;
|
||||
phig(3)=0.;
|
||||
phih(1)=-1.;
|
||||
phih(2)=0.;
|
||||
phih(3)=1.;
|
||||
djac=abs(x1*(y2-y3)+x2*(y3-y1)+x3*(y1-y2));
|
||||
for k=1:3
|
||||
phix(k)=(1./djac)*((-y1+y3)*phig(k)+(y1-y2)*phih(k));
|
||||
phiy(k)=(1./djac)*((x1-x3)*phig(k)+(-x1+x2)*phih(k));
|
||||
end
|
||||
delphi=[phix;phiy];
|
||||
nodalLset=[lSetLocal(NBelem(i,1));lSetLocal(NBelem(i,2));lSetLocal(NBelem(i,3))];
|
||||
nodalF=[F(NBelem(i,1));F(NBelem(i,2));F(NBelem(i,3))];
|
||||
delset=delphi*nodalLset;
|
||||
Floc=phi*nodalF;
|
||||
mMatL=mMatL+(phi'*phi)/3.;
|
||||
mMatGLSL=mMatGLSL+((delphi'*(delset/norm(delset)))*Floc*(h2/abs(Floc)))*phi/3.;
|
||||
f1L=f1L+phi'*Floc*norm(delset)/3.;
|
||||
f2L=f2L+(delphi'*(delset/norm(delset))*Floc)*(h2/abs(Floc))*Floc*norm(delset)/3.;
|
||||
vs=h2*((abs(visc+Floc*norm(delset)))/(norm(Floc*delset)+h2));
|
||||
f3L=f3L+vs*delphi'*delset/3.;
|
||||
end
|
||||
for k=1:3;
|
||||
for j=1:3;
|
||||
mMat(NBelem(i,j),NBelem(i,k))=mMat(NBelem(i,j),NBelem(i,k))+mMatL(j,k);
|
||||
mMatGLS(NBelem(i,j),NBelem(i,k))=mMatGLS(NBelem(i,j),NBelem(i,k))+mMatGLSL(j,k);
|
||||
end
|
||||
f1(NBelem(i,k))=f1(NBelem(i,k))+f1L(k);
|
||||
f2(NBelem(i,k))=f2(NBelem(i,k))+f2L(k);
|
||||
f3(NBelem(i,k))=f3(NBelem(i,k))+f3L(k);
|
||||
end
|
||||
end
|
||||
dt=0.01;
|
||||
lSetLocal=lSetLocal-((((mMat+mMatGLS)^-1)*dt)*(f1+f2+f3))';
|
||||
newlSet=lSetLocal;
|
||||
% Reinitialize LS
|
||||
nstat=zeros(NBNodes,1);
|
||||
for i=1:NBelems
|
||||
L1=sign(lSetLocal(NBelem(i,1)));
|
||||
L2=sign(lSetLocal(NBelem(i,2)));
|
||||
L3=sign(lSetLocal(NBelem(i,3)));
|
||||
if L1 ~= L2 || L1 ~= L3
|
||||
for j=1:3
|
||||
nstat(NBelem(i,j))=1;
|
||||
end
|
||||
end
|
||||
end
|
||||
maincheck=0;
|
||||
while(maincheck==0)
|
||||
lmin=1000.;
|
||||
avlmin=1000.;
|
||||
eindex=0;
|
||||
nindex=0;
|
||||
maincheck=1;
|
||||
for i=1:NBindex
|
||||
if nstat(NBelem(i,1))+nstat(NBelem(i,2))+nstat(NBelem(i,3))==2
|
||||
maincheck=0;
|
||||
check=0;
|
||||
ltot=0.;
|
||||
for j=1:3
|
||||
if nstat(NBelem(i,j))==0
|
||||
if abs(lSet(NBelem(i,j)))<=lmin
|
||||
check=1;
|
||||
tempindex=j;
|
||||
end
|
||||
end
|
||||
ltot=ltot+abs(lSet(NBelem(i,j)));
|
||||
end
|
||||
if check==1 & ltot/3.<=avlmin
|
||||
eindex=i;
|
||||
nindex=tempindex;
|
||||
lmin=lSet(NBelem(eindex,nindex));
|
||||
avlmin=ltot/3.;
|
||||
end
|
||||
end
|
||||
end
|
||||
if maincheck==0
|
||||
% Find New LS for point
|
||||
xp=Node(NBelem(eindex,nindex),1);
|
||||
yp=Node(NBelem(eindex,nindex),2);
|
||||
count=0;
|
||||
for i=1:3
|
||||
if i~=nindex
|
||||
count=count+1;
|
||||
x(count)=Node(NBelem(eindex,i),1);
|
||||
y(count)=Node(NBelem(eindex,i),2);
|
||||
lloc(count)=newlSet(NBelem(eindex,i));
|
||||
end
|
||||
end
|
||||
delxa=x(1)-xp;
|
||||
delya=y(1)-yp;
|
||||
delxb=x(2)-xp;
|
||||
delyb=y(2)-yp;
|
||||
N=[delxa delya; delxb delyb];
|
||||
M=N^-1;
|
||||
A=(M(1)*M(1)+M(2)*M(2));
|
||||
B=(M(3)*M(3)+M(4)*M(4));
|
||||
C=2.*(M(1)*M(3)+M(2)*M(4));
|
||||
a=A+B+C;
|
||||
b=-2.*lloc(1)*A-2.*lloc(2)*B-C*(lloc(1)+lloc(2));
|
||||
c=lloc(1)*lloc(1)*A+lloc(2)*lloc(2)*B+lloc(1)*lloc(2)*C-1.;
|
||||
templ1=(-b+sqrt(b*b-4.*a*c))/(2.*a);
|
||||
templ2=(-b-sqrt(b*b-4.*a*c))/(2.*a);
|
||||
if abs(templ1)>abs(templ2)
|
||||
newlSet(NBelem(eindex,nindex))=templ1;
|
||||
else
|
||||
newlSet(NBelem(eindex,nindex))=templ2;
|
||||
end
|
||||
nstat(NBelem(eindex,nindex))=1;
|
||||
end
|
||||
end
|
||||
% lSet=newlSet;
|
||||
end
|
||||
lSet'
|
||||
|
||||
|
||||
|
||||
|
||||
331
Unpublished/XFEM/1D_Solver/F2DLevelSetFMM.m
Normal file
331
Unpublished/XFEM/1D_Solver/F2DLevelSetFMM.m
Normal file
|
|
@ -0,0 +1,331 @@
|
|||
function [] = F2DLevelSetFMM()
|
||||
clear all
|
||||
% Define Main Solution Mesh
|
||||
NumX=32;
|
||||
NumY=32;
|
||||
delX=0.25;
|
||||
delY=0.25;
|
||||
for j=1:NumY+1
|
||||
for i=1:NumX+1
|
||||
index=i+(NumX+1)*(j-1);
|
||||
Node(index,1)=single((i-1.))*delX;
|
||||
Node(index,2)=single((j-1.))*delY;
|
||||
end
|
||||
end
|
||||
numNodes=(NumX+1)*(NumY+1);
|
||||
for j=1:NumY
|
||||
for i=1:NumX
|
||||
index=i+NumX*(j-1);
|
||||
Element(index,1)=i+(NumX+1)*(j-1);
|
||||
Element(index,2)=i+(NumX+1)*(j-1)+1;
|
||||
Element(index,3)=i+(NumX+1)*(j)+1;
|
||||
Element(index,4)=i+(NumX+1)*(j);
|
||||
end
|
||||
end
|
||||
numElem=(NumX)*(NumY);
|
||||
% Define Initial Level Set
|
||||
centx=4.;
|
||||
centy=4.;
|
||||
rad=2.1;
|
||||
for i=1:numNodes;
|
||||
dist=sqrt((Node(i,1)-centx)*(Node(i,1)-centx)+(Node(i,2)-centy)*(Node(i,2)-centy));
|
||||
lSet(i)=dist-rad;
|
||||
end
|
||||
%for i=1:numNodes;
|
||||
% dist=Node(i,1)-0.1;
|
||||
% lSet(i)=dist;
|
||||
%end
|
||||
% Plot initial level set
|
||||
[X Y]=meshgrid(0:0.25:8);
|
||||
Z=zeros(33);
|
||||
for i=1:1089
|
||||
Z(i)=lSet(i);
|
||||
end
|
||||
surf(X,Y,Z)
|
||||
% LS Algorithm Parameters
|
||||
lSet'
|
||||
bandwidth=10;
|
||||
% Loop through timesteps
|
||||
for tstep=1:10
|
||||
% Identify Narrow Band Elements
|
||||
NBElems=0;
|
||||
NBNodes=0;
|
||||
NGlobal=zeros(numNodes);
|
||||
for i=1:numElem
|
||||
check=0;
|
||||
for iNd=1:4
|
||||
if abs(lSet(Element(i,iNd)))<=bandwidth*delX
|
||||
check=1;
|
||||
end
|
||||
end
|
||||
% If an element is in the narrow band split it into triangles
|
||||
if check==1
|
||||
for j=1:4
|
||||
if NGlobal(Element(i,j))==0
|
||||
NBNodes=NBNodes+1;
|
||||
NGlobal(Element(i,j))=NBNodes;
|
||||
NLocal(NBNodes)=Element(i,j);
|
||||
end
|
||||
end
|
||||
NBElems=NBElems+1;
|
||||
NBelem(NBElems,1)=NGlobal(Element(i,1));
|
||||
NBelem(NBElems,2)=NGlobal(Element(i,2));
|
||||
NBelem(NBElems,3)=NGlobal(Element(i,3));
|
||||
NBElems=NBElems+1;
|
||||
NBelem(NBElems,1)=NGlobal(Element(i,1));
|
||||
NBelem(NBElems,2)=NGlobal(Element(i,3));
|
||||
NBelem(NBElems,3)=NGlobal(Element(i,4));
|
||||
end
|
||||
end
|
||||
% Get local Level Set
|
||||
for i=1:NBNodes
|
||||
lSetLocal(i)=lSet(NLocal(i));
|
||||
end
|
||||
% Velocity BC
|
||||
F=zeros(NBNodes,1);
|
||||
for i=1:NBElems
|
||||
L1=sign(lSetLocal(NBelem(i,1)));
|
||||
L2=sign(lSetLocal(NBelem(i,2)));
|
||||
L3=sign(lSetLocal(NBelem(i,3)));
|
||||
if L1 ~= L2 || L1 ~= L3
|
||||
F(NBelem(i,1))= 1.;
|
||||
F(NBelem(i,2))= 1.;
|
||||
F(NBelem(i,3))= 1.;
|
||||
end
|
||||
end
|
||||
% Assemble 'Stiffness' Matrices
|
||||
A=zeros(NBNodes);
|
||||
for i=1:NBElems
|
||||
gx(1)=2./3.;
|
||||
gx(2)=1./6.;
|
||||
gx(3)=1./6.;
|
||||
hx(1)=1./6.;
|
||||
hx(2)=1./6.;
|
||||
hx(3)=2./3.;
|
||||
AfL=zeros(3);
|
||||
AfLGLS=zeros(3);
|
||||
x1=Node(NLocal(NBelem(i,1)),1);
|
||||
y1=Node(NLocal(NBelem(i,1)),2);
|
||||
x2=Node(NLocal(NBelem(i,2)),1);
|
||||
y2=Node(NLocal(NBelem(i,2)),2);
|
||||
x3=Node(NLocal(NBelem(i,3)),1);
|
||||
y3=Node(NLocal(NBelem(i,3)),2);
|
||||
for j=1:3
|
||||
g=gx(j);
|
||||
h=hx(j);
|
||||
phi(1)=1.-g-h;
|
||||
phi(2)=g;
|
||||
phi(3)=h;
|
||||
phig(1)=-1.;
|
||||
phig(2)=1.;
|
||||
phig(3)=0.;
|
||||
phih(1)=-1.;
|
||||
phih(2)=0.;
|
||||
phih(3)=1.;
|
||||
djac=2*abs(x1*(y2-y3)+x2*(y3-y1)+x3*(y1-y2));
|
||||
for k=1:3
|
||||
phix(k)=(1./djac)*((-y1+y3)*phig(k)+(y1-y2)*phih(k));
|
||||
phiy(k)=(1./djac)*((x1-x3)*phig(k)+(-x1+x2)*phih(k));
|
||||
end
|
||||
delphi=[phix;phiy];
|
||||
nodalLset=[lSetLocal(NBelem(i,1));lSetLocal(NBelem(i,2));lSetLocal(NBelem(i,3))];
|
||||
set=phi*nodalLset;
|
||||
delset=delphi*nodalLset;
|
||||
AfL=AfL+(phi'*sign(set))*(delset'*delphi)/3.;
|
||||
AfLGLS=AfLGLS+(delphi'*delset)*(1./norm(delset))*(delset'*delphi)/3.;
|
||||
end
|
||||
sum=AfL+AfLGLS;
|
||||
for k=1:3;
|
||||
for j=1:3;
|
||||
A(NBelem(i,j),NBelem(i,k))=A(NBelem(i,j),NBelem(i,k))+sum(j,k);
|
||||
end
|
||||
end
|
||||
end
|
||||
% Apply BCs
|
||||
RHS=zeros(NBNodes,1);
|
||||
Sub=A*F;
|
||||
iindex=0;
|
||||
for i=1:NBNodes
|
||||
if F(i)==0.
|
||||
iindex=iindex+1;
|
||||
RHSred(iindex)=RHS(i)-Sub(i);
|
||||
Fred=0.;
|
||||
jindex=0;
|
||||
for j=1:NBNodes
|
||||
if F(j)==0.
|
||||
jindex=jindex+1;
|
||||
Ared(iindex,jindex)=A(i,j);
|
||||
end
|
||||
end
|
||||
end
|
||||
end
|
||||
% Solve for Fred
|
||||
Fred=(Ared^-1)*RHSred';
|
||||
% Get F
|
||||
iindex=0;
|
||||
for i=1:NBNodes
|
||||
if F(i)==0.
|
||||
iindex=iindex+1;
|
||||
F(i)=Fred(iindex);
|
||||
end
|
||||
end
|
||||
% Update level set
|
||||
mMat=zeros(NBNodes);
|
||||
mMatGLS=zeros(NBNodes);
|
||||
f1=zeros(NBNodes,1);
|
||||
f2=zeros(NBNodes,1);
|
||||
f3=zeros(NBNodes,1);
|
||||
h2=0.00001;
|
||||
visc=0.0005;
|
||||
for i=1:NBElems
|
||||
mMatL=zeros(3);
|
||||
mMatGLSL=zeros(3);
|
||||
f1L=zeros(3,1);
|
||||
f2L=zeros(3,1);
|
||||
f3L=zeros(3,1);
|
||||
gx(1)=2./3.;
|
||||
gx(2)=1./6.;
|
||||
gx(3)=1./6.;
|
||||
hx(1)=1./6.;
|
||||
hx(2)=1./6.;
|
||||
hx(3)=2./3.;
|
||||
x1=Node(NLocal(NBelem(i,1)),1);
|
||||
y1=Node(NLocal(NBelem(i,1)),2);
|
||||
x2=Node(NLocal(NBelem(i,2)),1);
|
||||
y2=Node(NLocal(NBelem(i,2)),2);
|
||||
x3=Node(NLocal(NBelem(i,3)),1);
|
||||
y3=Node(NLocal(NBelem(i,3)),2);
|
||||
for j=1:3
|
||||
g=gx(j);
|
||||
h=hx(j);
|
||||
phi(1)=1.-g-h;
|
||||
phi(2)=g;
|
||||
phi(3)=h;
|
||||
phig(1)=-1.;
|
||||
phig(2)=1.;
|
||||
phig(3)=0.;
|
||||
phih(1)=-1.;
|
||||
phih(2)=0.;
|
||||
phih(3)=1.;
|
||||
djac=abs(x1*(y2-y3)+x2*(y3-y1)+x3*(y1-y2));
|
||||
for k=1:3
|
||||
phix(k)=(1./djac)*((-y1+y3)*phig(k)+(y1-y2)*phih(k));
|
||||
phiy(k)=(1./djac)*((x1-x3)*phig(k)+(-x1+x2)*phih(k));
|
||||
end
|
||||
delphi=[phix;phiy];
|
||||
nodalLset=[lSetLocal(NBelem(i,1));lSetLocal(NBelem(i,2));lSetLocal(NBelem(i,3))];
|
||||
nodalF=[F(NBelem(i,1));F(NBelem(i,2));F(NBelem(i,3))];
|
||||
delset=delphi*nodalLset;
|
||||
Floc=phi*nodalF;
|
||||
mMatL=mMatL+(phi'*phi)/3.;
|
||||
mMatGLSL=mMatGLSL+((delphi'*(delset/norm(delset)))*Floc*(h2/abs(Floc)))*phi/3.;
|
||||
f1L=f1L+phi'*Floc*norm(delset)/3.;
|
||||
f2L=f2L+(delphi'*(delset/norm(delset))*Floc)*(h2/abs(Floc))*Floc*norm(delset)/3.;
|
||||
vs=h2*((abs(visc+Floc*norm(delset)))/(norm(Floc*delset)+h2));
|
||||
f3L=f3L+vs*delphi'*delset/3.;
|
||||
end
|
||||
for k=1:3;
|
||||
for j=1:3;
|
||||
mMat(NBelem(i,j),NBelem(i,k))=mMat(NBelem(i,j),NBelem(i,k))+mMatL(j,k);
|
||||
mMatGLS(NBelem(i,j),NBelem(i,k))=mMatGLS(NBelem(i,j),NBelem(i,k))+mMatGLSL(j,k);
|
||||
end
|
||||
f1(NBelem(i,k))=f1(NBelem(i,k))+f1L(k);
|
||||
f2(NBelem(i,k))=f2(NBelem(i,k))+f2L(k);
|
||||
f3(NBelem(i,k))=f3(NBelem(i,k))+f3L(k);
|
||||
end
|
||||
end
|
||||
dt=0.01;
|
||||
lSetLocal=lSetLocal-((((mMat+mMatGLS)^-1)*dt)*(f1+f2+f3))';
|
||||
newlSet=lSetLocal;
|
||||
% Reinitialize LS
|
||||
nstat=zeros(NBNodes,1);
|
||||
for i=1:NBElems
|
||||
L1=sign(lSetLocal(NBelem(i,1)));
|
||||
L2=sign(lSetLocal(NBelem(i,2)));
|
||||
L3=sign(lSetLocal(NBelem(i,3)));
|
||||
if L1 ~= L2 || L1 ~= L3
|
||||
for j=1:3
|
||||
nstat(NBelem(i,j))=1;
|
||||
end
|
||||
end
|
||||
end
|
||||
maincheck=0;
|
||||
while(maincheck==0)
|
||||
lmin=1000.;
|
||||
avlmin=1000.;
|
||||
eindex=0;
|
||||
nindex=0;
|
||||
maincheck=1;
|
||||
for i=1:NBElems
|
||||
if nstat(NBelem(i,1))+nstat(NBelem(i,2))+nstat(NBelem(i,3))==2
|
||||
maincheck=0;
|
||||
check=0;
|
||||
ltot=0.;
|
||||
for j=1:3
|
||||
if nstat(NBelem(i,j))==0
|
||||
if abs(lSetLocal(NBelem(i,j)))<=lmin
|
||||
check=1;
|
||||
tempindex=j;
|
||||
end
|
||||
end
|
||||
ltot=ltot+abs(lSetLocal(NBelem(i,j)));
|
||||
end
|
||||
if check==1 & ltot/3.<=avlmin
|
||||
eindex=i;
|
||||
nindex=tempindex;
|
||||
lmin=lSetLocal(NBelem(eindex,nindex));
|
||||
avlmin=ltot/3.;
|
||||
end
|
||||
end
|
||||
end
|
||||
if maincheck==0
|
||||
% Find New LS for point
|
||||
xp=Node(NLocal(NBelem(eindex,nindex)),1);
|
||||
yp=Node(NLocal(NBelem(eindex,nindex)),2);
|
||||
count=0;
|
||||
for i=1:3
|
||||
if i~=nindex
|
||||
count=count+1;
|
||||
x(count)=Node(NLocal(NBelem(eindex,i)),1);
|
||||
y(count)=Node(NLocal(NBelem(eindex,i)),2);
|
||||
lloc(count)=newlSet(NBelem(eindex,i));
|
||||
end
|
||||
end
|
||||
delxa=x(1)-xp;
|
||||
delya=y(1)-yp;
|
||||
delxb=x(2)-xp;
|
||||
delyb=y(2)-yp;
|
||||
N=[delxa delya; delxb delyb];
|
||||
M=N^-1;
|
||||
A=(M(1)*M(1)+M(2)*M(2));
|
||||
B=(M(3)*M(3)+M(4)*M(4));
|
||||
C=2.*(M(1)*M(3)+M(2)*M(4));
|
||||
a=A+B+C;
|
||||
b=-2.*lloc(1)*A-2.*lloc(2)*B-C*(lloc(1)+lloc(2));
|
||||
c=lloc(1)*lloc(1)*A+lloc(2)*lloc(2)*B+lloc(1)*lloc(2)*C-1.;
|
||||
templ1=(-b+sqrt(b*b-4.*a*c))/(2.*a);
|
||||
templ2=(-b-sqrt(b*b-4.*a*c))/(2.*a);
|
||||
if abs(templ1)>abs(templ2)
|
||||
newlSet(NBelem(eindex,nindex))=templ1;
|
||||
else
|
||||
newlSet(NBelem(eindex,nindex))=templ2;
|
||||
end
|
||||
nstat(NBelem(eindex,nindex))=1;
|
||||
end
|
||||
end
|
||||
% lSetLocal=newlSet;
|
||||
% Update Global Level Set
|
||||
for i=1:NBNodes
|
||||
lSet(NLocal(i))=lSetLocal(i);
|
||||
end
|
||||
end
|
||||
lSet'
|
||||
[X Y]=meshgrid(0:0.25:8);
|
||||
Z=zeros(33);
|
||||
for i=1:1089
|
||||
Z(i)=lSet(i);
|
||||
end
|
||||
surf(X,Y,Z)
|
||||
|
||||
|
||||
|
||||
221
Unpublished/XFEM/1D_Solver/FESolveX.m
Normal file
221
Unpublished/XFEM/1D_Solver/FESolveX.m
Normal file
|
|
@ -0,0 +1,221 @@
|
|||
function [] = FESolveX()
|
||||
% MATLAB based XFEM Solver
|
||||
% J. Grogan (2012)
|
||||
clear all
|
||||
% Define Geometry
|
||||
len=10.;
|
||||
% Define Section Properties
|
||||
rho=1.;
|
||||
% Generate Mesh
|
||||
numElem=10;
|
||||
charlen=len/numElem;
|
||||
ndCoords=linspace(0,len,numElem+1);
|
||||
numNodes=size(ndCoords,2);
|
||||
indx=1:numElem;
|
||||
elemNodes(:,1)=indx;
|
||||
elemNodes(:,2)=indx+1;
|
||||
% dofs per node
|
||||
ndof=2;
|
||||
% initial interface position
|
||||
dpos=5.;
|
||||
% Initial temperatures
|
||||
Tnew=zeros(numNodes*2,1);
|
||||
%storage
|
||||
stored(1)=dpos;
|
||||
for e=1:numElem
|
||||
crdn1=ndCoords(elemNodes(e,1));
|
||||
if crdn1<=dpos
|
||||
Tnew(2*elemNodes(e,1)-1)=1.;
|
||||
end
|
||||
end
|
||||
% Define Time Step
|
||||
dtime=0.05;
|
||||
tsteps=20;
|
||||
time=0.;
|
||||
% penalty term
|
||||
beta=40.;
|
||||
% Loop through time steps
|
||||
for ts=1:tsteps
|
||||
% Get interface velocity
|
||||
d(1)=dpos+charlen;
|
||||
d(2)=dpos+3*charlen/4;
|
||||
d(3)=dpos+charlen/4;
|
||||
d(4)=dpos;
|
||||
for e=1:numElem
|
||||
crdn1=ndCoords(elemNodes(e,1));
|
||||
crdn2=ndCoords(elemNodes(e,2));
|
||||
for j=1:4
|
||||
if d(j)>=crdn1 & d(j)<crdn2
|
||||
elen=abs(crdn2-crdn1);
|
||||
ajacob=elen/2.;
|
||||
point=(d(j)-crdn1)/ajacob-1.;
|
||||
theta(1)=abs(crdn1-dpos)*sign(crdn1-dpos);
|
||||
theta(2)=abs(crdn2-dpos)*sign(crdn2-dpos);
|
||||
tmp1a=Tnew(elemNodes(e,1)*2-1);
|
||||
tmp1b=Tnew(elemNodes(e,1)*2);
|
||||
tmp2a=Tnew(elemNodes(e,2)*2-1);
|
||||
tmp2b=Tnew(elemNodes(e,2)*2);
|
||||
xi=point;
|
||||
gm(1)=(1.-xi)/2.;
|
||||
gm(3)=(1.+xi)/2.;
|
||||
term=theta(1)*gm(1)+theta(2)*gm(3);
|
||||
gm(2)=gm(1)*(abs(term)-abs(theta(1)));
|
||||
gm(4)=gm(3)*(abs(term)-abs(theta(2)));
|
||||
t(j)=gm(1)*tmp1a+gm(2)*tmp1b+gm(3)*tmp2a+gm(4)*tmp2b;
|
||||
end
|
||||
end
|
||||
end
|
||||
vel=(0.5/charlen)*(2*t(1)+t(2)-t(3)-2*t(4));
|
||||
% Update interface position
|
||||
dpos=dpos+vel*dtime;
|
||||
stored(ts+1)=dpos;
|
||||
K=zeros(numNodes*ndof,numNodes*ndof);
|
||||
M=zeros(numNodes*ndof,numNodes*ndof);
|
||||
pforce=zeros(numNodes*ndof,1);
|
||||
% Loop Through Elements
|
||||
for e=1:numElem
|
||||
Ke=zeros(2*ndof);
|
||||
Me=zeros(2*ndof);
|
||||
crdn1=ndCoords(elemNodes(e,1));
|
||||
crdn2=ndCoords(elemNodes(e,2));
|
||||
theta(1)=abs(crdn1-dpos)*sign(crdn1-dpos);
|
||||
theta(2)=abs(crdn2-dpos)*sign(crdn2-dpos);
|
||||
enr=2;
|
||||
elen=abs(crdn2-crdn1);
|
||||
ajacob=elen/2.;
|
||||
if sign(theta(1))~=sign(theta(2))
|
||||
% enriched element
|
||||
enr=4;
|
||||
% get interface position on element
|
||||
point=(dpos-crdn1)/ajacob-1.;
|
||||
% devide element for sub integration
|
||||
len1=abs(-point-1.);
|
||||
len2=abs(1.-point);
|
||||
mid1=-1+len1/2.;
|
||||
mid2=1-len2/2.;
|
||||
gpx(1)=-(len1/2.)/sqrt(3.)+mid1;
|
||||
gpx(2)=(len1/2.)/sqrt(3.)+mid1;
|
||||
gpx(3)=-(len2/2.)/sqrt(3.)+mid2;
|
||||
gpx(4)=(len2/2.)/sqrt(3.)+mid2;
|
||||
w(1)=(len1/2.);
|
||||
w(2)=(len1/2.);
|
||||
w(3)=(len2/2.);
|
||||
w(4)=(len2/2.);
|
||||
fdofs(1)=2*elemNodes(e,1);
|
||||
fdofs(2)=2*elemNodes(e,2);
|
||||
else
|
||||
% regular element - fix extra dofs
|
||||
gpx(1)=-1/sqrt(3.);
|
||||
gpx(2)=1/sqrt(3.);
|
||||
w(1)=1.;
|
||||
w(2)=1.;
|
||||
end
|
||||
% Loop Through Int Points
|
||||
for i=1:enr;
|
||||
c=gpx(i);
|
||||
phi(1)=(1.-c)/2.;
|
||||
phi(3)=(1.+c)/2.;
|
||||
term=theta(1)*phi(1)+theta(2)*phi(3);
|
||||
if term<0
|
||||
cond=0.;
|
||||
spec=0.01;
|
||||
else
|
||||
cond=1.;
|
||||
spec=1.;
|
||||
end
|
||||
phi(2)=phi(1)*(abs(term)-abs(theta(1)));
|
||||
phi(4)=phi(3)*(abs(term)-abs(theta(2)));
|
||||
phic(1)=-0.5;
|
||||
phic(3)=0.5;
|
||||
dterm=sign(term)*(phic(1)*theta(1)+phic(3)*theta(2));
|
||||
phic(2)=phic(1)*(abs(term)-abs(theta(1)))+phi(1)*dterm;
|
||||
phic(4)=phic(3)*(abs(term)-abs(theta(2)))+phi(3)*dterm;
|
||||
phix(1)=phic(1)/ajacob;
|
||||
phix(2)=phic(2)/ajacob;
|
||||
phix(3)=phic(3)/ajacob;
|
||||
phix(4)=phic(4)/ajacob;
|
||||
we=ajacob*w(i);
|
||||
Ke=Ke+we*cond*phix'*phix;
|
||||
Me=Me+(we*rho*spec*phi'*phi)/dtime;
|
||||
end
|
||||
% Add penalty term and get temp gradient on interface
|
||||
if enr==4;
|
||||
xi=point;
|
||||
gm(1)=(1.-xi)/2.;
|
||||
gm(3)=(1.+xi)/2.;
|
||||
term=theta(1)*gm(1)+theta(2)*gm(3);
|
||||
gm(2)=gm(1)*(abs(term)-abs(theta(1)));
|
||||
gm(4)=gm(3)*(abs(term)-abs(theta(2)));
|
||||
tpos=gm(1)*Tnew(1)+gm(2)*Tnew(2)+gm(3)*Tnew(3)+gm(4)*Tnew(4);
|
||||
pen=beta*(gm'*gm);
|
||||
pfL=beta*1*gm';
|
||||
Ke=Ke+pen;
|
||||
else
|
||||
pen=zeros(4);
|
||||
pfL=zeros(4,1);
|
||||
end
|
||||
% Assemble Global Matrices
|
||||
gnum=2.*elemNodes(e,1)-1.;
|
||||
for i=1:4;
|
||||
for j=1:4;
|
||||
K(gnum+j-1,gnum+i-1)=K(gnum+j-1,gnum+i-1)+Ke(j,i);
|
||||
M(gnum+j-1,gnum+i-1)=M(gnum+j-1,gnum+i-1)+Me(j,i);
|
||||
end
|
||||
pforce(gnum+i-1)=pforce(gnum+i-1)+pfL(i);
|
||||
end
|
||||
end
|
||||
%Remove inactive DOFs(Reduce Matrices)
|
||||
T1=1;
|
||||
RHS=M*Tnew;
|
||||
iindex=0;
|
||||
for i=1:ndof*numNodes;
|
||||
check=1;
|
||||
if i==fdofs(1)|i==fdofs(2)
|
||||
check=0;
|
||||
elseif mod(i,2)~=0 & i~=1
|
||||
check=0;
|
||||
end
|
||||
if check==0
|
||||
jindex=0;
|
||||
iindex=iindex+1;
|
||||
for j=1:ndof*numNodes;
|
||||
check=1;
|
||||
if j==fdofs(1)|j==fdofs(2)
|
||||
check=0;
|
||||
elseif mod(j,2)~=0 & j~=1
|
||||
check=0;
|
||||
end
|
||||
if check==0
|
||||
jindex=jindex+1;
|
||||
Kred(iindex,jindex)=K(i,j);
|
||||
Mred(iindex,jindex)=M(i,j);
|
||||
end
|
||||
end
|
||||
Subr(iindex)=(K(i,1)+M(i,1))*T1;
|
||||
RHSr(iindex)=RHS(i);
|
||||
pforcer(iindex)=pforce(i);
|
||||
end
|
||||
end
|
||||
%Solve
|
||||
Mred+Kred;
|
||||
StiffI=(Mred+Kred)^-1;
|
||||
Tnewr=StiffI*(RHSr'-Subr'+pforcer');
|
||||
iindex=0.;
|
||||
for i=1:ndof*numNodes;
|
||||
check=1;
|
||||
if i==fdofs(1)|i==fdofs(2)
|
||||
check=0;
|
||||
elseif mod(i,2)~=0 & i~=1
|
||||
check=0;
|
||||
end
|
||||
if check==0
|
||||
iindex=iindex+1;
|
||||
Tnew(i)=Tnewr(iindex);
|
||||
else
|
||||
Tnew(i)=0.;
|
||||
end
|
||||
end
|
||||
Tnew(1)=1.;
|
||||
Tnew
|
||||
end
|
||||
stored'
|
||||
128
Unpublished/XFEM/1D_Solver/GetF.m
Normal file
128
Unpublished/XFEM/1D_Solver/GetF.m
Normal file
|
|
@ -0,0 +1,128 @@
|
|||
function [] = GetF()
|
||||
% set up grid
|
||||
gd=0.;
|
||||
numElem=4;
|
||||
eLen=0.25;
|
||||
for i=1:numElem+1
|
||||
ndCrd(i)=gd;
|
||||
gd=gd+eLen;
|
||||
end
|
||||
for i=1:numElem
|
||||
elemNod(i,1)=i;
|
||||
elemNod(i,2)=i+1;
|
||||
end
|
||||
% Initial level set
|
||||
dpos=0.1;
|
||||
for i=1:numElem+1
|
||||
lSet(i)=sign(ndCrd(i)-dpos)*abs(dpos-ndCrd(i));
|
||||
end
|
||||
lSet'
|
||||
for tstep=1:1
|
||||
% Velocity BC
|
||||
F=zeros(numElem+1,1);
|
||||
for i=1:numElem
|
||||
if sign(lSet(elemNod(i,1)))~=sign(lSet(elemNod(i,2)))
|
||||
F(elemNod(i,1))= 0.0005;
|
||||
F(elemNod(i,2))= 0.0005;
|
||||
end
|
||||
end
|
||||
% Assemble 'Stiffness' Matrices
|
||||
A=zeros(numElem+1);
|
||||
for i=1:numElem
|
||||
pos(1)=-1/sqrt(3);
|
||||
pos(2)=1/sqrt(3);
|
||||
AfL=zeros(2);
|
||||
AfLGLS=zeros(2);
|
||||
for j=1:2
|
||||
shp(1)=(1-pos(j))/2.;
|
||||
shp(2)=(1+pos(j))/2.;
|
||||
dshp(1)=-0.5;
|
||||
dshp(2)=0.5;
|
||||
rset=shp(1)*lSet(elemNod(i,1))+shp(2)*lSet(elemNod(i,2));
|
||||
dls=dshp(1)*lSet(elemNod(i,1))+dshp(2)*lSet(elemNod(i,2));
|
||||
AfL=AfL+shp'*sign(rset)*(dls*dshp);
|
||||
AfLGLS=AfLGLS+(dshp'*dls)*(0.25/abs(dls))*(dls*dshp);
|
||||
end
|
||||
for k=1:2;
|
||||
for j=1:2;
|
||||
A(elemNod(i,j),elemNod(i,k))=A(elemNod(i,j),elemNod(i,k))+AfL(j,k)+AfLGLS(j,k)
|
||||
end
|
||||
end
|
||||
end
|
||||
% Apply BCs
|
||||
RHS=zeros(numElem+1,1);
|
||||
Sub=A*F;
|
||||
iindex=0;
|
||||
for i=1:numElem+1
|
||||
if F(i)==0.
|
||||
iindex=iindex+1;
|
||||
RHSred(iindex)=RHS(i)-Sub(i);
|
||||
Fred=0.;
|
||||
jindex=0;
|
||||
for j=1:numElem+1
|
||||
if F(j)==0.
|
||||
jindex=jindex+1;
|
||||
Ared(iindex,jindex)=A(i,j);
|
||||
end
|
||||
end
|
||||
end
|
||||
end
|
||||
% Solve for Fred
|
||||
Fred=(Ared^-1)*RHSred';
|
||||
% Get F
|
||||
iindex=0;
|
||||
for i=1:numElem+1
|
||||
if F(i)==0.
|
||||
iindex=iindex+1;
|
||||
F(i)=Fred(iindex);
|
||||
end
|
||||
end
|
||||
% Update level set
|
||||
mMat=zeros(numElem+1);
|
||||
mMatGLS=zeros(numElem+1);
|
||||
f1=zeros(numElem+1,1);
|
||||
f2=zeros(numElem+1,1);
|
||||
f3=zeros(numElem+1,1);
|
||||
h=0.25;
|
||||
visc=0.000;
|
||||
for i=1:numElem
|
||||
pos(1)=-1/sqrt(3);
|
||||
pos(2)=1/sqrt(3);
|
||||
mMatL=zeros(2);
|
||||
mMatGLSL=zeros(2);
|
||||
f1L=zeros(2,1);
|
||||
f2L=zeros(2,1);
|
||||
f3L=zeros(2,1);
|
||||
for j=1:2
|
||||
shp(1)=(1-pos(j))/2.;
|
||||
shp(2)=(1+pos(j))/2.;
|
||||
dshp(1)=-0.5;
|
||||
dshp(2)=0.5;
|
||||
Floc=shp(1)*F(elemNod(i,1))+shp(2)*F(elemNod(i,2));
|
||||
rset=shp(1)*lSet(elemNod(i,1))+shp(2)*lSet(elemNod(i,2));
|
||||
dls=dshp(1)*lSet(elemNod(i,1))+dshp(2)*lSet(elemNod(i,2));
|
||||
mMatL=mMatL+shp'*shp;
|
||||
mMatGLSL=mMatGLSL+((dshp'*(dls/abs(dls)))*Floc*(h/abs(Floc)))*shp;
|
||||
f1L=f1L+shp'*Floc*abs(dls);
|
||||
f2L=f2L+(dshp'*(dls/abs(dls))*Floc)*(h/abs(Floc))*Floc*abs(dls);
|
||||
vs=h*((abs(visc+Floc*abs(dls)))/(abs(Floc*dls)+h));
|
||||
f3L=f3L+vs*dshp'*dls;
|
||||
end
|
||||
for k=1:2;
|
||||
for j=1:2;
|
||||
mMat(elemNod(i,j),elemNod(i,k))=mMat(elemNod(i,j),elemNod(i,k))+mMatL(j,k);
|
||||
mMatGLS(elemNod(i,j),elemNod(i,k))=mMatGLS(elemNod(i,j),elemNod(i,k))+mMatGLSL(j,k);
|
||||
end
|
||||
f1(elemNod(i,k))=f1(elemNod(i,k))+f1L(k);
|
||||
f2(elemNod(i,k))=f2(elemNod(i,k))+f2L(k);
|
||||
f3(elemNod(i,k))=f3(elemNod(i,k))+f3L(k);
|
||||
end
|
||||
end
|
||||
dt=0.01;
|
||||
lSet=lSet-((((mMat+mMatGLS)^-1)/dt)*(f1+f2+f3))';
|
||||
lSet';
|
||||
end
|
||||
|
||||
|
||||
|
||||
|
||||
200
Unpublished/XFEM/1D_Solver/GetF2D.asv
Normal file
200
Unpublished/XFEM/1D_Solver/GetF2D.asv
Normal file
|
|
@ -0,0 +1,200 @@
|
|||
function [] = GetF2D_()
|
||||
clear all
|
||||
% Define Main Solution Mesh
|
||||
NumX=10;
|
||||
NumY=10;
|
||||
delX=1.;
|
||||
delY=1.;
|
||||
for j=1:NumY+1
|
||||
for i=1:NumX+1
|
||||
index=i+(NumX+1)*(j-1);
|
||||
Node(index,1)=single((i-1.))*delX;
|
||||
Node(index,2)=single((j-1.))*delY;
|
||||
end
|
||||
end
|
||||
numNodes=(NumX+1)*(NumY+1);
|
||||
for j=1:NumY
|
||||
for i=1:NumX
|
||||
index=i+NumX*(j-1);
|
||||
Element(index,1)=i+(NumX+1)*(j-1);
|
||||
Element(index,2)=i+(NumX+1)*(j-1)+1;
|
||||
Element(index,3)=i+(NumX+1)*(j)+1;
|
||||
Element(index,4)=i+(NumX+1)*(j);
|
||||
end
|
||||
end
|
||||
numElem=(NumX)*(NumY);
|
||||
% Define Initial Level Set
|
||||
centx=5.;
|
||||
centy=5.;
|
||||
rad=2.5;
|
||||
for i=1:numNodes;
|
||||
dist=sqrt((Node(i,1)-centx)*(Node(i,1)-centx)+(Node(i,2)-centy)*(Node(i,2)-centy));
|
||||
lSet(i)=dist-rad;
|
||||
end
|
||||
% Plot initial level set
|
||||
[X,Y]=meshgrid(0:1.:10);
|
||||
Z=zeros(11);
|
||||
for i=1:numNodes
|
||||
Z(i)=lSet(i);
|
||||
end
|
||||
surf(X,Y,Z)
|
||||
% LS Algorithm Parameters
|
||||
bandwith=10.;
|
||||
% Loop through timesteps
|
||||
for tstep=1:1
|
||||
% Identify Narrow Band Elements
|
||||
NBindex=0;
|
||||
for i=1:numElem
|
||||
check=0;
|
||||
for iNd=1:4
|
||||
if abs(lSet(Element(i,iNd)))<=bandwidth*delX
|
||||
check=1;
|
||||
end
|
||||
end
|
||||
% If an element is in the narrow band split it into triangles
|
||||
if check==1
|
||||
NBindex=NBindex+1;
|
||||
NBelem(NBindex,1)=Element(i,1);
|
||||
NBelem(NBindex,2)=Element(i,2);
|
||||
NBelem(NBindex,3)=Element(i,3);
|
||||
NBindex=NBindex+1;
|
||||
NBelem(NBindex,1)=Element(i,1);
|
||||
NBelem(NBindex,2)=Element(i,3);
|
||||
NBelem(NBindex,3)=Element(i,4);
|
||||
end
|
||||
end
|
||||
% Velocity BC
|
||||
F=zeros(numNodes,1);
|
||||
for i=1:NBindex
|
||||
if lSet(NBelem(i,1))~=lSet(NBelem(i,2)) || lSet(NBelem(i,1))~=lSet(NBelem(i,3))
|
||||
F(NBelem(i,1))= 0.0005;
|
||||
F(NBelem(i,2))= 0.0005;
|
||||
F(NBelem(i,3))= 0.0005;
|
||||
end
|
||||
end
|
||||
% Assemble 'Stiffness' Matrices
|
||||
A=zeros(numNodes);
|
||||
for i=1:NBindex
|
||||
gpos=1/sqrt(3.);
|
||||
gx(1)=-gpos;
|
||||
gx(2)=gpos;
|
||||
gx(3)=gpos;
|
||||
gx(4)=-gpos;
|
||||
hx(1)=-gpos;
|
||||
hx(2)=-gpos;
|
||||
hx(3)=gpos;
|
||||
hx(4)=gpos;
|
||||
AfL=zeros(4);
|
||||
AfLGLS=zeros(4);
|
||||
for j=1:4
|
||||
g=gx(j);
|
||||
h=hx(j);
|
||||
phi(1)=0.25*(1.-g)*(1.-h);
|
||||
phi(2)=0.25*(1.+g)*(1.-h);
|
||||
phi(3)=0.25*(1.+g)*(1.+h);
|
||||
phi(4)=0.25*(1.-g)*(1.+h);
|
||||
phig(1)=0.25*-(1.-h);
|
||||
phig(2)=0.25*(1.-h);
|
||||
phig(3)=0.25*(1.+h);
|
||||
phig(4)=0.25*-(1.+h);
|
||||
rset=phi(1)*lSet(Element(i,1))+phi(2)*lSet(Element(i,2))+phi(3)*lSet(Element(i,3))+phi(4)*lSet(Element(i,4));
|
||||
dls=phig(1)*lSet(Element(i,1))+phig(2)*lSet(Element(i,2))+phig(3)*lSet(Element(i,3))+phig(4)*lSet(Element(i,4));
|
||||
AfL=AfL+(phi'*sign(rset))*(dls*phig);
|
||||
AfLGLS=AfLGLS+(phig'*dls)*(1./abs(dls))*(dls*phig);
|
||||
end
|
||||
for k=1:4;
|
||||
for j=1:4;
|
||||
A(Element(i,j),Element(i,k))=A(Element(i,j),Element(i,k))+AfL(j,k)+AfLGLS(j,k);
|
||||
end
|
||||
end
|
||||
end
|
||||
% Apply BCs
|
||||
RHS=zeros(numNodes,1);
|
||||
Sub=A*F;
|
||||
iindex=0;
|
||||
for i=1:numNodes
|
||||
if F(i)==0.
|
||||
iindex=iindex+1;
|
||||
RHSred(iindex)=RHS(i)-Sub(i);
|
||||
Fred=0.;
|
||||
jindex=0;
|
||||
for j=1:numNodes
|
||||
if F(j)==0.
|
||||
jindex=jindex+1;
|
||||
Ared(iindex,jindex)=A(i,j);
|
||||
end
|
||||
end
|
||||
end
|
||||
end
|
||||
% Solve for Fred
|
||||
Fred=(Ared^-1)*RHSred';
|
||||
% Get F
|
||||
iindex=0;
|
||||
for i=1:numNodes
|
||||
if F(i)==0.
|
||||
iindex=iindex+1;
|
||||
F(i)=Fred(iindex);
|
||||
end
|
||||
end
|
||||
% Update level set
|
||||
mMat=zeros(numNodes);
|
||||
mMatGLS=zeros(numNodes);
|
||||
f1=zeros(numNodes,1);
|
||||
f2=zeros(numNodes,1);
|
||||
f3=zeros(numNodes,1);
|
||||
h=1.;
|
||||
visc=0.000;
|
||||
for i=1:numElem
|
||||
gpos=1/sqrt(3.);
|
||||
gx(1)=-gpos;
|
||||
gx(2)=gpos;
|
||||
gx(3)=gpos;
|
||||
gx(4)=-gpos;
|
||||
hx(1)=-gpos;
|
||||
hx(2)=-gpos;
|
||||
hx(3)=gpos;
|
||||
hx(4)=gpos;
|
||||
mMatL=zeros(4);
|
||||
mMatGLSL=zeros(4);
|
||||
f1L=zeros(4,1);
|
||||
f2L=zeros(4,1);
|
||||
f3L=zeros(4,1);
|
||||
for j=1:4
|
||||
g=gx(j);
|
||||
h=hx(j);
|
||||
phi(1)=0.25*(1.-g)*(1.-h);
|
||||
phi(2)=0.25*(1.+g)*(1.-h);
|
||||
phi(3)=0.25*(1.+g)*(1.+h);
|
||||
phi(4)=0.25*(1.-g)*(1.+h);
|
||||
phig(1)=0.25*-(1.-h);
|
||||
phig(2)=0.25*(1.-h);
|
||||
phig(3)=0.25*(1.+h);
|
||||
phig(4)=0.25*-(1.+h);
|
||||
Floc=phi(1)*F(Element(i,1))+phi(2)*F(Element(i,2))+phi(3)*F(Element(i,3))+phi(4)*F(Element(i,4));
|
||||
rset=phi(1)*lSet(Element(i,1))+phi(2)*lSet(Element(i,2))+phi(3)*lSet(Element(i,3))+phi(4)*lSet(Element(i,4));
|
||||
dls=phig(1)*lSet(Element(i,1))+phig(2)*lSet(Element(i,2))+phig(3)*lSet(Element(i,3))+phig(4)*lSet(Element(i,4));
|
||||
mMatL=mMatL+phi'*phi;
|
||||
mMatGLSL=mMatGLSL+((phig'*(dls/abs(dls)))*Floc*(h/abs(Floc)))*phi;
|
||||
f1L=f1L+phi'*Floc*abs(dls);
|
||||
f2L=f2L+(phig'*(dls/abs(dls))*Floc)*(h/abs(Floc))*Floc*abs(dls);
|
||||
vs=h*((abs(visc+Floc*abs(dls)))/(abs(Floc*dls)+h));
|
||||
f3L=f3L+vs*phig'*dls;
|
||||
end
|
||||
for k=1:4;
|
||||
for j=1:4;
|
||||
mMat(Element(i,j),Element(i,k))=mMat(Element(i,j),Element(i,k))+mMatL(j,k);
|
||||
mMatGLS(Element(i,j),Element(i,k))=mMatGLS(Element(i,j),Element(i,k))+mMatGLSL(j,k);
|
||||
end
|
||||
f1(Element(i,k))=f1(Element(i,k))+f1L(k);
|
||||
f2(Element(i,k))=f2(Element(i,k))+f2L(k);
|
||||
f3(Element(i,k))=f3(Element(i,k))+f3L(k);
|
||||
end
|
||||
end
|
||||
dt=0.01;
|
||||
lSet=lSet-((((mMat+mMatGLS)^-1)/dt)*(f1+f2+f3))';
|
||||
end
|
||||
%scatter3(Node(:,1), Node(:,2), lSet');
|
||||
|
||||
|
||||
|
||||
|
||||
200
Unpublished/XFEM/1D_Solver/GetF2D.m
Normal file
200
Unpublished/XFEM/1D_Solver/GetF2D.m
Normal file
|
|
@ -0,0 +1,200 @@
|
|||
function [] = GetF2D()
|
||||
clear all
|
||||
% Define Main Solution Mesh
|
||||
NumX=10;
|
||||
NumY=10;
|
||||
delX=1.;
|
||||
delY=1.;
|
||||
for j=1:NumY+1
|
||||
for i=1:NumX+1
|
||||
index=i+(NumX+1)*(j-1);
|
||||
Node(index,1)=single((i-1.))*delX;
|
||||
Node(index,2)=single((j-1.))*delY;
|
||||
end
|
||||
end
|
||||
numNodes=(NumX+1)*(NumY+1);
|
||||
for j=1:NumY
|
||||
for i=1:NumX
|
||||
index=i+NumX*(j-1);
|
||||
Element(index,1)=i+(NumX+1)*(j-1);
|
||||
Element(index,2)=i+(NumX+1)*(j-1)+1;
|
||||
Element(index,3)=i+(NumX+1)*(j)+1;
|
||||
Element(index,4)=i+(NumX+1)*(j);
|
||||
end
|
||||
end
|
||||
numElem=(NumX)*(NumY);
|
||||
% Define Initial Level Set
|
||||
centx=5.;
|
||||
centy=5.;
|
||||
rad=2.5;
|
||||
for i=1:numNodes;
|
||||
dist=sqrt((Node(i,1)-centx)*(Node(i,1)-centx)+(Node(i,2)-centy)*(Node(i,2)-centy));
|
||||
lSet(i)=dist-rad;
|
||||
end
|
||||
% Plot initial level set
|
||||
[X,Y]=meshgrid(0:1.:10);
|
||||
Z=zeros(11);
|
||||
for i=1:numNodes
|
||||
Z(i)=lSet(i);
|
||||
end
|
||||
surf(X,Y,Z)
|
||||
% LS Algorithm Parameters
|
||||
bandwith=10.;
|
||||
% Loop through timesteps
|
||||
for tstep=1:1
|
||||
% Identify Narrow Band Elements
|
||||
NBindex=0;
|
||||
for i=1:numElem
|
||||
check=0;
|
||||
for iNd=1:4
|
||||
if abs(lSet(Element(i,iNd)))<=bandwidth*delX
|
||||
check=1;
|
||||
end
|
||||
end
|
||||
% If an element is in the narrow band split it into triangles
|
||||
if check==1
|
||||
NBindex=NBindex+1;
|
||||
NBelem(NBindex,1)=Element(i,1);
|
||||
NBelem(NBindex,2)=Element(i,2);
|
||||
NBelem(NBindex,3)=Element(i,3);
|
||||
NBindex=NBindex+1;
|
||||
NBelem(NBindex,1)=Element(i,1);
|
||||
NBelem(NBindex,2)=Element(i,3);
|
||||
NBelem(NBindex,3)=Element(i,4);
|
||||
end
|
||||
end
|
||||
% Velocity BC
|
||||
F=zeros(numNodes,1);
|
||||
for i=1:NBindex
|
||||
if lSet(NBelem(i,1))~=lSet(NBelem(i,2)) || lSet(NBelem(i,1))~=lSet(NBelem(i,3))
|
||||
F(NBelem(i,1))= 0.0005;
|
||||
F(NBelem(i,2))= 0.0005;
|
||||
F(NBelem(i,3))= 0.0005;
|
||||
end
|
||||
end
|
||||
% Assemble 'Stiffness' Matrices
|
||||
A=zeros(numNodes);
|
||||
for i=1:NBindex
|
||||
gpos=1/sqrt(3.);
|
||||
gx(1)=-gpos;
|
||||
gx(2)=gpos;
|
||||
gx(3)=gpos;
|
||||
gx(4)=-gpos;
|
||||
hx(1)=-gpos;
|
||||
hx(2)=-gpos;
|
||||
hx(3)=gpos;
|
||||
hx(4)=gpos;
|
||||
AfL=zeros(4);
|
||||
AfLGLS=zeros(4);
|
||||
for j=1:4
|
||||
g=gx(j);
|
||||
h=hx(j);
|
||||
phi(1)=0.25*(1.-g)*(1.-h);
|
||||
phi(2)=0.25*(1.+g)*(1.-h);
|
||||
phi(3)=0.25*(1.+g)*(1.+h);
|
||||
phi(4)=0.25*(1.-g)*(1.+h);
|
||||
phig(1)=0.25*-(1.-h);
|
||||
phig(2)=0.25*(1.-h);
|
||||
phig(3)=0.25*(1.+h);
|
||||
phig(4)=0.25*-(1.+h);
|
||||
rset=phi(1)*lSet(Element(i,1))+phi(2)*lSet(Element(i,2))+phi(3)*lSet(Element(i,3))+phi(4)*lSet(Element(i,4));
|
||||
dls=phig(1)*lSet(Element(i,1))+phig(2)*lSet(Element(i,2))+phig(3)*lSet(Element(i,3))+phig(4)*lSet(Element(i,4));
|
||||
AfL=AfL+(phi'*sign(rset))*(dls*phig);
|
||||
AfLGLS=AfLGLS+(phig'*dls)*(1./abs(dls))*(dls*phig);
|
||||
end
|
||||
for k=1:4;
|
||||
for j=1:4;
|
||||
A(Element(i,j),Element(i,k))=A(Element(i,j),Element(i,k))+AfL(j,k)+AfLGLS(j,k)
|
||||
end
|
||||
end
|
||||
end
|
||||
% Apply BCs
|
||||
RHS=zeros(numNodes,1);
|
||||
Sub=A*F;
|
||||
iindex=0;
|
||||
for i=1:numNodes
|
||||
if F(i)==0.
|
||||
iindex=iindex+1;
|
||||
RHSred(iindex)=RHS(i)-Sub(i);
|
||||
Fred=0.;
|
||||
jindex=0;
|
||||
for j=1:numNodes
|
||||
if F(j)==0.
|
||||
jindex=jindex+1;
|
||||
Ared(iindex,jindex)=A(i,j);
|
||||
end
|
||||
end
|
||||
end
|
||||
end
|
||||
% Solve for Fred
|
||||
Fred=(Ared^-1)*RHSred';
|
||||
% Get F
|
||||
iindex=0;
|
||||
for i=1:numNodes
|
||||
if F(i)==0.
|
||||
iindex=iindex+1;
|
||||
F(i)=Fred(iindex);
|
||||
end
|
||||
end
|
||||
% Update level set
|
||||
mMat=zeros(numNodes);
|
||||
mMatGLS=zeros(numNodes);
|
||||
f1=zeros(numNodes,1);
|
||||
f2=zeros(numNodes,1);
|
||||
f3=zeros(numNodes,1);
|
||||
h=1.;
|
||||
visc=0.000;
|
||||
for i=1:numElem
|
||||
gpos=1/sqrt(3.);
|
||||
gx(1)=-gpos;
|
||||
gx(2)=gpos;
|
||||
gx(3)=gpos;
|
||||
gx(4)=-gpos;
|
||||
hx(1)=-gpos;
|
||||
hx(2)=-gpos;
|
||||
hx(3)=gpos;
|
||||
hx(4)=gpos;
|
||||
mMatL=zeros(4);
|
||||
mMatGLSL=zeros(4);
|
||||
f1L=zeros(4,1);
|
||||
f2L=zeros(4,1);
|
||||
f3L=zeros(4,1);
|
||||
for j=1:4
|
||||
g=gx(j);
|
||||
h=hx(j);
|
||||
phi(1)=0.25*(1.-g)*(1.-h);
|
||||
phi(2)=0.25*(1.+g)*(1.-h);
|
||||
phi(3)=0.25*(1.+g)*(1.+h);
|
||||
phi(4)=0.25*(1.-g)*(1.+h);
|
||||
phig(1)=0.25*-(1.-h);
|
||||
phig(2)=0.25*(1.-h);
|
||||
phig(3)=0.25*(1.+h);
|
||||
phig(4)=0.25*-(1.+h);
|
||||
Floc=phi(1)*F(Element(i,1))+phi(2)*F(Element(i,2))+phi(3)*F(Element(i,3))+phi(4)*F(Element(i,4));
|
||||
rset=phi(1)*lSet(Element(i,1))+phi(2)*lSet(Element(i,2))+phi(3)*lSet(Element(i,3))+phi(4)*lSet(Element(i,4));
|
||||
dls=phig(1)*lSet(Element(i,1))+phig(2)*lSet(Element(i,2))+phig(3)*lSet(Element(i,3))+phig(4)*lSet(Element(i,4));
|
||||
mMatL=mMatL+phi'*phi;
|
||||
mMatGLSL=mMatGLSL+((phig'*(dls/abs(dls)))*Floc*(h/abs(Floc)))*phi;
|
||||
f1L=f1L+phi'*Floc*abs(dls);
|
||||
f2L=f2L+(phig'*(dls/abs(dls))*Floc)*(h/abs(Floc))*Floc*abs(dls);
|
||||
vs=h*((abs(visc+Floc*abs(dls)))/(abs(Floc*dls)+h));
|
||||
f3L=f3L+vs*phig'*dls;
|
||||
end
|
||||
for k=1:4;
|
||||
for j=1:4;
|
||||
mMat(Element(i,j),Element(i,k))=mMat(Element(i,j),Element(i,k))+mMatL(j,k);
|
||||
mMatGLS(Element(i,j),Element(i,k))=mMatGLS(Element(i,j),Element(i,k))+mMatGLSL(j,k);
|
||||
end
|
||||
f1(Element(i,k))=f1(Element(i,k))+f1L(k);
|
||||
f2(Element(i,k))=f2(Element(i,k))+f2L(k);
|
||||
f3(Element(i,k))=f3(Element(i,k))+f3L(k);
|
||||
end
|
||||
end
|
||||
dt=0.01;
|
||||
lSet=lSet-((((mMat+mMatGLS)^-1)/dt)*(f1+f2+f3))';
|
||||
end
|
||||
%scatter3(Node(:,1), Node(:,2), lSet');
|
||||
|
||||
|
||||
|
||||
|
||||
232
Unpublished/XFEM/1D_Solver/GetF2D_T.asv
Normal file
232
Unpublished/XFEM/1D_Solver/GetF2D_T.asv
Normal file
|
|
@ -0,0 +1,232 @@
|
|||
function [] = GetF2D_T()
|
||||
clear all
|
||||
% Define Main Solution Mesh
|
||||
NumX=2;
|
||||
NumY=1;
|
||||
delX=1.;
|
||||
delY=1.;
|
||||
for j=1:NumY+1
|
||||
for i=1:NumX+1
|
||||
index=i+(NumX+1)*(j-1);
|
||||
Node(index,1)=single((i-1.))*delX;
|
||||
Node(index,2)=single((j-1.))*delY;
|
||||
end
|
||||
end
|
||||
numNodes=(NumX+1)*(NumY+1);
|
||||
for j=1:NumY
|
||||
for i=1:NumX
|
||||
index=i+NumX*(j-1);
|
||||
Element(index,1)=i+(NumX+1)*(j-1);
|
||||
Element(index,2)=i+(NumX+1)*(j-1)+1;
|
||||
Element(index,3)=i+(NumX+1)*(j)+1;
|
||||
Element(index,4)=i+(NumX+1)*(j);
|
||||
end
|
||||
end
|
||||
numElem=(NumX)*(NumY);
|
||||
% Define Initial Level Set
|
||||
%centx=5.;
|
||||
%centy=5.;
|
||||
%rad=2.5;
|
||||
%for i=1:numNodes;
|
||||
% dist=sqrt((Node(i,1)-centx)*(Node(i,1)-centx)+(Node(i,2)-centy)*(Node(i,2)-centy));
|
||||
% lSet(i)=dist-rad;
|
||||
%end
|
||||
for i=1:numNodes;
|
||||
dist=Node(i,1)-0.1;
|
||||
lSet(i)=dist;
|
||||
end
|
||||
% Plot initial level set
|
||||
%[X]=meshgrid(0:1.:10);
|
||||
%Z=zeros(11);
|
||||
%for i=1:numNodes
|
||||
% Z(i)=lSet(i);
|
||||
%end
|
||||
%surf(X,Z)
|
||||
% LS Algorithm Parameters
|
||||
bandwidth=10.;
|
||||
% Loop through timesteps
|
||||
for tstep=1:1
|
||||
% Identify Narrow Band Elements
|
||||
NBindex=0;
|
||||
for i=1:numElem
|
||||
check=0;
|
||||
for iNd=1:4
|
||||
if abs(lSet(Element(i,iNd)))<=bandwidth*delX
|
||||
check=1;
|
||||
end
|
||||
end
|
||||
% If an element is in the narrow band split it into triangles
|
||||
if check==1
|
||||
NBindex=NBindex+1;
|
||||
NBelem(NBindex,1)=Element(i,1);
|
||||
NBelem(NBindex,2)=Element(i,2);
|
||||
NBelem(NBindex,3)=Element(i,3);
|
||||
NBindex=NBindex+1;
|
||||
NBelem(NBindex,1)=Element(i,1);
|
||||
NBelem(NBindex,2)=Element(i,3);
|
||||
NBelem(NBindex,3)=Element(i,4);
|
||||
end
|
||||
end
|
||||
% Velocity BC
|
||||
F=zeros(numNodes,1);
|
||||
for i=1:NBindex
|
||||
if sign(lSet(NBelem(i,1)))~=sign(lSet(NBelem(i,2)))||sign(lSet(NBelem(i,1)))~=sign(lSet(NBelem(i,3)))
|
||||
F(NBelem(i,1))= 0.05;
|
||||
F(NBelem(i,2))= 0.05;
|
||||
F(NBelem(i,3))= 0.05;
|
||||
end
|
||||
end
|
||||
% Assemble 'Stiffness' Matrices
|
||||
A=zeros(numNodes);
|
||||
for i=1:NBindex
|
||||
gx(1)=2./3.;
|
||||
gx(2)=1./6.;
|
||||
gx(3)=1./6.;
|
||||
hx(1)=1./6.;
|
||||
hx(2)=1./6.;
|
||||
hx(3)=2./3.;
|
||||
AfL=zeros(3);
|
||||
AfLGLS=zeros(3);
|
||||
x1=Node(NBelem(i,1),1);
|
||||
y1=Node(NBelem(i,1),2);
|
||||
x2=Node(NBelem(i,2),1);
|
||||
y2=Node(NBelem(i,2),2);
|
||||
x3=Node(NBelem(i,3),1);
|
||||
y3=Node(NBelem(i,3),2);
|
||||
for j=1:3
|
||||
g=gx(j);
|
||||
h=hx(j);
|
||||
phi(1)=1.-g-h;
|
||||
phi(2)=g;
|
||||
phi(3)=h;
|
||||
phig(1)=-1.;
|
||||
phig(2)=1.;
|
||||
phig(3)=0.;
|
||||
phih(1)=-1.;
|
||||
phih(2)=0.;
|
||||
phih(3)=1.;
|
||||
djac=2*abs(x1*(y2-y3)+x2*(y3-y1)+x3*(y1-y2));
|
||||
for k=1:3
|
||||
phix(k)=(1./djac)*((-y1+y3)*phig(k)+(y1-y2)*phih(k));
|
||||
phiy(k)=(1./djac)*((x1-x3)*phig(k)+(-x1+x2)*phih(k));
|
||||
end
|
||||
delphi=[phix;phiy];
|
||||
nodalLset=[lSet(NBelem(i,1));lSet(NBelem(i,2));lSet(NBelem(i,3))];
|
||||
set=phi*nodalLset;
|
||||
delset=delphi*nodalLset;
|
||||
AfL=AfL+(phi'*sign(set))*(delset'*delphi)/3.;
|
||||
AfLGLS=AfLGLS+(delphi'*delset)*(1./norm(delset))*(delset'*delphi)/3.;
|
||||
end
|
||||
sum=AfL+AfLGLS;
|
||||
for k=1:3;
|
||||
for j=1:3;
|
||||
A(NBelem(i,j),NBelem(i,k))=A(NBelem(i,j),NBelem(i,k))+sum(j,k);
|
||||
end
|
||||
end
|
||||
end
|
||||
% Apply BCs
|
||||
RHS=zeros(numNodes,1);
|
||||
Sub=A*F;
|
||||
iindex=0;
|
||||
for i=1:numNodes
|
||||
if F(i)==0.
|
||||
iindex=iindex+1;
|
||||
RHSred(iindex)=RHS(i)-Sub(i);
|
||||
Fred=0.;
|
||||
jindex=0;
|
||||
for j=1:numNodes
|
||||
if F(j)==0.
|
||||
jindex=jindex+1;
|
||||
Ared(iindex,jindex)=A(i,j);
|
||||
end
|
||||
end
|
||||
end
|
||||
end
|
||||
% Solve for Fred
|
||||
Fred=(Ared^-1)*RHSred';
|
||||
% Get F
|
||||
iindex=0;
|
||||
for i=1:numNodes
|
||||
if F(i)==0.
|
||||
iindex=iindex+1;
|
||||
F(i)=Fred(iindex);
|
||||
end
|
||||
end
|
||||
% Update level set
|
||||
mMat=zeros(numNodes);
|
||||
mMatGLS=zeros(numNodes);
|
||||
f1=zeros(numNodes,1);
|
||||
f2=zeros(numNodes,1);
|
||||
f3=zeros(numNodes,1);
|
||||
h=1.;
|
||||
visc=0.001;
|
||||
for i=1:NBindex
|
||||
mMatL=zeros(3);
|
||||
mMatGLSL=zeros(3);
|
||||
f1L=zeros(3,1);
|
||||
f2L=zeros(3,1);
|
||||
f3L=zeros(3,1);
|
||||
gx(1)=2./3.;
|
||||
gx(2)=1./6.;
|
||||
gx(3)=1./6.;
|
||||
hx(1)=1./6.;
|
||||
hx(2)=1./6.;
|
||||
hx(3)=2./3.;
|
||||
x1=Node(NBelem(i,1),1);
|
||||
y1=Node(NBelem(i,1),2);
|
||||
x2=Node(NBelem(i,2),1);
|
||||
y2=Node(NBelem(i,2),2);
|
||||
x3=Node(NBelem(i,3),1);
|
||||
y3=Node(NBelem(i,3),2);
|
||||
for j=1:3
|
||||
g=gx(j);
|
||||
h=hx(j);
|
||||
phi(1)=1.-g-h;
|
||||
phi(2)=g;
|
||||
phi(3)=h;
|
||||
phig(1)=-1.;
|
||||
phig(2)=1.;
|
||||
phig(3)=0.;
|
||||
phih(1)=-1.;
|
||||
phih(2)=0.;
|
||||
phih(3)=1.;
|
||||
djac=abs(x1*(y2-y3)+x2*(y3-y1)+x3*(y1-y2));
|
||||
for k=1:3
|
||||
phix(k)=(1./djac)*((-y1+y3)*phig(k)+(y1-y2)*phih(k));
|
||||
phiy(k)=(1./djac)*((x1-x3)*phig(k)+(-x1+x2)*phih(k));
|
||||
end
|
||||
delphi=[phix;phiy];
|
||||
nodalLset=[lSet(NBelem(i,1));lSet(NBelem(i,2));lSet(NBelem(i,3))];
|
||||
nodalF=[F(NBelem(i,1));F(NBelem(i,2));F(NBelem(i,3))];
|
||||
delset=delphi*nodalLset;
|
||||
Floc=phi*nodalF;
|
||||
mMatL=mMatL+(phi'*phi)/3.;
|
||||
mMatGLSL=mMatGLSL+((delphi'*(delset/norm(delset)))*Floc*(h/abs(Floc)))*phi/3.;
|
||||
f1L=f1L+phi'*Floc*norm(delset)/3.;
|
||||
f2L=f2L+(delphi'*(delset/norm(delset))*Floc)*(h/abs(Floc))*Floc*norm(delset)/3.;
|
||||
vs=h*((abs(visc+Floc*norm(delset)))/(norm(Floc*delset)+h));
|
||||
f3L=f3L+vs*delphi'*delset/3.;
|
||||
end
|
||||
for k=1:3;
|
||||
for j=1:3;
|
||||
mMat(NBelem(i,j),NBelem(i,k))=mMat(NBelem(i,j),NBelem(i,k))+mMatL(j,k);
|
||||
mMatGLS(NBelem(i,j),NBelem(i,k))=mMatGLS(NBelem(i,j),NBelem(i,k))+mMatGLSL(j,k);
|
||||
end
|
||||
f1(NBelem(i,k))=f1(NBelem(i,k))+f1L(k);
|
||||
f2(NBelem(i,k))=f2(NBelem(i,k))+f2L(k);
|
||||
f3(NBelem(i,k))=f3(NBelem(i,k))+f3L(k);
|
||||
end
|
||||
end
|
||||
|
||||
(mMat+mMatGLS)^-1
|
||||
f1+f2+f3
|
||||
dt=0.0001;
|
||||
-((((mMat+mMatGLS)^-1)*dt)*(f1+f2+f3))'
|
||||
lSet=lSet-((((mMat+mMatGLS)^-1)*dt)*(f1+f2+f3))';
|
||||
end
|
||||
lSet';
|
||||
%scatter3(Node(:,1), Node(:,2), lSet');
|
||||
|
||||
|
||||
|
||||
|
||||
233
Unpublished/XFEM/1D_Solver/GetF2D_T.m
Normal file
233
Unpublished/XFEM/1D_Solver/GetF2D_T.m
Normal file
|
|
@ -0,0 +1,233 @@
|
|||
function [] = GetF2D_T()
|
||||
clear all
|
||||
% Define Main Solution Mesh
|
||||
NumX=2;
|
||||
NumY=1;
|
||||
delX=1.;
|
||||
delY=1.;
|
||||
for j=1:NumY+1
|
||||
for i=1:NumX+1
|
||||
index=i+(NumX+1)*(j-1);
|
||||
Node(index,1)=single((i-1.))*delX;
|
||||
Node(index,2)=single((j-1.))*delY;
|
||||
end
|
||||
end
|
||||
numNodes=(NumX+1)*(NumY+1);
|
||||
for j=1:NumY
|
||||
for i=1:NumX
|
||||
index=i+NumX*(j-1);
|
||||
Element(index,1)=i+(NumX+1)*(j-1);
|
||||
Element(index,2)=i+(NumX+1)*(j-1)+1;
|
||||
Element(index,3)=i+(NumX+1)*(j)+1;
|
||||
Element(index,4)=i+(NumX+1)*(j);
|
||||
end
|
||||
end
|
||||
numElem=(NumX)*(NumY);
|
||||
% Define Initial Level Set
|
||||
%centx=5.;
|
||||
%centy=5.;
|
||||
%rad=2.5;
|
||||
%for i=1:numNodes;
|
||||
% dist=sqrt((Node(i,1)-centx)*(Node(i,1)-centx)+(Node(i,2)-centy)*(Node(i,2)-centy));
|
||||
% lSet(i)=dist-rad;
|
||||
%end
|
||||
for i=1:numNodes;
|
||||
dist=Node(i,1)-1.5;
|
||||
lSet(i)=dist;
|
||||
end
|
||||
% Plot initial level set
|
||||
%[X]=meshgrid(0:1.:10);
|
||||
%Z=zeros(11);
|
||||
%for i=1:numNodes
|
||||
% Z(i)=lSet(i);
|
||||
%end
|
||||
%surf(X,Z)
|
||||
% LS Algorithm Parameters
|
||||
bandwidth=10.;
|
||||
% Loop through timesteps
|
||||
for tstep=1:1
|
||||
% Identify Narrow Band Elements
|
||||
NBindex=0;
|
||||
for i=1:numElem
|
||||
check=0;
|
||||
for iNd=1:4
|
||||
if abs(lSet(Element(i,iNd)))<=bandwidth*delX
|
||||
check=1;
|
||||
end
|
||||
end
|
||||
% If an element is in the narrow band split it into triangles
|
||||
if check==1
|
||||
NBindex=NBindex+1;
|
||||
NBelem(NBindex,1)=Element(i,1);
|
||||
NBelem(NBindex,2)=Element(i,2);
|
||||
NBelem(NBindex,3)=Element(i,3);
|
||||
NBindex=NBindex+1;
|
||||
NBelem(NBindex,1)=Element(i,1);
|
||||
NBelem(NBindex,2)=Element(i,3);
|
||||
NBelem(NBindex,3)=Element(i,4);
|
||||
end
|
||||
end
|
||||
% Velocity BC
|
||||
F=zeros(numNodes,1);
|
||||
for i=1:NBindex
|
||||
if sign(lSet(NBelem(i,1)))~=sign(lSet(NBelem(i,2)))||sign(lSet(NBelem(i,1)))~=sign(lSet(NBelem(i,3)))
|
||||
F(NBelem(i,1))= 0.05;
|
||||
F(NBelem(i,2))= 0.05;
|
||||
F(NBelem(i,3))= 0.05;
|
||||
end
|
||||
end
|
||||
% Assemble 'Stiffness' Matrices
|
||||
A=zeros(numNodes);
|
||||
for i=1:NBindex
|
||||
gx(1)=2./3.;
|
||||
gx(2)=1./6.;
|
||||
gx(3)=1./6.;
|
||||
hx(1)=1./6.;
|
||||
hx(2)=1./6.;
|
||||
hx(3)=2./3.;
|
||||
AfL=zeros(3);
|
||||
AfLGLS=zeros(3);
|
||||
x1=Node(NBelem(i,1),1);
|
||||
y1=Node(NBelem(i,1),2);
|
||||
x2=Node(NBelem(i,2),1);
|
||||
y2=Node(NBelem(i,2),2);
|
||||
x3=Node(NBelem(i,3),1);
|
||||
y3=Node(NBelem(i,3),2);
|
||||
for j=1:3
|
||||
g=gx(j);
|
||||
h=hx(j);
|
||||
phi(1)=1.-g-h;
|
||||
phi(2)=g;
|
||||
phi(3)=h;
|
||||
phig(1)=-1.;
|
||||
phig(2)=1.;
|
||||
phig(3)=0.;
|
||||
phih(1)=-1.;
|
||||
phih(2)=0.;
|
||||
phih(3)=1.;
|
||||
djac=2*abs(x1*(y2-y3)+x2*(y3-y1)+x3*(y1-y2));
|
||||
for k=1:3
|
||||
phix(k)=(1./djac)*((-y1+y3)*phig(k)+(y1-y2)*phih(k));
|
||||
phiy(k)=(1./djac)*((x1-x3)*phig(k)+(-x1+x2)*phih(k));
|
||||
end
|
||||
delphi=[phix;phiy];
|
||||
nodalLset=[lSet(NBelem(i,1));lSet(NBelem(i,2));lSet(NBelem(i,3))];
|
||||
set=phi*nodalLset;
|
||||
delset=delphi*nodalLset;
|
||||
AfL=AfL+(phi'*sign(set))*(delset'*delphi)/3.;
|
||||
AfLGLS=AfLGLS+(delphi'*delset)*(1./norm(delset))*(delset'*delphi)/3.;
|
||||
end
|
||||
sum=AfL+AfLGLS;
|
||||
for k=1:3;
|
||||
for j=1:3;
|
||||
A(NBelem(i,j),NBelem(i,k))=A(NBelem(i,j),NBelem(i,k))+sum(j,k);
|
||||
end
|
||||
end
|
||||
end
|
||||
% Apply BCs
|
||||
RHS=zeros(numNodes,1);
|
||||
Sub=A*F;
|
||||
iindex=0;
|
||||
for i=1:numNodes
|
||||
if F(i)==0.
|
||||
iindex=iindex+1;
|
||||
RHSred(iindex)=RHS(i)-Sub(i);
|
||||
Fred=0.;
|
||||
jindex=0;
|
||||
for j=1:numNodes
|
||||
if F(j)==0.
|
||||
jindex=jindex+1;
|
||||
Ared(iindex,jindex)=A(i,j);
|
||||
end
|
||||
end
|
||||
end
|
||||
end
|
||||
% Solve for Fred
|
||||
Fred=(Ared^-1)*RHSred';
|
||||
% Get F
|
||||
iindex=0;
|
||||
for i=1:numNodes
|
||||
if F(i)==0.
|
||||
iindex=iindex+1;
|
||||
F(i)=Fred(iindex);
|
||||
end
|
||||
end
|
||||
% Update level set
|
||||
mMat=zeros(numNodes);
|
||||
mMatGLS=zeros(numNodes);
|
||||
f1=zeros(numNodes,1);
|
||||
f2=zeros(numNodes,1);
|
||||
f3=zeros(numNodes,1);
|
||||
h=1.;
|
||||
visc=0.0005;
|
||||
for i=1:NBindex
|
||||
mMatL=zeros(3);
|
||||
mMatGLSL=zeros(3);
|
||||
f1L=zeros(3,1);
|
||||
f2L=zeros(3,1);
|
||||
f3L=zeros(3,1);
|
||||
gx(1)=2./3.;
|
||||
gx(2)=1./6.;
|
||||
gx(3)=1./6.;
|
||||
hx(1)=1./6.;
|
||||
hx(2)=1./6.;
|
||||
hx(3)=2./3.;
|
||||
x1=Node(NBelem(i,1),1);
|
||||
y1=Node(NBelem(i,1),2);
|
||||
x2=Node(NBelem(i,2),1);
|
||||
y2=Node(NBelem(i,2),2);
|
||||
x3=Node(NBelem(i,3),1);
|
||||
y3=Node(NBelem(i,3),2);
|
||||
for j=1:3
|
||||
g=gx(j);
|
||||
h=hx(j);
|
||||
phi(1)=1.-g-h;
|
||||
phi(2)=g;
|
||||
phi(3)=h;
|
||||
phig(1)=-1.;
|
||||
phig(2)=1.;
|
||||
phig(3)=0.;
|
||||
phih(1)=-1.;
|
||||
phih(2)=0.;
|
||||
phih(3)=1.;
|
||||
djac=abs(x1*(y2-y3)+x2*(y3-y1)+x3*(y1-y2));
|
||||
for k=1:3
|
||||
phix(k)=(1./djac)*((-y1+y3)*phig(k)+(y1-y2)*phih(k));
|
||||
phiy(k)=(1./djac)*((x1-x3)*phig(k)+(-x1+x2)*phih(k));
|
||||
end
|
||||
delphi=[phix;phiy];
|
||||
nodalLset=[lSet(NBelem(i,1));lSet(NBelem(i,2));lSet(NBelem(i,3))];
|
||||
nodalF=[F(NBelem(i,1));F(NBelem(i,2));F(NBelem(i,3))];
|
||||
delset=delphi*nodalLset;
|
||||
Floc=phi*nodalF;
|
||||
mMatL=mMatL+(phi'*phi)/3.;
|
||||
mMatGLSL=mMatGLSL+((delphi'*(delset/norm(delset)))*Floc*(h/abs(Floc)))*phi/3.;
|
||||
f1L=f1L+phi'*Floc*norm(delset)/3.;
|
||||
f2L=f2L+(delphi'*(delset/norm(delset))*Floc)*(h/abs(Floc))*Floc*norm(delset)/3.;
|
||||
vs=h*((abs(visc+Floc*norm(delset)))/(norm(Floc*delset)+h));
|
||||
f3L=f3L+vs*delphi'*delset/3.;
|
||||
end
|
||||
for k=1:3;
|
||||
for j=1:3;
|
||||
mMat(NBelem(i,j),NBelem(i,k))=mMat(NBelem(i,j),NBelem(i,k))+mMatL(j,k);
|
||||
mMatGLS(NBelem(i,j),NBelem(i,k))=mMatGLS(NBelem(i,j),NBelem(i,k))+mMatGLSL(j,k);
|
||||
end
|
||||
f1(NBelem(i,k))=f1(NBelem(i,k))+f1L(k);
|
||||
f2(NBelem(i,k))=f2(NBelem(i,k))+f2L(k);
|
||||
f3(NBelem(i,k))=f3(NBelem(i,k))+f3L(k);
|
||||
end
|
||||
end
|
||||
mMat
|
||||
mMatGLS
|
||||
(mMat+mMatGLS)^-1
|
||||
f1+f2+f3
|
||||
dt=0.1;
|
||||
-((((mMat+mMatGLS)^-1)*dt)*(f1+f2+f3))'
|
||||
lSet=lSet-((((mMat+mMatGLS)^-1)*dt)*(f1+f2+f3))';
|
||||
end
|
||||
lSet';
|
||||
%scatter3(Node(:,1), Node(:,2), lSet');
|
||||
|
||||
|
||||
|
||||
|
||||
234
Unpublished/XFEM/1D_Solver/GetF2D_Z.m
Normal file
234
Unpublished/XFEM/1D_Solver/GetF2D_Z.m
Normal file
|
|
@ -0,0 +1,234 @@
|
|||
function [] = GetF2D_Z()
|
||||
clear all
|
||||
% Define Main Solution Mesh
|
||||
NumX=8;
|
||||
NumY=8;
|
||||
delX=1.;
|
||||
delY=1.;
|
||||
for j=1:NumY+1
|
||||
for i=1:NumX+1
|
||||
index=i+(NumX+1)*(j-1);
|
||||
Node(index,1)=single((i-1.))*delX;
|
||||
Node(index,2)=single((j-1.))*delY;
|
||||
end
|
||||
end
|
||||
numNodes=(NumX+1)*(NumY+1);
|
||||
for j=1:NumY
|
||||
for i=1:NumX
|
||||
index=i+NumX*(j-1);
|
||||
Element(index,1)=i+(NumX+1)*(j-1);
|
||||
Element(index,2)=i+(NumX+1)*(j-1)+1;
|
||||
Element(index,3)=i+(NumX+1)*(j)+1;
|
||||
Element(index,4)=i+(NumX+1)*(j);
|
||||
end
|
||||
end
|
||||
numElem=(NumX)*(NumY);
|
||||
% Define Initial Level Set
|
||||
centx=4.;
|
||||
centy=4.;
|
||||
rad=2.1;
|
||||
for i=1:numNodes;
|
||||
dist=sqrt((Node(i,1)-centx)*(Node(i,1)-centx)+(Node(i,2)-centy)*(Node(i,2)-centy));
|
||||
lSet(i)=dist-rad;
|
||||
end
|
||||
%for i=1:numNodes;
|
||||
% dist=Node(i,1)-0.1;
|
||||
% lSet(i)=dist;
|
||||
%end
|
||||
% Plot initial level set
|
||||
[X Y]=meshgrid(0:1.:8);
|
||||
Z=zeros(9);
|
||||
for i=1:81
|
||||
Z(i)=lSet(i);
|
||||
end
|
||||
surf(X,Y,Z)
|
||||
% LS Algorithm Parameters
|
||||
lSet'
|
||||
bandwidth=10.;
|
||||
% Loop through timesteps
|
||||
for tstep=1:100
|
||||
% Identify Narrow Band Elements
|
||||
NBindex=0;
|
||||
for i=1:numElem
|
||||
check=0;
|
||||
for iNd=1:4
|
||||
if abs(lSet(Element(i,iNd)))<=bandwidth*delX
|
||||
check=1;
|
||||
end
|
||||
end
|
||||
% If an element is in the narrow band split it into triangles
|
||||
if check==1
|
||||
NBindex=NBindex+1;
|
||||
NBelem(NBindex,1)=Element(i,1);
|
||||
NBelem(NBindex,2)=Element(i,2);
|
||||
NBelem(NBindex,3)=Element(i,3);
|
||||
NBindex=NBindex+1;
|
||||
NBelem(NBindex,1)=Element(i,1);
|
||||
NBelem(NBindex,2)=Element(i,3);
|
||||
NBelem(NBindex,3)=Element(i,4);
|
||||
end
|
||||
end
|
||||
% Velocity BC
|
||||
F=zeros(numNodes,1);
|
||||
for i=1:NBindex
|
||||
if sign(lSet(NBelem(i,1)))~=sign(lSet(NBelem(i,2)))||sign(lSet(NBelem(i,1)))~=sign(lSet(NBelem(i,3)))
|
||||
F(NBelem(i,1))= 1.;
|
||||
F(NBelem(i,2))= 1.;
|
||||
F(NBelem(i,3))= 1.;
|
||||
end
|
||||
end
|
||||
% Assemble 'Stiffness' Matrices
|
||||
A=zeros(numNodes);
|
||||
for i=1:NBindex
|
||||
gx(1)=2./3.;
|
||||
gx(2)=1./6.;
|
||||
gx(3)=1./6.;
|
||||
hx(1)=1./6.;
|
||||
hx(2)=1./6.;
|
||||
hx(3)=2./3.;
|
||||
AfL=zeros(3);
|
||||
AfLGLS=zeros(3);
|
||||
x1=Node(NBelem(i,1),1);
|
||||
y1=Node(NBelem(i,1),2);
|
||||
x2=Node(NBelem(i,2),1);
|
||||
y2=Node(NBelem(i,2),2);
|
||||
x3=Node(NBelem(i,3),1);
|
||||
y3=Node(NBelem(i,3),2);
|
||||
for j=1:3
|
||||
g=gx(j);
|
||||
h=hx(j);
|
||||
phi(1)=1.-g-h;
|
||||
phi(2)=g;
|
||||
phi(3)=h;
|
||||
phig(1)=-1.;
|
||||
phig(2)=1.;
|
||||
phig(3)=0.;
|
||||
phih(1)=-1.;
|
||||
phih(2)=0.;
|
||||
phih(3)=1.;
|
||||
djac=2*abs(x1*(y2-y3)+x2*(y3-y1)+x3*(y1-y2));
|
||||
for k=1:3
|
||||
phix(k)=(1./djac)*((-y1+y3)*phig(k)+(y1-y2)*phih(k));
|
||||
phiy(k)=(1./djac)*((x1-x3)*phig(k)+(-x1+x2)*phih(k));
|
||||
end
|
||||
delphi=[phix;phiy];
|
||||
nodalLset=[lSet(NBelem(i,1));lSet(NBelem(i,2));lSet(NBelem(i,3))];
|
||||
set=phi*nodalLset;
|
||||
delset=delphi*nodalLset;
|
||||
AfL=AfL+(phi'*sign(set))*(delset'*delphi)/3.;
|
||||
AfLGLS=AfLGLS+(delphi'*delset)*(1./norm(delset))*(delset'*delphi)/3.;
|
||||
end
|
||||
sum=AfL+AfLGLS;
|
||||
for k=1:3;
|
||||
for j=1:3;
|
||||
A(NBelem(i,j),NBelem(i,k))=A(NBelem(i,j),NBelem(i,k))+sum(j,k);
|
||||
end
|
||||
end
|
||||
end
|
||||
% Apply BCs
|
||||
RHS=zeros(numNodes,1);
|
||||
Sub=A*F;
|
||||
iindex=0;
|
||||
for i=1:numNodes
|
||||
if F(i)==0.
|
||||
iindex=iindex+1;
|
||||
RHSred(iindex)=RHS(i)-Sub(i);
|
||||
Fred=0.;
|
||||
jindex=0;
|
||||
for j=1:numNodes
|
||||
if F(j)==0.
|
||||
jindex=jindex+1;
|
||||
Ared(iindex,jindex)=A(i,j);
|
||||
end
|
||||
end
|
||||
end
|
||||
end
|
||||
% Solve for Fred
|
||||
Fred=(Ared^-1)*RHSred';
|
||||
% Get F
|
||||
iindex=0;
|
||||
for i=1:numNodes
|
||||
if F(i)==0.
|
||||
iindex=iindex+1;
|
||||
F(i)=Fred(iindex);
|
||||
end
|
||||
end
|
||||
% Update level set
|
||||
mMat=zeros(numNodes);
|
||||
mMatGLS=zeros(numNodes);
|
||||
f1=zeros(numNodes,1);
|
||||
f2=zeros(numNodes,1);
|
||||
f3=zeros(numNodes,1);
|
||||
h2=0.00001;
|
||||
visc=0.0005;
|
||||
for i=1:NBindex
|
||||
mMatL=zeros(3);
|
||||
mMatGLSL=zeros(3);
|
||||
f1L=zeros(3,1);
|
||||
f2L=zeros(3,1);
|
||||
f3L=zeros(3,1);
|
||||
gx(1)=2./3.;
|
||||
gx(2)=1./6.;
|
||||
gx(3)=1./6.;
|
||||
hx(1)=1./6.;
|
||||
hx(2)=1./6.;
|
||||
hx(3)=2./3.;
|
||||
x1=Node(NBelem(i,1),1);
|
||||
y1=Node(NBelem(i,1),2);
|
||||
x2=Node(NBelem(i,2),1);
|
||||
y2=Node(NBelem(i,2),2);
|
||||
x3=Node(NBelem(i,3),1);
|
||||
y3=Node(NBelem(i,3),2);
|
||||
for j=1:3
|
||||
g=gx(j);
|
||||
h=hx(j);
|
||||
phi(1)=1.-g-h;
|
||||
phi(2)=g;
|
||||
phi(3)=h;
|
||||
phig(1)=-1.;
|
||||
phig(2)=1.;
|
||||
phig(3)=0.;
|
||||
phih(1)=-1.;
|
||||
phih(2)=0.;
|
||||
phih(3)=1.;
|
||||
djac=abs(x1*(y2-y3)+x2*(y3-y1)+x3*(y1-y2));
|
||||
for k=1:3
|
||||
phix(k)=(1./djac)*((-y1+y3)*phig(k)+(y1-y2)*phih(k));
|
||||
phiy(k)=(1./djac)*((x1-x3)*phig(k)+(-x1+x2)*phih(k));
|
||||
end
|
||||
delphi=[phix;phiy];
|
||||
nodalLset=[lSet(NBelem(i,1));lSet(NBelem(i,2));lSet(NBelem(i,3))];
|
||||
nodalF=[F(NBelem(i,1));F(NBelem(i,2));F(NBelem(i,3))];
|
||||
delset=delphi*nodalLset;
|
||||
Floc=phi*nodalF;
|
||||
mMatL=mMatL+(phi'*phi)/3.;
|
||||
mMatGLSL=mMatGLSL+((delphi'*(delset/norm(delset)))*Floc*(h2/abs(Floc)))*phi/3.;
|
||||
f1L=f1L+phi'*Floc*norm(delset)/3.;
|
||||
f2L=f2L+(delphi'*(delset/norm(delset))*Floc)*(h2/abs(Floc))*Floc*norm(delset)/3.;
|
||||
vs=h2*((abs(visc+Floc*norm(delset)))/(norm(Floc*delset)+h2));
|
||||
f3L=f3L+vs*delphi'*delset/3.;
|
||||
end
|
||||
for k=1:3;
|
||||
for j=1:3;
|
||||
mMat(NBelem(i,j),NBelem(i,k))=mMat(NBelem(i,j),NBelem(i,k))+mMatL(j,k);
|
||||
mMatGLS(NBelem(i,j),NBelem(i,k))=mMatGLS(NBelem(i,j),NBelem(i,k))+mMatGLSL(j,k);
|
||||
end
|
||||
f1(NBelem(i,k))=f1(NBelem(i,k))+f1L(k);
|
||||
f2(NBelem(i,k))=f2(NBelem(i,k))+f2L(k);
|
||||
f3(NBelem(i,k))=f3(NBelem(i,k))+f3L(k);
|
||||
end
|
||||
end
|
||||
dt=0.01;
|
||||
lSet=lSet-((((mMat+mMatGLS)^-1)*dt)*(f1+f2+f3))';
|
||||
end
|
||||
lSet'
|
||||
%[X Y]=meshgrid(0:1.:8);
|
||||
%Z=zeros(9);
|
||||
%for i=1:81
|
||||
% Z(i)=lSet(i);
|
||||
%end
|
||||
%surf(X,Y,Z)
|
||||
|
||||
|
||||
|
||||
|
||||
2
Unpublished/XFEM/1D_Solver/testGrid.asv
Normal file
2
Unpublished/XFEM/1D_Solver/testGrid.asv
Normal file
|
|
@ -0,0 +1,2 @@
|
|||
function [] = testGrid()
|
||||
|
||||
4
Unpublished/XFEM/1D_Solver/testGrid.m
Normal file
4
Unpublished/XFEM/1D_Solver/testGrid.m
Normal file
|
|
@ -0,0 +1,4 @@
|
|||
function [] = testGrid()
|
||||
[X,Y]=meshgrid(1:1:10);
|
||||
Z=2*X+Y
|
||||
surf(X,Y,Z)
|
||||
202
Unpublished/XFEM/2D_Solver/2D_XCor.for
Normal file
202
Unpublished/XFEM/2D_Solver/2D_XCor.for
Normal file
|
|
@ -0,0 +1,202 @@
|
|||
c 2D XFEM Corrosion Element
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
subroutine uel(rhs,amatrx,svars,energy,ndofel,nrhs,nsvars,props,
|
||||
1 nprops,coords,mcrd,nnode,u,du,v,a,jtype,time,dtime,kstep,kinc,
|
||||
2 jelem,params,ndload,jdltyp,adlmag,predef,npredf,lflags,
|
||||
3 mlvarx,ddlmag,mdload,pnewdt,jprops,njprop,period)
|
||||
c
|
||||
include 'aba_param.inc'
|
||||
c
|
||||
dimension rhs(mlvarx,*),amatrx(ndofel,ndofel),svars(nsvars),
|
||||
1 energy(8),props(*),coords(mcrd,nnode),
|
||||
2 u(ndofel),du(mlvarx,*),v(ndofel),a(ndofel),time(2),
|
||||
3 params(3),jdltyp(mdload,*),adlmag(mdload,*),
|
||||
4 ddlmag(mdload,*),predef(2,npredf,nnode),lflags(*),jprops(*)
|
||||
c
|
||||
dimension phig(8),phih(8),phi(8),phix(8),phiy(8)
|
||||
dimension crdnx(4),crdny(4),w(8),dndg(4),dndh(4)
|
||||
dimension theta(4),rjac(2,2),rjaci(2,2)
|
||||
c
|
||||
parameter(zero=0.d0,one=1.d0)
|
||||
c material property definition
|
||||
thick = 1.
|
||||
rho = 1.
|
||||
beta=40.
|
||||
vel=0.0
|
||||
dpos=0.25+vel*time(2)
|
||||
c initialization (nrhs=1)
|
||||
do k1=1,ndofel
|
||||
rhs(k1,nrhs)=zero
|
||||
do k2=1,ndofel
|
||||
amatrx(k2,k1)=zero
|
||||
enddo
|
||||
enddo
|
||||
if (lflags(1).eq.33) then
|
||||
do icrd=1,4
|
||||
crdnx(icrd)=coords(1,icrd)
|
||||
crdny(icrd)=coords(2,icrd)
|
||||
theta(icrd)=abs(crdnx(icrd)-dpos)*
|
||||
1 sign(1.,crdnx(icrd)-dpos)
|
||||
enddo
|
||||
if sign(1.,theta(1))/=sign(1.,theta(2))then
|
||||
c Enriched
|
||||
ienr=8
|
||||
elen=abs(crdnx(2)-crdnx(1))
|
||||
frac=abs(dpos-crdnx(1))/elen
|
||||
rlen1=2.*frac
|
||||
rlen2=2.*(1.-frac)
|
||||
rmid1=-1+rlen1/2.
|
||||
rmid2=1-rlen2/2.
|
||||
gx(1)=rmid1-(rlen1/2.)/sqrt(3.)
|
||||
gx(2)=rmid1+(rlen1/2.)/sqrt(3.)
|
||||
gx(3)=rmid1+(rlen1/2.)/sqrt(3.)
|
||||
gx(4)=rmid1-(rlen1/2.)/sqrt(3.)
|
||||
gx(5)=rmid2-(rlen2/2.)/sqrt(3.)
|
||||
gx(6)=rmid2+(rlen2/2.)/sqrt(3.)
|
||||
gx(7)=rmid2+(rlen2/2.)/sqrt(3.)
|
||||
gx(8)=rmid2-(rlen2/2.)/sqrt(3.)
|
||||
gpos=1/sqrt(3.)
|
||||
hx(1)=-gpos
|
||||
hx(2)=-gpos
|
||||
hx(3)=+gpos
|
||||
hx(4)=+gpos
|
||||
hx(5)=-gpos
|
||||
hx(6)=-gpos
|
||||
hx(7)=+gpos
|
||||
hx(8)=+gpos
|
||||
do iw=1,4
|
||||
w(iw)=frac/2.;
|
||||
w(iw+4)=(1.-frac)/2.;
|
||||
enddo
|
||||
else
|
||||
c Normal Shp Funs
|
||||
ienr=4
|
||||
gpos=1./sqrt(3.)
|
||||
gx(1)=-gpos
|
||||
gx(2)=gpos
|
||||
gx(3)=gpos
|
||||
gx(4)=-gpos
|
||||
hx(1)=-gpos
|
||||
hx(2)=-gpos
|
||||
hx(3)=gpos
|
||||
hx(4)=gpos
|
||||
do iw=1,4
|
||||
w(iw)=1.
|
||||
enddo
|
||||
endif
|
||||
c assemble amatrx and rhs
|
||||
do k=1,ienr
|
||||
c loop through gauss pts
|
||||
g=gx(k)
|
||||
h=hx(k)
|
||||
phi(1)=0.25*(1.-g)*(1.-h)
|
||||
phi(3)=0.25*(1.+g)*(1.-h)
|
||||
phi(5)=0.25*(1.+g)*(1.+h)
|
||||
phi(7)=0.25*(1.-g)*(1.+h)
|
||||
riLS=theta(1)*phi(1)+theta(2)*phi(3)+
|
||||
1 theta(3)*phi(5)+theta(4)*phi(7)
|
||||
if (riLS<0.)then
|
||||
cond=0.
|
||||
spec=0.01
|
||||
else
|
||||
cond=1.
|
||||
spec=1.
|
||||
endif
|
||||
do iter=1,4
|
||||
phi(2*iter)=phi(2*iter-1)*
|
||||
1 (abs(riLS)-abs(theta(iter)))
|
||||
enddo
|
||||
phig(1)=0.25*-(1.-h)
|
||||
phig(3)=0.25*(1.-h)
|
||||
phig(5)=0.25*(1.+h)
|
||||
phig(7)=0.25*-(1.+h)
|
||||
phih(1)=0.25*-(1.-g)
|
||||
phih(3)=0.25*-(1.+g)
|
||||
phih(5)=0.25*(1.+g)
|
||||
phih(7)=0.25*(1.-g)
|
||||
diLSg=sign(1.,iLS)*(phig(1)*theta(1)+phig(3)*
|
||||
1 theta(2)+phig(5)*theta(3)+phig(7)*theta(4))
|
||||
diLSh=sign(1.,iLS)*(phih(1)*theta(1)+phih(3)*
|
||||
1 theta(2)+phih(5)*theta(3)+phih(7)*theta(4))
|
||||
do iter=1,4
|
||||
phig(2*iter)=phig(2*iter-1)*(abs(iLS)-
|
||||
1 abs(theta(iter)))+phi(2*iter-1)*diLSg
|
||||
phih(2*iter)=phih(2*iter-1)*(abs(iLS)-
|
||||
1 abs(theta(iter)))+phi(2*iter-1)*diLSh
|
||||
enddo
|
||||
rjac=0.
|
||||
do iter=1,4
|
||||
rjac(1,1)=rjac(1,1)+phig(2*iter-1)*crdnx(iter)
|
||||
rjac(1,2)=rjac(1,2)+phig(2*iter-1)*crdny(iter)
|
||||
rjac(2,1)=rjac(2,1)+phih(2*iter-1)*crdnx(iter)
|
||||
rjac(2,2)=rjac(2,2)+phih(2*iter-1)*crdny(iter)
|
||||
enddo
|
||||
djac=rjac(1,1)*rjac(2,2)-rjac(1,2)*rjac(2,1)
|
||||
rjaci(1,1)= rjac(2,2)/djac
|
||||
rjaci(2,2)= rjac(1,1)/djac
|
||||
rjaci(1,2)=-rjac(1,2)/djac
|
||||
rjaci(2,1)=-rjac(2,1)/djac
|
||||
do iter=1,8
|
||||
phix(iter)=rjaci(1,1)*phig(iter)+rjaci(1,2)*phih(iter)
|
||||
phiy(iter)=rjaci(2,1)*phig(iter)+rjaci(2,2)*phih(iter)
|
||||
enddo
|
||||
dtdx=zero
|
||||
dtdy=zero
|
||||
t =zero
|
||||
told=zero
|
||||
do i=1,8
|
||||
dtdx=u(i)*phix(i)+dtdx
|
||||
dtdy=u(i)*phiy(i)+dtdy
|
||||
t=u(i)*phi(i)+t
|
||||
told=(u(i)-du(i,nrhs))*phi(i)+told
|
||||
end do
|
||||
dtdt=(t-told)/dtime
|
||||
we=w(k)*djac
|
||||
do ki=1,8
|
||||
c loop over nodes
|
||||
rhs(ki,nrhs) = rhs(ki,nrhs) -
|
||||
1 we*(phi(ki)*rho*spec*dtdt +
|
||||
2 cond*(phix(ki)*dtdx + phiy(ki)*dtdy))
|
||||
do kj=1,8
|
||||
amatrx(ki,kj)= amatrx(ki,kj) +
|
||||
1 we*(phi(ki)*phi(kj)*rho*spec/dtime +
|
||||
1 cond*(phix(ki)*phix(kj)+phiy(ki)*phiy(kj)))
|
||||
end do
|
||||
end do
|
||||
enddo
|
||||
c if interface is in the element a penalty term is needed
|
||||
if(enr==4)then
|
||||
xi=point
|
||||
gm(1)=(1.-xi)/2.
|
||||
gm(3)=(1.+xi)/2.
|
||||
term=theta(1)*gm(1)+theta(2)*gm(3)
|
||||
gm(2)=gm(1)*(abs(term)-abs(theta(1)))
|
||||
gm(4)=gm(3)*(abs(term)-abs(theta(2)))
|
||||
term2=gm(1)*u(1)+gm(2)*u(2)+gm(3)*u(3)+gm(4)*u(4)
|
||||
diff=abs(term2-1.)
|
||||
c add penalty flux/force: BGtc
|
||||
targetT=1.
|
||||
do i=1,4
|
||||
rhs(i,nrhs)=rhs(i,nrhs)+beta*gm(i)*diff
|
||||
enddo
|
||||
c find GtG
|
||||
gm2=0.
|
||||
do i=1,4
|
||||
do j=1,4
|
||||
gm2(i,j)=gm(i)*gm(j)
|
||||
enddo
|
||||
enddo
|
||||
c add penalty stiffness
|
||||
do i=1,4
|
||||
do j=1,4
|
||||
amatrx(i,j)=amatrx(i,j)+beta*gm2(i,j)
|
||||
enddo
|
||||
enddo
|
||||
endif
|
||||
end if
|
||||
return
|
||||
end
|
||||
78
Unpublished/XFEM/2D_Solver/AbInp.inp
Normal file
78
Unpublished/XFEM/2D_Solver/AbInp.inp
Normal file
|
|
@ -0,0 +1,78 @@
|
|||
*Heading
|
||||
** Job name: Job-1 Model name: Model-1
|
||||
** Generated by: Abaqus/CAE 6.12-1
|
||||
*Preprint, echo=NO, model=NO, history=NO, contact=NO
|
||||
**
|
||||
** PARTS
|
||||
**
|
||||
*Part, name=Part-1
|
||||
*Node
|
||||
1, 0., 0., 0.
|
||||
2, 1., 0., 0.
|
||||
3, 1., 1., 0.
|
||||
4, 0., 1., 0.
|
||||
5, 1., 2., 0.
|
||||
6, 0., 2., 0.
|
||||
*USER ELEMENT,NODES=4,TYPE=U1,PROP=1,COORDINATES=2,VAR=2,unsymm
|
||||
11,
|
||||
*Element, type=U1,ELSET=UEL
|
||||
1, 1, 2,3,4
|
||||
2, 4, 3,5,6
|
||||
*UEL Property, Elset=UEL
|
||||
1.
|
||||
*End Part
|
||||
**
|
||||
**
|
||||
** ASSEMBLY
|
||||
**
|
||||
*Assembly, name=Assembly
|
||||
**
|
||||
*Instance, name=Part-1-1, part=Part-1
|
||||
*End Instance
|
||||
**
|
||||
*Nset, nset=_PickedSet16, internal, instance=Part-1-1
|
||||
1,3,5
|
||||
*Nset, nset=_PickedSet17, internal, instance=Part-1-1
|
||||
2,4,6
|
||||
*Nset, nset=Set-6, instance=Part-1-1
|
||||
1,3,5
|
||||
*End Assembly
|
||||
**
|
||||
** MATERIALS
|
||||
**
|
||||
*Material, name=Material-1
|
||||
*Conductivity
|
||||
1.,
|
||||
*Density
|
||||
1.,
|
||||
*Specific Heat
|
||||
1.,
|
||||
** ----------------------------------------------------------------
|
||||
**
|
||||
** Name: Predefined Field-1 Type: Temperature
|
||||
*Initial Conditions, type=TEMPERATURE
|
||||
_PickedSet16, 1.,0.
|
||||
** Name: Predefined Field-2 Type: Temperature
|
||||
*Initial Conditions, type=TEMPERATURE
|
||||
_PickedSet17, 0.,0.
|
||||
** STEP: Step-1
|
||||
**
|
||||
*Step, name=Step-1
|
||||
*Heat Transfer, end=PERIOD, deltmx=100.
|
||||
0.1, 1., 1e-09, 0.1,
|
||||
**
|
||||
** BOUNDARY CONDITIONS
|
||||
**
|
||||
** Name: BC-1 Type: Temperature
|
||||
*Boundary
|
||||
Set-6, 11, 11, 1.
|
||||
**
|
||||
** OUTPUT REQUESTS
|
||||
**
|
||||
*Restart, write, frequency=0
|
||||
**
|
||||
** FIELD OUTPUT: F-Output-1
|
||||
**
|
||||
*Output, field, variable=PRESELECT
|
||||
*Output, history, frequency=0
|
||||
*End Step
|
||||
331
Unpublished/XFEM/2D_Solver/F2DLevelSetFMM.m
Normal file
331
Unpublished/XFEM/2D_Solver/F2DLevelSetFMM.m
Normal file
|
|
@ -0,0 +1,331 @@
|
|||
function [] = F2DLevelSetFMM()
|
||||
clear all
|
||||
% Define Main Solution Mesh
|
||||
NumX=32;
|
||||
NumY=32;
|
||||
delX=0.25;
|
||||
delY=0.25;
|
||||
for j=1:NumY+1
|
||||
for i=1:NumX+1
|
||||
index=i+(NumX+1)*(j-1);
|
||||
Node(index,1)=single((i-1.))*delX;
|
||||
Node(index,2)=single((j-1.))*delY;
|
||||
end
|
||||
end
|
||||
numNodes=(NumX+1)*(NumY+1);
|
||||
for j=1:NumY
|
||||
for i=1:NumX
|
||||
index=i+NumX*(j-1);
|
||||
Element(index,1)=i+(NumX+1)*(j-1);
|
||||
Element(index,2)=i+(NumX+1)*(j-1)+1;
|
||||
Element(index,3)=i+(NumX+1)*(j)+1;
|
||||
Element(index,4)=i+(NumX+1)*(j);
|
||||
end
|
||||
end
|
||||
numElem=(NumX)*(NumY);
|
||||
% Define Initial Level Set
|
||||
centx=4.;
|
||||
centy=4.;
|
||||
rad=2.1;
|
||||
for i=1:numNodes;
|
||||
dist=sqrt((Node(i,1)-centx)*(Node(i,1)-centx)+(Node(i,2)-centy)*(Node(i,2)-centy));
|
||||
lSet(i)=dist-rad;
|
||||
end
|
||||
%for i=1:numNodes;
|
||||
% dist=Node(i,1)-0.1;
|
||||
% lSet(i)=dist;
|
||||
%end
|
||||
% Plot initial level set
|
||||
[X Y]=meshgrid(0:0.25:8);
|
||||
Z=zeros(33);
|
||||
for i=1:1089
|
||||
Z(i)=lSet(i);
|
||||
end
|
||||
surf(X,Y,Z)
|
||||
% LS Algorithm Parameters
|
||||
lSet'
|
||||
bandwidth=10;
|
||||
% Loop through timesteps
|
||||
for tstep=1:10
|
||||
% Identify Narrow Band Elements
|
||||
NBElems=0;
|
||||
NBNodes=0;
|
||||
NGlobal=zeros(numNodes);
|
||||
for i=1:numElem
|
||||
check=0;
|
||||
for iNd=1:4
|
||||
if abs(lSet(Element(i,iNd)))<=bandwidth*delX
|
||||
check=1;
|
||||
end
|
||||
end
|
||||
% If an element is in the narrow band split it into triangles
|
||||
if check==1
|
||||
for j=1:4
|
||||
if NGlobal(Element(i,j))==0
|
||||
NBNodes=NBNodes+1;
|
||||
NGlobal(Element(i,j))=NBNodes;
|
||||
NLocal(NBNodes)=Element(i,j);
|
||||
end
|
||||
end
|
||||
NBElems=NBElems+1;
|
||||
NBelem(NBElems,1)=NGlobal(Element(i,1));
|
||||
NBelem(NBElems,2)=NGlobal(Element(i,2));
|
||||
NBelem(NBElems,3)=NGlobal(Element(i,3));
|
||||
NBElems=NBElems+1;
|
||||
NBelem(NBElems,1)=NGlobal(Element(i,1));
|
||||
NBelem(NBElems,2)=NGlobal(Element(i,3));
|
||||
NBelem(NBElems,3)=NGlobal(Element(i,4));
|
||||
end
|
||||
end
|
||||
% Get local Level Set
|
||||
for i=1:NBNodes
|
||||
lSetLocal(i)=lSet(NLocal(i));
|
||||
end
|
||||
% Velocity BC
|
||||
F=zeros(NBNodes,1);
|
||||
for i=1:NBElems
|
||||
L1=sign(lSetLocal(NBelem(i,1)));
|
||||
L2=sign(lSetLocal(NBelem(i,2)));
|
||||
L3=sign(lSetLocal(NBelem(i,3)));
|
||||
if L1 ~= L2 || L1 ~= L3
|
||||
F(NBelem(i,1))= 1.;
|
||||
F(NBelem(i,2))= 1.;
|
||||
F(NBelem(i,3))= 1.;
|
||||
end
|
||||
end
|
||||
% Assemble 'Stiffness' Matrices
|
||||
A=zeros(NBNodes);
|
||||
for i=1:NBElems
|
||||
gx(1)=2./3.;
|
||||
gx(2)=1./6.;
|
||||
gx(3)=1./6.;
|
||||
hx(1)=1./6.;
|
||||
hx(2)=1./6.;
|
||||
hx(3)=2./3.;
|
||||
AfL=zeros(3);
|
||||
AfLGLS=zeros(3);
|
||||
x1=Node(NLocal(NBelem(i,1)),1);
|
||||
y1=Node(NLocal(NBelem(i,1)),2);
|
||||
x2=Node(NLocal(NBelem(i,2)),1);
|
||||
y2=Node(NLocal(NBelem(i,2)),2);
|
||||
x3=Node(NLocal(NBelem(i,3)),1);
|
||||
y3=Node(NLocal(NBelem(i,3)),2);
|
||||
for j=1:3
|
||||
g=gx(j);
|
||||
h=hx(j);
|
||||
phi(1)=1.-g-h;
|
||||
phi(2)=g;
|
||||
phi(3)=h;
|
||||
phig(1)=-1.;
|
||||
phig(2)=1.;
|
||||
phig(3)=0.;
|
||||
phih(1)=-1.;
|
||||
phih(2)=0.;
|
||||
phih(3)=1.;
|
||||
djac=2*abs(x1*(y2-y3)+x2*(y3-y1)+x3*(y1-y2));
|
||||
for k=1:3
|
||||
phix(k)=(1./djac)*((-y1+y3)*phig(k)+(y1-y2)*phih(k));
|
||||
phiy(k)=(1./djac)*((x1-x3)*phig(k)+(-x1+x2)*phih(k));
|
||||
end
|
||||
delphi=[phix;phiy];
|
||||
nodalLset=[lSetLocal(NBelem(i,1));lSetLocal(NBelem(i,2));lSetLocal(NBelem(i,3))];
|
||||
set=phi*nodalLset;
|
||||
delset=delphi*nodalLset;
|
||||
AfL=AfL+(phi'*sign(set))*(delset'*delphi)/3.;
|
||||
AfLGLS=AfLGLS+(delphi'*delset)*(1./norm(delset))*(delset'*delphi)/3.;
|
||||
end
|
||||
sum=AfL+AfLGLS;
|
||||
for k=1:3;
|
||||
for j=1:3;
|
||||
A(NBelem(i,j),NBelem(i,k))=A(NBelem(i,j),NBelem(i,k))+sum(j,k);
|
||||
end
|
||||
end
|
||||
end
|
||||
% Apply BCs
|
||||
RHS=zeros(NBNodes,1);
|
||||
Sub=A*F;
|
||||
iindex=0;
|
||||
for i=1:NBNodes
|
||||
if F(i)==0.
|
||||
iindex=iindex+1;
|
||||
RHSred(iindex)=RHS(i)-Sub(i);
|
||||
Fred=0.;
|
||||
jindex=0;
|
||||
for j=1:NBNodes
|
||||
if F(j)==0.
|
||||
jindex=jindex+1;
|
||||
Ared(iindex,jindex)=A(i,j);
|
||||
end
|
||||
end
|
||||
end
|
||||
end
|
||||
% Solve for Fred
|
||||
Fred=(Ared^-1)*RHSred';
|
||||
% Get F
|
||||
iindex=0;
|
||||
for i=1:NBNodes
|
||||
if F(i)==0.
|
||||
iindex=iindex+1;
|
||||
F(i)=Fred(iindex);
|
||||
end
|
||||
end
|
||||
% Update level set
|
||||
mMat=zeros(NBNodes);
|
||||
mMatGLS=zeros(NBNodes);
|
||||
f1=zeros(NBNodes,1);
|
||||
f2=zeros(NBNodes,1);
|
||||
f3=zeros(NBNodes,1);
|
||||
h2=0.00001;
|
||||
visc=0.0005;
|
||||
for i=1:NBElems
|
||||
mMatL=zeros(3);
|
||||
mMatGLSL=zeros(3);
|
||||
f1L=zeros(3,1);
|
||||
f2L=zeros(3,1);
|
||||
f3L=zeros(3,1);
|
||||
gx(1)=2./3.;
|
||||
gx(2)=1./6.;
|
||||
gx(3)=1./6.;
|
||||
hx(1)=1./6.;
|
||||
hx(2)=1./6.;
|
||||
hx(3)=2./3.;
|
||||
x1=Node(NLocal(NBelem(i,1)),1);
|
||||
y1=Node(NLocal(NBelem(i,1)),2);
|
||||
x2=Node(NLocal(NBelem(i,2)),1);
|
||||
y2=Node(NLocal(NBelem(i,2)),2);
|
||||
x3=Node(NLocal(NBelem(i,3)),1);
|
||||
y3=Node(NLocal(NBelem(i,3)),2);
|
||||
for j=1:3
|
||||
g=gx(j);
|
||||
h=hx(j);
|
||||
phi(1)=1.-g-h;
|
||||
phi(2)=g;
|
||||
phi(3)=h;
|
||||
phig(1)=-1.;
|
||||
phig(2)=1.;
|
||||
phig(3)=0.;
|
||||
phih(1)=-1.;
|
||||
phih(2)=0.;
|
||||
phih(3)=1.;
|
||||
djac=abs(x1*(y2-y3)+x2*(y3-y1)+x3*(y1-y2));
|
||||
for k=1:3
|
||||
phix(k)=(1./djac)*((-y1+y3)*phig(k)+(y1-y2)*phih(k));
|
||||
phiy(k)=(1./djac)*((x1-x3)*phig(k)+(-x1+x2)*phih(k));
|
||||
end
|
||||
delphi=[phix;phiy];
|
||||
nodalLset=[lSetLocal(NBelem(i,1));lSetLocal(NBelem(i,2));lSetLocal(NBelem(i,3))];
|
||||
nodalF=[F(NBelem(i,1));F(NBelem(i,2));F(NBelem(i,3))];
|
||||
delset=delphi*nodalLset;
|
||||
Floc=phi*nodalF;
|
||||
mMatL=mMatL+(phi'*phi)/3.;
|
||||
mMatGLSL=mMatGLSL+((delphi'*(delset/norm(delset)))*Floc*(h2/abs(Floc)))*phi/3.;
|
||||
f1L=f1L+phi'*Floc*norm(delset)/3.;
|
||||
f2L=f2L+(delphi'*(delset/norm(delset))*Floc)*(h2/abs(Floc))*Floc*norm(delset)/3.;
|
||||
vs=h2*((abs(visc+Floc*norm(delset)))/(norm(Floc*delset)+h2));
|
||||
f3L=f3L+vs*delphi'*delset/3.;
|
||||
end
|
||||
for k=1:3;
|
||||
for j=1:3;
|
||||
mMat(NBelem(i,j),NBelem(i,k))=mMat(NBelem(i,j),NBelem(i,k))+mMatL(j,k);
|
||||
mMatGLS(NBelem(i,j),NBelem(i,k))=mMatGLS(NBelem(i,j),NBelem(i,k))+mMatGLSL(j,k);
|
||||
end
|
||||
f1(NBelem(i,k))=f1(NBelem(i,k))+f1L(k);
|
||||
f2(NBelem(i,k))=f2(NBelem(i,k))+f2L(k);
|
||||
f3(NBelem(i,k))=f3(NBelem(i,k))+f3L(k);
|
||||
end
|
||||
end
|
||||
dt=0.01;
|
||||
lSetLocal=lSetLocal-((((mMat+mMatGLS)^-1)*dt)*(f1+f2+f3))';
|
||||
newlSet=lSetLocal;
|
||||
% Reinitialize LS
|
||||
nstat=zeros(NBNodes,1);
|
||||
for i=1:NBElems
|
||||
L1=sign(lSetLocal(NBelem(i,1)));
|
||||
L2=sign(lSetLocal(NBelem(i,2)));
|
||||
L3=sign(lSetLocal(NBelem(i,3)));
|
||||
if L1 ~= L2 || L1 ~= L3
|
||||
for j=1:3
|
||||
nstat(NBelem(i,j))=1;
|
||||
end
|
||||
end
|
||||
end
|
||||
maincheck=0;
|
||||
while(maincheck==0)
|
||||
lmin=1000.;
|
||||
avlmin=1000.;
|
||||
eindex=0;
|
||||
nindex=0;
|
||||
maincheck=1;
|
||||
for i=1:NBElems
|
||||
if nstat(NBelem(i,1))+nstat(NBelem(i,2))+nstat(NBelem(i,3))==2
|
||||
maincheck=0;
|
||||
check=0;
|
||||
ltot=0.;
|
||||
for j=1:3
|
||||
if nstat(NBelem(i,j))==0
|
||||
if abs(lSetLocal(NBelem(i,j)))<=lmin
|
||||
check=1;
|
||||
tempindex=j;
|
||||
end
|
||||
end
|
||||
ltot=ltot+abs(lSetLocal(NBelem(i,j)));
|
||||
end
|
||||
if check==1 & ltot/3.<=avlmin
|
||||
eindex=i;
|
||||
nindex=tempindex;
|
||||
lmin=lSetLocal(NBelem(eindex,nindex));
|
||||
avlmin=ltot/3.;
|
||||
end
|
||||
end
|
||||
end
|
||||
if maincheck==0
|
||||
% Find New LS for point
|
||||
xp=Node(NLocal(NBelem(eindex,nindex)),1);
|
||||
yp=Node(NLocal(NBelem(eindex,nindex)),2);
|
||||
count=0;
|
||||
for i=1:3
|
||||
if i~=nindex
|
||||
count=count+1;
|
||||
x(count)=Node(NLocal(NBelem(eindex,i)),1);
|
||||
y(count)=Node(NLocal(NBelem(eindex,i)),2);
|
||||
lloc(count)=newlSet(NBelem(eindex,i));
|
||||
end
|
||||
end
|
||||
delxa=x(1)-xp;
|
||||
delya=y(1)-yp;
|
||||
delxb=x(2)-xp;
|
||||
delyb=y(2)-yp;
|
||||
N=[delxa delya; delxb delyb];
|
||||
M=N^-1;
|
||||
A=(M(1)*M(1)+M(2)*M(2));
|
||||
B=(M(3)*M(3)+M(4)*M(4));
|
||||
C=2.*(M(1)*M(3)+M(2)*M(4));
|
||||
a=A+B+C;
|
||||
b=-2.*lloc(1)*A-2.*lloc(2)*B-C*(lloc(1)+lloc(2));
|
||||
c=lloc(1)*lloc(1)*A+lloc(2)*lloc(2)*B+lloc(1)*lloc(2)*C-1.;
|
||||
templ1=(-b+sqrt(b*b-4.*a*c))/(2.*a);
|
||||
templ2=(-b-sqrt(b*b-4.*a*c))/(2.*a);
|
||||
if abs(templ1)>abs(templ2)
|
||||
newlSet(NBelem(eindex,nindex))=templ1;
|
||||
else
|
||||
newlSet(NBelem(eindex,nindex))=templ2;
|
||||
end
|
||||
nstat(NBelem(eindex,nindex))=1;
|
||||
end
|
||||
end
|
||||
% lSetLocal=newlSet;
|
||||
% Update Global Level Set
|
||||
for i=1:NBNodes
|
||||
lSet(NLocal(i))=lSetLocal(i);
|
||||
end
|
||||
end
|
||||
lSet'
|
||||
[X Y]=meshgrid(0:0.25:8);
|
||||
Z=zeros(33);
|
||||
for i=1:1089
|
||||
Z(i)=lSet(i);
|
||||
end
|
||||
surf(X,Y,Z)
|
||||
|
||||
|
||||
|
||||
165
Unpublished/XFEM/2D_Solver/FESolve2DS.asv
Normal file
165
Unpublished/XFEM/2D_Solver/FESolve2DS.asv
Normal file
|
|
@ -0,0 +1,165 @@
|
|||
function [] = FESolve2DS()
|
||||
% MATLAB based 2-D XFEM Solver
|
||||
% J. Grogan (2012)
|
||||
clear all
|
||||
% Define Mesh
|
||||
NumX=4;
|
||||
NumY=1;
|
||||
delX=0.25;
|
||||
delY=0.25;
|
||||
for j=1:NumY+1
|
||||
for i=1:NumX+1
|
||||
index=i+(NumX+1)*(j-1);
|
||||
Node(index,1)=single((i-1.))*delX;
|
||||
Node(index,2)=single((j-1.))*delY;
|
||||
end
|
||||
end
|
||||
numNodes=(NumX+1)*(NumY+1);
|
||||
for j=1:NumY
|
||||
for i=1:NumX
|
||||
index=i+NumX*(j-1);
|
||||
Element(index,1)=i+(NumX+1)*(j-1);
|
||||
Element(index,2)=i+(NumX+1)*(j-1)+1;
|
||||
Element(index,3)=i+(NumX+1)*(j)+1;
|
||||
Element(index,4)=i+(NumX+1)*(j);
|
||||
end
|
||||
end
|
||||
numElem=(NumX)*(NumY);
|
||||
% dofs per node
|
||||
ndof=1;
|
||||
% Define Section Properties
|
||||
rho=1.;
|
||||
% initial interface position
|
||||
dpos=0.6;
|
||||
% Initial temperatures
|
||||
Tnew=zeros(numNodes*2,1);
|
||||
Bound=zeros(numNodes*2,1);
|
||||
stored(1)=dpos;
|
||||
for e=1:numElem
|
||||
for n=1:4
|
||||
crdn=Node(Element(e,n),1);
|
||||
if crdn<=dpos
|
||||
Tnew(2*Element(e,n)-1)=1.;
|
||||
end
|
||||
if crdn<0.01
|
||||
Bound(2*Element(e,n)-1)=1.;
|
||||
end
|
||||
end
|
||||
end
|
||||
% Define Time Step
|
||||
dtime=0.01;
|
||||
tsteps=10;
|
||||
time=0.;
|
||||
% Loop through time steps
|
||||
for ts=1:tsteps
|
||||
K=zeros(numNodes*ndof,numNodes*ndof);
|
||||
M=zeros(numNodes*ndof,numNodes*ndof);
|
||||
pforce=zeros(numNodes*ndof,1);
|
||||
% Loop Through Elements
|
||||
for e=1:numElem
|
||||
Ke=zeros(4*ndof);
|
||||
Me=zeros(4*ndof);
|
||||
for icrd=1:4;
|
||||
crdnx(icrd)=Node(Element(e,icrd),1);
|
||||
crdny(icrd)=Node(Element(e,icrd),2);
|
||||
end
|
||||
% regular element - fix extra dofs
|
||||
enr=4;
|
||||
gpos=1/sqrt(3.);
|
||||
gx(1)=-gpos;
|
||||
gx(2)=gpos;
|
||||
gx(3)=gpos;
|
||||
gx(4)=-gpos;
|
||||
hx(1)=-gpos;
|
||||
hx(2)=-gpos;
|
||||
hx(3)=gpos;
|
||||
hx(4)=gpos;
|
||||
for iw=1:4
|
||||
w(iw)=1.;
|
||||
end
|
||||
% Loop Through Int Points
|
||||
for i=1:enr;
|
||||
g=gx(i);
|
||||
h=hx(i);
|
||||
phi(1)=0.25*(1.-g)*(1.-h);
|
||||
phi(2)=0.25*(1.+g)*(1.-h);
|
||||
phi(3)=0.25*(1.+g)*(1.+h);
|
||||
phi(4)=0.25*(1.-g)*(1.+h);
|
||||
cond=1.;
|
||||
spec=1.;
|
||||
phig(1)=0.25*-(1.-h);
|
||||
phig(2)=0.25*(1.-h);
|
||||
phig(3)=0.25*(1.+h);
|
||||
phig(4)=0.25*-(1.+h);
|
||||
phih(1)=0.25*-(1.-g);
|
||||
phih(2)=0.25*-(1.+g);
|
||||
phih(3)=0.25*(1.+g);
|
||||
phih(4)=0.25*(1.-g);
|
||||
rjac=zeros(2,2);
|
||||
for iter=1:4
|
||||
rjac(1,1)=rjac(1,1)+phig(iter)*crdnx(iter);
|
||||
rjac(1,2)=rjac(1,2)+phig(iter)*crdny(iter);
|
||||
rjac(2,1)=rjac(2,1)+phih(iter)*crdnx(iter);
|
||||
rjac(2,2)=rjac(2,2)+phih(iter)*crdny(iter);
|
||||
end
|
||||
djac=rjac(1,1)*rjac(2,2)-rjac(1,2)*rjac(2,1);
|
||||
rjaci(1,1)= rjac(2,2)/djac;
|
||||
rjaci(2,2)= rjac(1,1)/djac;
|
||||
rjaci(1,2)=-rjac(1,2)/djac;
|
||||
rjaci(2,1)=-rjac(2,1)/djac ;
|
||||
for iter=1:4
|
||||
phix(iter)=rjaci(1,1)*phig(iter)+rjaci(1,2)*phih(iter);
|
||||
phiy(iter)=rjaci(2,1)*phig(iter)+rjaci(2,2)*phih(iter);
|
||||
end
|
||||
we=w(i)*djac;
|
||||
Ke=Ke+we*cond*(phix'*phix+phiy'*phiy);
|
||||
Me=Me+(we*rho*spec*phi'*phi)/dtime;
|
||||
end
|
||||
% Assemble Global Matrices
|
||||
gnum(1)=2*Element(e,1)-1;
|
||||
gnum(2)=2*Element(e,2)-1;
|
||||
gnum(3)=2*Element(e,3)-1;
|
||||
gnum(4)=2*Element(e,4)-1;
|
||||
for i=1:4;
|
||||
for j=1:4;
|
||||
K(gnum(j),gnum(i))=K(gnum(j),gnum(i))+Ke(j,i);
|
||||
K(gnum(j)+1,gnum(i)+1)=K(gnum(j)+1,gnum(i)+1)+Ke(2*j,2*i);
|
||||
M(gnum(j),gnum(i))=M(gnum(j),gnum(i))+Me(2*j-1,2*i-1);
|
||||
M(gnum(j)+1,gnum(i)+1)=M(gnum(j)+1,gnum(i)+1)+Me(2*j,2*i);
|
||||
end
|
||||
end
|
||||
for i=1:4;
|
||||
pforce(gnum(i))=pforce(gnum(i))+pfL(2*i-1);
|
||||
pforce(gnum(i)+1)=pforce(gnum(i)+1)+pfL(2*i);
|
||||
end
|
||||
end
|
||||
%Remove inactive DOFs(Reduce Matrices)
|
||||
A=K+M;
|
||||
Sub=A*Bound;
|
||||
RHS=M*Tnew-Sub+pforce;
|
||||
iindex=0;
|
||||
for i=1:ndof*numNodes;
|
||||
if Bound(i)==0.;
|
||||
iindex=iindex+1;
|
||||
RHSR(iindex)=RHS(i);
|
||||
jindex=0;
|
||||
for j=1:ndof*numNodes;
|
||||
if Bound(j)==0.;
|
||||
jindex=jindex+1;
|
||||
AR(iindex,jindex)=A(i,j);
|
||||
end
|
||||
end
|
||||
end
|
||||
end
|
||||
%Solve
|
||||
Tnewr=(AR^-1)*RHSR';
|
||||
iindex=0;
|
||||
for i=1:ndof*numNodes;
|
||||
if Bound(i)==0.;
|
||||
iindex=iindex+1;
|
||||
Tnew(i)=Tnewr(iindex);
|
||||
end
|
||||
end
|
||||
Tnew
|
||||
end
|
||||
stored';
|
||||
151
Unpublished/XFEM/2D_Solver/FESolve2DS.m
Normal file
151
Unpublished/XFEM/2D_Solver/FESolve2DS.m
Normal file
|
|
@ -0,0 +1,151 @@
|
|||
function [] = FESolve2DS()
|
||||
% MATLAB based 2-D XFEM Solver
|
||||
% J. Grogan (2012)
|
||||
clear all
|
||||
% Define Mesh
|
||||
NumX=4;
|
||||
NumY=1;
|
||||
delX=0.25;
|
||||
delY=0.25;
|
||||
for j=1:NumY+1
|
||||
for i=1:NumX+1
|
||||
index=i+(NumX+1)*(j-1);
|
||||
Node(index,1)=single((i-1.))*delX;
|
||||
Node(index,2)=single((j-1.))*delY;
|
||||
end
|
||||
end
|
||||
numNodes=(NumX+1)*(NumY+1);
|
||||
for j=1:NumY
|
||||
for i=1:NumX
|
||||
index=i+NumX*(j-1);
|
||||
Element(index,1)=i+(NumX+1)*(j-1);
|
||||
Element(index,2)=i+(NumX+1)*(j-1)+1;
|
||||
Element(index,3)=i+(NumX+1)*(j)+1;
|
||||
Element(index,4)=i+(NumX+1)*(j);
|
||||
end
|
||||
end
|
||||
numElem=(NumX)*(NumY);
|
||||
% Define Section Properties
|
||||
rho=1.;
|
||||
% Initial temperatures
|
||||
Tnew=zeros(numNodes,1);
|
||||
Bound=zeros(numNodes,1);
|
||||
for e=1:numElem
|
||||
for n=1:4
|
||||
crdn=Node(Element(e,n),1);
|
||||
if crdn<=0.6
|
||||
Tnew(Element(e,n))=1.;
|
||||
end
|
||||
if crdn<0.01
|
||||
Bound(Element(e,n))=1.;
|
||||
end
|
||||
end
|
||||
end
|
||||
% Define Time Step
|
||||
dtime=0.01;
|
||||
tsteps=10;
|
||||
time=0.;
|
||||
% Loop through time steps
|
||||
for ts=1:tsteps
|
||||
K=zeros(numNodes,numNodes);
|
||||
M=zeros(numNodes,numNodes);
|
||||
% Loop Through Elements
|
||||
for e=1:numElem
|
||||
Ke=zeros(4);
|
||||
Me=zeros(4);
|
||||
for icrd=1:4;
|
||||
crdnx(icrd)=Node(Element(e,icrd),1);
|
||||
crdny(icrd)=Node(Element(e,icrd),2);
|
||||
end
|
||||
% regular element - fix extra dofs
|
||||
gpos=1/sqrt(3.);
|
||||
gx(1)=-gpos;
|
||||
gx(2)=gpos;
|
||||
gx(3)=gpos;
|
||||
gx(4)=-gpos;
|
||||
hx(1)=-gpos;
|
||||
hx(2)=-gpos;
|
||||
hx(3)=gpos;
|
||||
hx(4)=gpos;
|
||||
for iw=1:4
|
||||
w(iw)=1.;
|
||||
end
|
||||
% Loop Through Int Points
|
||||
for i=1:4;
|
||||
g=gx(i);
|
||||
h=hx(i);
|
||||
phi(1)=0.25*(1.-g)*(1.-h);
|
||||
phi(2)=0.25*(1.+g)*(1.-h);
|
||||
phi(3)=0.25*(1.+g)*(1.+h);
|
||||
phi(4)=0.25*(1.-g)*(1.+h);
|
||||
cond=1.;
|
||||
spec=1.;
|
||||
phig(1)=0.25*-(1.-h);
|
||||
phig(2)=0.25*(1.-h);
|
||||
phig(3)=0.25*(1.+h);
|
||||
phig(4)=0.25*-(1.+h);
|
||||
phih(1)=0.25*-(1.-g);
|
||||
phih(2)=0.25*-(1.+g);
|
||||
phih(3)=0.25*(1.+g);
|
||||
phih(4)=0.25*(1.-g);
|
||||
rjac=zeros(2,2);
|
||||
for iter=1:4
|
||||
rjac(1,1)=rjac(1,1)+phig(iter)*crdnx(iter);
|
||||
rjac(1,2)=rjac(1,2)+phig(iter)*crdny(iter);
|
||||
rjac(2,1)=rjac(2,1)+phih(iter)*crdnx(iter);
|
||||
rjac(2,2)=rjac(2,2)+phih(iter)*crdny(iter);
|
||||
end
|
||||
djac=rjac(1,1)*rjac(2,2)-rjac(1,2)*rjac(2,1);
|
||||
rjaci(1,1)= rjac(2,2)/djac;
|
||||
rjaci(2,2)= rjac(1,1)/djac;
|
||||
rjaci(1,2)=-rjac(1,2)/djac;
|
||||
rjaci(2,1)=-rjac(2,1)/djac ;
|
||||
for iter=1:4
|
||||
phix(iter)=rjaci(1,1)*phig(iter)+rjaci(1,2)*phih(iter);
|
||||
phiy(iter)=rjaci(2,1)*phig(iter)+rjaci(2,2)*phih(iter);
|
||||
end
|
||||
we=w(i)*djac;
|
||||
Ke=Ke+we*cond*(phix'*phix+phiy'*phiy);
|
||||
Me=Me+(we*rho*spec*phi'*phi)/dtime;
|
||||
end
|
||||
% Assemble Global Matrices
|
||||
gnum(1)=Element(e,1);
|
||||
gnum(2)=Element(e,2);
|
||||
gnum(3)=Element(e,3);
|
||||
gnum(4)=Element(e,4);
|
||||
for i=1:4;
|
||||
for j=1:4;
|
||||
K(gnum(j),gnum(i))=K(gnum(j),gnum(i))+Ke(j,i);
|
||||
M(gnum(j),gnum(i))=M(gnum(j),gnum(i))+Me(j,i);
|
||||
end
|
||||
end
|
||||
end
|
||||
%Remove inactive DOFs(Reduce Matrices)
|
||||
A=K+M;
|
||||
Sub=A*Bound;
|
||||
RHS=M*Tnew-Sub;
|
||||
iindex=0;
|
||||
for i=1:numNodes;
|
||||
if Bound(i)==0.;
|
||||
iindex=iindex+1;
|
||||
RHSR(iindex)=RHS(i);
|
||||
jindex=0;
|
||||
for j=1:numNodes;
|
||||
if Bound(j)==0.;
|
||||
jindex=jindex+1;
|
||||
AR(iindex,jindex)=A(i,j);
|
||||
end
|
||||
end
|
||||
end
|
||||
end
|
||||
%Solve
|
||||
Tnewr=(AR^-1)*RHSR';
|
||||
iindex=0;
|
||||
for i=1:numNodes;
|
||||
if Bound(i)==0.;
|
||||
iindex=iindex+1;
|
||||
Tnew(i)=Tnewr(iindex);
|
||||
end
|
||||
end
|
||||
Tnew
|
||||
end
|
||||
411
Unpublished/XFEM/2D_Solver/FESolveX2D.asv
Normal file
411
Unpublished/XFEM/2D_Solver/FESolveX2D.asv
Normal file
|
|
@ -0,0 +1,411 @@
|
|||
function [] = FESolveX2D()
|
||||
% MATLAB based 2-D XFEM Solver
|
||||
% J. Grogan (2012)
|
||||
clear all
|
||||
% Define Mesh
|
||||
NumX=4;
|
||||
NumY=1;
|
||||
delX=0.25;
|
||||
delY=0.25;
|
||||
for j=1:NumY+1
|
||||
for i=1:NumX+1
|
||||
index=i+(NumX+1)*(j-1);
|
||||
Node(index,1)=single((i-1.))*delX;
|
||||
Node(index,2)=single((j-1.))*delY;
|
||||
end
|
||||
end
|
||||
numNodes=(NumX+1)*(NumY+1);
|
||||
for j=1:NumY
|
||||
for i=1:NumX
|
||||
index=i+NumX*(j-1);
|
||||
Element(index,1)=i+(NumX+1)*(j-1);
|
||||
Element(index,2)=i+(NumX+1)*(j-1)+1;
|
||||
Element(index,3)=i+(NumX+1)*(j)+1;
|
||||
Element(index,4)=i+(NumX+1)*(j);
|
||||
end
|
||||
end
|
||||
numElem=(NumX)*(NumY);
|
||||
% dofs per node
|
||||
ndof=2;
|
||||
% Define Section Properties
|
||||
rho=1.;
|
||||
% initial interface position
|
||||
dpos=0.6;
|
||||
% Initial temperatures
|
||||
Tnew=zeros(numNodes*2,1);
|
||||
Bound=zeros(numNodes*2,1);
|
||||
stored(1)=dpos;
|
||||
for e=1:numElem
|
||||
for n=1:4
|
||||
crdn=Node(Element(e,n),1);
|
||||
if crdn<=dpos
|
||||
Tnew(2*Element(e,n)-1)=1.;
|
||||
end
|
||||
if crdn<0.01
|
||||
Bound(2*Element(e,n)-1)=1.;
|
||||
end
|
||||
end
|
||||
end
|
||||
% Define Time Step
|
||||
dtime=0.01;
|
||||
tsteps=10;
|
||||
time=0.;
|
||||
% penalty term
|
||||
Penalty=00.;
|
||||
% Loop through time steps
|
||||
for ts=1:tsteps
|
||||
eNodes=zeros(2*numNodes,1);
|
||||
% Get interface velocity
|
||||
d(1)=dpos+delX;
|
||||
d(2)=dpos+3*delX/4;
|
||||
d(3)=dpos+delX/4;
|
||||
d(4)=dpos;
|
||||
for e=1:numElem
|
||||
crdn1=Node(Element(e,1),1);
|
||||
crdn2=Node(Element(e,2),1);
|
||||
for j=1:4
|
||||
if d(j)>=crdn1 && d(j)<crdn2
|
||||
elen=abs(crdn2-crdn1);
|
||||
ajacob=elen/2.;
|
||||
point=(d(j)-crdn1)/ajacob-1.;
|
||||
theta(1)=abs(crdn1-dpos)*sign(crdn1-dpos);
|
||||
theta(2)=abs(crdn2-dpos)*sign(crdn2-dpos);
|
||||
tmp1a=Tnew(Element(e,1)*2-1);
|
||||
tmp1b=Tnew(Element(e,1)*2);
|
||||
tmp2a=Tnew(Element(e,2)*2-1);
|
||||
tmp2b=Tnew(Element(e,2)*2);
|
||||
xi=point;
|
||||
gm(1)=(1.-xi)/2.;
|
||||
gm(3)=(1.+xi)/2.;
|
||||
term=theta(1)*gm(1)+theta(2)*gm(3);
|
||||
gm(2)=gm(1)*(abs(term)-abs(theta(1)));
|
||||
gm(4)=gm(3)*(abs(term)-abs(theta(2)));
|
||||
t(j)=gm(1)*tmp1a+gm(2)*tmp1b+gm(3)*tmp2a+gm(4)*tmp2b;
|
||||
end
|
||||
end
|
||||
end
|
||||
% vel=-0.1*(0.5/delX)*(2*t(1)+t(2)-t(3)-2*t(4))
|
||||
vel=0.0;
|
||||
% Update interface position
|
||||
dpos=dpos+vel*dtime;
|
||||
stored(ts+1)=dpos;
|
||||
K=zeros(numNodes*ndof,numNodes*ndof);
|
||||
M=zeros(numNodes*ndof,numNodes*ndof);
|
||||
pforce=zeros(numNodes*ndof,1);
|
||||
% Loop Through Elements
|
||||
for e=1:numElem
|
||||
Ke=zeros(4*ndof);
|
||||
Me=zeros(4*ndof);
|
||||
for icrd=1:4;
|
||||
crdnx(icrd)=Node(Element(e,icrd),1);
|
||||
crdny(icrd)=Node(Element(e,icrd),2);
|
||||
theta(icrd)=abs(crdnx(icrd)-dpos)*sign(crdnx(icrd)-dpos);
|
||||
end
|
||||
if sign(theta(1))~=sign(theta(2))
|
||||
% possible enriched element
|
||||
npart=10;
|
||||
enr=npart*npart;
|
||||
for sdx=1:npart
|
||||
for sdy=1:npart
|
||||
midx=-1.-1./npart+(2./npart)*sdx;
|
||||
midy=-1.-1./npart+(2./npart)*sdy;
|
||||
subindex=npart*(sdy-1)+sdx;
|
||||
gpos=1./(sqrt(3.)*npart);
|
||||
gx(subindex,1)=midx-gpos;
|
||||
gx(subindex,2)=midx+gpos;
|
||||
gx(subindex,3)=midx+gpos;
|
||||
gx(subindex,4)=midx-gpos;
|
||||
hx(subindex,1)=midy-gpos;
|
||||
hx(subindex,2)=midy-gpos;
|
||||
hx(subindex,3)=midy+gpos;
|
||||
hx(subindex,4)=midy+gpos;
|
||||
end
|
||||
end
|
||||
% check if int points are on different sides of front
|
||||
check=0;
|
||||
for i=1:enr
|
||||
for j=1:4
|
||||
g=gx(i,j);
|
||||
h=hx(i,j);
|
||||
phi(1)=0.25*(1.-g)*(1.-h);
|
||||
phi(3)=0.25*(1.+g)*(1.-h);
|
||||
phi(5)=0.25*(1.+g)*(1.+h);
|
||||
phi(7)=0.25*(1.-g)*(1.+h);
|
||||
iLS=theta(1)*phi(1)+theta(2)*phi(3)+theta(3)*phi(5)+theta(4)*phi(7);
|
||||
if i==1 && j==1
|
||||
sgn=sign(iLS);
|
||||
else
|
||||
if sign(iLS)~=sgn
|
||||
check=1;
|
||||
end
|
||||
end
|
||||
end
|
||||
end
|
||||
if check==0
|
||||
% regular element - fix extra dofs
|
||||
enr=1;
|
||||
gpos=1/sqrt(3.);
|
||||
gx(1,1)=-gpos;
|
||||
gx(1,2)=gpos;
|
||||
gx(1,3)=gpos;
|
||||
gx(1,4)=-gpos;
|
||||
hx(1,1)=-gpos;
|
||||
hx(1,2)=-gpos;
|
||||
hx(1,3)=gpos;
|
||||
hx(1,4)=gpos;
|
||||
end
|
||||
|
||||
|
||||
eNodes(2*Element(e,1))=1;
|
||||
eNodes(2*Element(e,2))=1;
|
||||
eNodes(2*Element(e,3))=1;
|
||||
eNodes(2*Element(e,4))=1;
|
||||
% enriched element
|
||||
enr=8;
|
||||
% get interface position on element
|
||||
elen=abs(crdnx(2)-crdnx(1));
|
||||
frac=abs(dpos-crdnx(1))/elen;
|
||||
len1=2.*frac;
|
||||
len2=2.*(1.-frac);
|
||||
% devide element for sub integration
|
||||
mid1=-1+len1/2.;
|
||||
mid2=1-len2/2.;
|
||||
gx(1)=mid1-(len1/2.)/sqrt(3.);
|
||||
gx(2)=mid1+(len1/2.)/sqrt(3.);
|
||||
gx(3)=mid1+(len1/2.)/sqrt(3.);
|
||||
gx(4)=mid1-(len1/2.)/sqrt(3.);
|
||||
gx(5)=mid2-(len2/2.)/sqrt(3.);
|
||||
gx(6)=mid2+(len2/2.)/sqrt(3.);
|
||||
gx(7)=mid2+(len2/2.)/sqrt(3.);
|
||||
gx(8)=mid2-(len2/2.)/sqrt(3.);
|
||||
gpos=1/sqrt(3.);
|
||||
hx(1)=-gpos;
|
||||
hx(2)=-gpos;
|
||||
hx(3)=+gpos;
|
||||
hx(4)=+gpos;
|
||||
hx(5)=-gpos;
|
||||
hx(6)=-gpos;
|
||||
hx(7)=+gpos;
|
||||
hx(8)=+gpos;
|
||||
for iw=1:4
|
||||
w(iw)=frac/2.;
|
||||
w(iw+4)=(1.-frac)/2.;
|
||||
end
|
||||
else
|
||||
% regular element - fix extra dofs
|
||||
enr=4;
|
||||
gpos=1/sqrt(3.);
|
||||
gx(1)=-gpos;
|
||||
gx(2)=gpos;
|
||||
gx(3)=gpos;
|
||||
gx(4)=-gpos;
|
||||
hx(1)=-gpos;
|
||||
hx(2)=-gpos;
|
||||
hx(3)=gpos;
|
||||
hx(4)=gpos;
|
||||
for iw=1:4
|
||||
w(iw)=1.;
|
||||
end
|
||||
end
|
||||
% Loop Through Int Points
|
||||
for i=1:enr;
|
||||
g=gx(i);
|
||||
h=hx(i);
|
||||
phi(1)=0.25*(1.-g)*(1.-h);
|
||||
phi(3)=0.25*(1.+g)*(1.-h);
|
||||
phi(5)=0.25*(1.+g)*(1.+h);
|
||||
phi(7)=0.25*(1.-g)*(1.+h);
|
||||
iLS=theta(1)*phi(1)+theta(2)*phi(3)+theta(3)*phi(5)+theta(4)*phi(7);
|
||||
cond=1.;
|
||||
spec=1.;
|
||||
for iter=1:4
|
||||
if enr==8
|
||||
phi(2*iter)=phi(2*iter-1)*(abs(iLS)-abs(theta(iter)));
|
||||
else
|
||||
phi(2*iter)=0.;
|
||||
end
|
||||
end
|
||||
phig(1)=0.25*-(1.-h);
|
||||
phig(3)=0.25*(1.-h);
|
||||
phig(5)=0.25*(1.+h);
|
||||
phig(7)=0.25*-(1.+h);
|
||||
phih(1)=0.25*-(1.-g);
|
||||
phih(3)=0.25*-(1.+g);
|
||||
phih(5)=0.25*(1.+g);
|
||||
phih(7)=0.25*(1.-g);
|
||||
diLSg=sign(iLS)*(phig(1)*theta(1)+phig(3)*theta(2)+phig(5)*theta(3)+phig(7)*theta(4));
|
||||
diLSh=sign(iLS)*(phih(1)*theta(1)+phih(3)*theta(2)+phih(5)*theta(3)+phih(7)*theta(4));
|
||||
for iter=1:4
|
||||
if enr==8
|
||||
phig(2*iter)=phig(2*iter-1)*(abs(iLS)-abs(theta(iter)))+phi(2*iter-1)*diLSg;
|
||||
phih(2*iter)=phih(2*iter-1)*(abs(iLS)-abs(theta(iter)))+phi(2*iter-1)*diLSh;
|
||||
else
|
||||
phig(2*iter)=0.;
|
||||
phih(2*iter)=0.;
|
||||
end
|
||||
end
|
||||
rjac=zeros(2,2);
|
||||
for iter=1:4
|
||||
rjac(1,1)=rjac(1,1)+phig(2*iter-1)*crdnx(iter);
|
||||
rjac(1,2)=rjac(1,2)+phig(2*iter-1)*crdny(iter);
|
||||
rjac(2,1)=rjac(2,1)+phih(2*iter-1)*crdnx(iter);
|
||||
rjac(2,2)=rjac(2,2)+phih(2*iter-1)*crdny(iter);
|
||||
end
|
||||
djac=rjac(1,1)*rjac(2,2)-rjac(1,2)*rjac(2,1);
|
||||
rjaci(1,1)= rjac(2,2)/djac;
|
||||
rjaci(2,2)= rjac(1,1)/djac;
|
||||
rjaci(1,2)=-rjac(1,2)/djac;
|
||||
rjaci(2,1)=-rjac(2,1)/djac ;
|
||||
for iter=1:8
|
||||
phix(iter)=rjaci(1,1)*phig(iter)+rjaci(1,2)*phih(iter);
|
||||
phiy(iter)=rjaci(2,1)*phig(iter)+rjaci(2,2)*phih(iter);
|
||||
end
|
||||
we=w(i)*djac;
|
||||
Ke=Ke+we*cond*(phix'*phix+phiy'*phiy);
|
||||
Me=Me+(we*rho*spec*phi'*phi)/dtime;
|
||||
end
|
||||
% Add penalty term and get temp gradient on interface
|
||||
if enr==8;
|
||||
count=0;
|
||||
if sign(theta(1))~=sign(theta(2))
|
||||
count=count+1;
|
||||
f=abs(theta(1))/(abs(theta(1))+abs(theta(2)));
|
||||
xi(count)=f*(crdnx(2)-crdnx(1))+crdnx(1);
|
||||
yi(count)=f*(crdny(2)-crdny(1))+crdny(1);
|
||||
gi(count)=(2.*xi(count)-(crdnx(1)+crdnx(2)))/(-crdnx(1)+crdnx(2));
|
||||
hi(count)=-1.;
|
||||
end
|
||||
if sign(theta(2))~=sign(theta(3))
|
||||
count=count+1;
|
||||
f=abs(theta(2))/(abs(theta(2))+abs(theta(3)));
|
||||
xi(count)=f*(crdnx(3)-crdnx(2))+crdnx(2);
|
||||
yi(count)=f*(crdny(3)-crdny(2))+crdny(2);
|
||||
gi(count)=1.;
|
||||
hi(count)=(2.*yi(count)-(crdny(2)+crdny(3)))/(-crdny(2)+crdny(3));
|
||||
end
|
||||
if sign(theta(3))~=sign(theta(4))
|
||||
count=count+1;
|
||||
f=abs(theta(3))/(abs(theta(3))+abs(theta(4)));
|
||||
xi(count)=f*(crdnx(4)-crdnx(3))+crdnx(3);
|
||||
yi(count)=f*(crdny(4)-crdny(3))+crdny(3);
|
||||
gi(count)=(2.*xi(count)-(crdnx(4)+crdnx(3)))/(-crdnx(4)+crdnx(3));
|
||||
hi(count)=1.;
|
||||
end
|
||||
if sign(theta(1))~=sign(theta(4))
|
||||
count=count+1;
|
||||
f=abs(theta(1))/(abs(theta(1))+abs(theta(4)));
|
||||
xi(count)=f*(crdnx(4)-crdnx(1))+crdnx(1);
|
||||
yi(count)=f*(crdny(4)-crdny(1))+crdny(1);
|
||||
gi(count)=-1.;
|
||||
hi(count)=(2.*yi(count)-(crdny(1)+crdny(4)))/(-crdny(4)+crdny(1));
|
||||
end
|
||||
c=zeros(2,1);
|
||||
c=(c+1.);
|
||||
for i=1:2;
|
||||
G(i,1)=0.25*(1.-gi(i))*(1.-hi(i));
|
||||
G(i,3)=0.25*(1.+gi(i))*(1.-hi(i));
|
||||
G(i,5)=0.25*(1.+gi(i))*(1.+hi(i));
|
||||
G(i,7)=0.25*(1.-gi(i))*(1.+hi(i));
|
||||
G(i,2)=-G(i,1)*abs(theta(1));
|
||||
G(i,4)=-G(i,3)*abs(theta(2));
|
||||
G(i,6)=-G(i,5)*abs(theta(3));
|
||||
G(i,8)=-G(i,7)*abs(theta(4));
|
||||
end
|
||||
pen=Penalty*(G'*G);
|
||||
pfL=Penalty*G'*c;
|
||||
Ke=Ke+pen;
|
||||
else
|
||||
pen=zeros(8);
|
||||
pfL=zeros(8,1);
|
||||
end
|
||||
% Assemble Global Matrices
|
||||
gnum(1)=2*Element(e,1)-1;
|
||||
gnum(2)=2*Element(e,2)-1;
|
||||
gnum(3)=2*Element(e,3)-1;
|
||||
gnum(4)=2*Element(e,4)-1;
|
||||
for i=1:4;
|
||||
for j=1:4;
|
||||
K(gnum(j),gnum(i))=K(gnum(j),gnum(i))+Ke(2*j-1,2*i-1);
|
||||
K(gnum(j)+1,gnum(i))=K(gnum(j)+1,gnum(i))+Ke(2*j,2*i-1);
|
||||
K(gnum(j),gnum(i)+1)=K(gnum(j),gnum(i)+1)+Ke(2*j-1,2*i);
|
||||
K(gnum(j)+1,gnum(i)+1)=K(gnum(j)+1,gnum(i)+1)+Ke(2*j,2*i);
|
||||
M(gnum(j),gnum(i))=M(gnum(j),gnum(i))+Me(2*j-1,2*i-1);
|
||||
M(gnum(j)+1,gnum(i))=M(gnum(j)+1,gnum(i))+Me(2*j,2*i-1);
|
||||
M(gnum(j),gnum(i)+1)=M(gnum(j),gnum(i)+1)+Me(2*j-1,2*i);
|
||||
M(gnum(j)+1,gnum(i)+1)=M(gnum(j)+1,gnum(i)+1)+Me(2*j,2*i);
|
||||
end
|
||||
end
|
||||
for i=1:4;
|
||||
pforce(gnum(i))=pforce(gnum(i))+pfL(2*i-1);
|
||||
pforce(gnum(i)+1)=pforce(gnum(i)+1)+pfL(2*i);
|
||||
end
|
||||
end
|
||||
%Remove NON-ENHANCED DOFs(Reduce Matrices)
|
||||
iindex=0.;
|
||||
for i=1:ndof*numNodes;
|
||||
check=0;
|
||||
if mod(i,2)==0 && eNodes(i)~=1
|
||||
check=1;
|
||||
end
|
||||
if check==0
|
||||
iindex=iindex+1;
|
||||
TR1(iindex)=Tnew(i);
|
||||
BR1(iindex)=Bound(i);
|
||||
pforceR1(iindex)=pforce(i);
|
||||
jindex=0;
|
||||
for j=1:ndof*numNodes;
|
||||
check=0;
|
||||
if mod(j,2)==0 && eNodes(j)~=1
|
||||
check=1;
|
||||
end
|
||||
if check==0
|
||||
jindex=jindex+1;
|
||||
MR1(iindex,jindex)=M(i,j);
|
||||
KR1(iindex,jindex)=K(i,j);
|
||||
end
|
||||
end
|
||||
end
|
||||
end
|
||||
AR1=KR1+MR1;
|
||||
SubR1=AR1*BR1';
|
||||
RHSR1=MR1*TR1'-SubR1+pforceR1';
|
||||
% Apply Boundary Conditions
|
||||
Biindex=0.;
|
||||
for i=1:iindex;
|
||||
if BR1(i)==0.;
|
||||
Biindex=Biindex+1;
|
||||
RHSR2(Biindex)=RHSR1(i);
|
||||
jindex=0;
|
||||
for j=1:iindex;
|
||||
check=0;
|
||||
if BR1(j)==0.;
|
||||
jindex=jindex+1;
|
||||
AR2(Biindex,jindex)=AR1(i,j);
|
||||
end
|
||||
end
|
||||
end
|
||||
end
|
||||
%Solve
|
||||
Tnewr=(AR2^-1)*RHSR2';
|
||||
% Restore Matrices
|
||||
Biindex=0;
|
||||
for i=1:iindex;
|
||||
if BR1(i)==0.;
|
||||
Biindex=Biindex+1;
|
||||
TR1(i)=Tnewr(Biindex);
|
||||
end
|
||||
end
|
||||
iindex=0;
|
||||
for i=1:ndof*numNodes;
|
||||
check=0;
|
||||
if mod(i,2)==0 && eNodes(i)~=1
|
||||
check=1;
|
||||
end
|
||||
if check==0
|
||||
iindex=iindex+1;
|
||||
Tnew(i)=TR1(iindex);
|
||||
end
|
||||
end
|
||||
Tnew
|
||||
end
|
||||
stored';
|
||||
364
Unpublished/XFEM/2D_Solver/FESolveX2D.m
Normal file
364
Unpublished/XFEM/2D_Solver/FESolveX2D.m
Normal file
|
|
@ -0,0 +1,364 @@
|
|||
function [] = FESolveX2D()
|
||||
% MATLAB based 2-D XFEM Solver
|
||||
% J. Grogan (2012)
|
||||
clear all
|
||||
% Define Mesh
|
||||
NumX=4;
|
||||
NumY=1;
|
||||
delX=0.25;
|
||||
delY=0.25;
|
||||
for j=1:NumY+1
|
||||
for i=1:NumX+1
|
||||
index=i+(NumX+1)*(j-1);
|
||||
Node(index,1)=single((i-1.))*delX;
|
||||
Node(index,2)=single((j-1.))*delY;
|
||||
end
|
||||
end
|
||||
numNodes=(NumX+1)*(NumY+1);
|
||||
for j=1:NumY
|
||||
for i=1:NumX
|
||||
index=i+NumX*(j-1);
|
||||
Element(index,1)=i+(NumX+1)*(j-1);
|
||||
Element(index,2)=i+(NumX+1)*(j-1)+1;
|
||||
Element(index,3)=i+(NumX+1)*(j)+1;
|
||||
Element(index,4)=i+(NumX+1)*(j);
|
||||
end
|
||||
end
|
||||
numElem=(NumX)*(NumY);
|
||||
% dofs per node
|
||||
ndof=2;
|
||||
% Define Section Properties
|
||||
rho=1.;
|
||||
% initial interface position
|
||||
dpos=0.6;
|
||||
% Initial temperatures
|
||||
Tnew=zeros(numNodes*2,1);
|
||||
Bound=zeros(numNodes*2,1);
|
||||
stored(1)=dpos;
|
||||
for e=1:numElem
|
||||
for n=1:4
|
||||
crdn=Node(Element(e,n),1);
|
||||
if crdn<=dpos
|
||||
Tnew(2*Element(e,n)-1)=1.;
|
||||
end
|
||||
if crdn<0.01
|
||||
Bound(2*Element(e,n)-1)=1.;
|
||||
end
|
||||
end
|
||||
end
|
||||
% Define Time Step
|
||||
dtime=0.01;
|
||||
tsteps=10;
|
||||
time=0.;
|
||||
% penalty term
|
||||
Penalty=50.;
|
||||
% Loop through time steps
|
||||
for ts=1:tsteps
|
||||
eNodes=zeros(2*numNodes,1);
|
||||
% Get interface velocity
|
||||
d(1)=dpos+delX;
|
||||
d(2)=dpos+3*delX/4;
|
||||
d(3)=dpos+delX/4;
|
||||
d(4)=dpos;
|
||||
for e=1:numElem
|
||||
crdn1=Node(Element(e,1),1);
|
||||
crdn2=Node(Element(e,2),1);
|
||||
for j=1:4
|
||||
if d(j)>=crdn1 && d(j)<crdn2
|
||||
elen=abs(crdn2-crdn1);
|
||||
ajacob=elen/2.;
|
||||
point=(d(j)-crdn1)/ajacob-1.;
|
||||
theta(1)=abs(crdn1-dpos)*sign(crdn1-dpos);
|
||||
theta(2)=abs(crdn2-dpos)*sign(crdn2-dpos);
|
||||
tmp1a=Tnew(Element(e,1)*2-1);
|
||||
tmp1b=Tnew(Element(e,1)*2);
|
||||
tmp2a=Tnew(Element(e,2)*2-1);
|
||||
tmp2b=Tnew(Element(e,2)*2);
|
||||
xi=point;
|
||||
gm(1)=(1.-xi)/2.;
|
||||
gm(3)=(1.+xi)/2.;
|
||||
term=theta(1)*gm(1)+theta(2)*gm(3);
|
||||
gm(2)=gm(1)*(abs(term)-abs(theta(1)));
|
||||
gm(4)=gm(3)*(abs(term)-abs(theta(2)));
|
||||
t(j)=gm(1)*tmp1a+gm(2)*tmp1b+gm(3)*tmp2a+gm(4)*tmp2b;
|
||||
end
|
||||
end
|
||||
end
|
||||
% vel=-0.1*(0.5/delX)*(2*t(1)+t(2)-t(3)-2*t(4))
|
||||
vel=0.0;
|
||||
% Update interface position
|
||||
dpos=dpos+vel*dtime;
|
||||
stored(ts+1)=dpos;
|
||||
K=zeros(numNodes*ndof,numNodes*ndof);
|
||||
M=zeros(numNodes*ndof,numNodes*ndof);
|
||||
pforce=zeros(numNodes*ndof,1);
|
||||
% Loop Through Elements
|
||||
for e=1:numElem
|
||||
Ke=zeros(4*ndof);
|
||||
Me=zeros(4*ndof);
|
||||
for icrd=1:4;
|
||||
crdnx(icrd)=Node(Element(e,icrd),1);
|
||||
crdny(icrd)=Node(Element(e,icrd),2);
|
||||
theta(icrd)=abs(crdnx(icrd)-dpos)*sign(crdnx(icrd)-dpos);
|
||||
end
|
||||
if sign(theta(1))~=sign(theta(2))
|
||||
% possible enriched element
|
||||
npart=10;
|
||||
enr=npart*npart;
|
||||
for sdx=1:npart
|
||||
for sdy=1:npart
|
||||
midx=-1.-1./npart+(2./npart)*sdx;
|
||||
midy=-1.-1./npart+(2./npart)*sdy;
|
||||
subindex=npart*(sdy-1)+sdx;
|
||||
gpos=1./(sqrt(3.)*npart);
|
||||
gx(subindex,1)=midx-gpos;
|
||||
gx(subindex,2)=midx+gpos;
|
||||
gx(subindex,3)=midx+gpos;
|
||||
gx(subindex,4)=midx-gpos;
|
||||
hx(subindex,1)=midy-gpos;
|
||||
hx(subindex,2)=midy-gpos;
|
||||
hx(subindex,3)=midy+gpos;
|
||||
hx(subindex,4)=midy+gpos;
|
||||
end
|
||||
end
|
||||
% check if int points are on different sides of front
|
||||
check=0;
|
||||
for i=1:enr
|
||||
for j=1:4
|
||||
g=gx(i,j);
|
||||
h=hx(i,j);
|
||||
phi(1)=0.25*(1.-g)*(1.-h);
|
||||
phi(3)=0.25*(1.+g)*(1.-h);
|
||||
phi(5)=0.25*(1.+g)*(1.+h);
|
||||
phi(7)=0.25*(1.-g)*(1.+h);
|
||||
iLS=theta(1)*phi(1)+theta(2)*phi(3)+theta(3)*phi(5)+theta(4)*phi(7);
|
||||
if i==1 && j==1
|
||||
sgn=sign(iLS);
|
||||
else
|
||||
if sign(iLS)~=sgn
|
||||
check=1;
|
||||
end
|
||||
end
|
||||
end
|
||||
end
|
||||
if check==0
|
||||
% regular element - fix extra dofs
|
||||
enr=1;
|
||||
gpos=1/sqrt(3.);
|
||||
gx(1,1)=-gpos;
|
||||
gx(1,2)=gpos;
|
||||
gx(1,3)=gpos;
|
||||
gx(1,4)=-gpos;
|
||||
hx(1,1)=-gpos;
|
||||
hx(1,2)=-gpos;
|
||||
hx(1,3)=gpos;
|
||||
hx(1,4)=gpos;
|
||||
end
|
||||
else
|
||||
% regular element - fix extra dofs
|
||||
enr=1;
|
||||
gpos=1/sqrt(3.);
|
||||
gx(1,1)=-gpos;
|
||||
gx(1,2)=gpos;
|
||||
gx(1,3)=gpos;
|
||||
gx(1,4)=-gpos;
|
||||
hx(1,1)=-gpos;
|
||||
hx(1,2)=-gpos;
|
||||
hx(1,3)=gpos;
|
||||
hx(1,4)=gpos;
|
||||
end
|
||||
% Loop Through Int Points
|
||||
for i=1:enr
|
||||
for j=1:4
|
||||
g=gx(i,j);
|
||||
h=hx(i,j);
|
||||
phi(1)=0.25*(1.-g)*(1.-h);
|
||||
phi(3)=0.25*(1.+g)*(1.-h);
|
||||
phi(5)=0.25*(1.+g)*(1.+h);
|
||||
phi(7)=0.25*(1.-g)*(1.+h);
|
||||
iLS=theta(1)*phi(1)+theta(2)*phi(3)+theta(3)*phi(5)+theta(4)*phi(7);
|
||||
cond=1.;
|
||||
spec=1.;
|
||||
for iter=1:4
|
||||
phi(2*iter)=phi(2*iter-1)*(abs(iLS)-abs(theta(iter)));
|
||||
end
|
||||
phig(1)=0.25*-(1.-h);
|
||||
phig(3)=0.25*(1.-h);
|
||||
phig(5)=0.25*(1.+h);
|
||||
phig(7)=0.25*-(1.+h);
|
||||
phih(1)=0.25*-(1.-g);
|
||||
phih(3)=0.25*-(1.+g);
|
||||
phih(5)=0.25*(1.+g);
|
||||
phih(7)=0.25*(1.-g);
|
||||
diLSg=sign(iLS)*(phig(1)*theta(1)+phig(3)*theta(2)+phig(5)*theta(3)+phig(7)*theta(4));
|
||||
diLSh=sign(iLS)*(phih(1)*theta(1)+phih(3)*theta(2)+phih(5)*theta(3)+phih(7)*theta(4));
|
||||
for iter=1:4
|
||||
phig(2*iter)=phig(2*iter-1)*(abs(iLS)-abs(theta(iter)))+phi(2*iter-1)*diLSg;
|
||||
phih(2*iter)=phih(2*iter-1)*(abs(iLS)-abs(theta(iter)))+phi(2*iter-1)*diLSh;
|
||||
end
|
||||
rjac=zeros(2,2);
|
||||
for iter=1:4
|
||||
rjac(1,1)=rjac(1,1)+phig(2*iter-1)*crdnx(iter);
|
||||
rjac(1,2)=rjac(1,2)+phig(2*iter-1)*crdny(iter);
|
||||
rjac(2,1)=rjac(2,1)+phih(2*iter-1)*crdnx(iter);
|
||||
rjac(2,2)=rjac(2,2)+phih(2*iter-1)*crdny(iter);
|
||||
end
|
||||
djac=rjac(1,1)*rjac(2,2)-rjac(1,2)*rjac(2,1);
|
||||
rjaci(1,1)= rjac(2,2)/djac;
|
||||
rjaci(2,2)= rjac(1,1)/djac;
|
||||
rjaci(1,2)=-rjac(1,2)/djac;
|
||||
rjaci(2,1)=-rjac(2,1)/djac ;
|
||||
for iter=1:8
|
||||
phix(iter)=rjaci(1,1)*phig(iter)+rjaci(1,2)*phih(iter);
|
||||
phiy(iter)=rjaci(2,1)*phig(iter)+rjaci(2,2)*phih(iter);
|
||||
end
|
||||
we=djac;
|
||||
Ke=Ke+(we*cond*(phix'*phix+phiy'*phiy))/double(enr);
|
||||
Me=Me+((we*rho*spec*phi'*phi)/dtime)/double(enr);
|
||||
end
|
||||
end
|
||||
% Add penalty term and get temp gradient on interface
|
||||
if enr>1;
|
||||
count=0;
|
||||
if sign(theta(1))~=sign(theta(2))
|
||||
count=count+1;
|
||||
f=abs(theta(1))/(abs(theta(1))+abs(theta(2)));
|
||||
xi(count)=f*(crdnx(2)-crdnx(1))+crdnx(1);
|
||||
yi(count)=f*(crdny(2)-crdny(1))+crdny(1);
|
||||
gi(count)=(2.*xi(count)-(crdnx(1)+crdnx(2)))/(-crdnx(1)+crdnx(2));
|
||||
hi(count)=-1.;
|
||||
end
|
||||
if sign(theta(2))~=sign(theta(3))
|
||||
count=count+1;
|
||||
f=abs(theta(2))/(abs(theta(2))+abs(theta(3)));
|
||||
xi(count)=f*(crdnx(3)-crdnx(2))+crdnx(2);
|
||||
yi(count)=f*(crdny(3)-crdny(2))+crdny(2);
|
||||
gi(count)=1.;
|
||||
hi(count)=(2.*yi(count)-(crdny(2)+crdny(3)))/(-crdny(2)+crdny(3));
|
||||
end
|
||||
if sign(theta(3))~=sign(theta(4))
|
||||
count=count+1;
|
||||
f=abs(theta(3))/(abs(theta(3))+abs(theta(4)));
|
||||
xi(count)=f*(crdnx(4)-crdnx(3))+crdnx(3);
|
||||
yi(count)=f*(crdny(4)-crdny(3))+crdny(3);
|
||||
gi(count)=(2.*xi(count)-(crdnx(4)+crdnx(3)))/(-crdnx(4)+crdnx(3));
|
||||
hi(count)=1.;
|
||||
end
|
||||
if sign(theta(1))~=sign(theta(4))
|
||||
count=count+1;
|
||||
f=abs(theta(1))/(abs(theta(1))+abs(theta(4)));
|
||||
xi(count)=f*(crdnx(4)-crdnx(1))+crdnx(1);
|
||||
yi(count)=f*(crdny(4)-crdny(1))+crdny(1);
|
||||
gi(count)=-1.;
|
||||
hi(count)=(2.*yi(count)-(crdny(1)+crdny(4)))/(-crdny(4)+crdny(1));
|
||||
end
|
||||
c=zeros(2,1);
|
||||
c=(c+1.);
|
||||
for i=1:2;
|
||||
G(i,1)=0.25*(1.-gi(i))*(1.-hi(i));
|
||||
G(i,3)=0.25*(1.+gi(i))*(1.-hi(i));
|
||||
G(i,5)=0.25*(1.+gi(i))*(1.+hi(i));
|
||||
G(i,7)=0.25*(1.-gi(i))*(1.+hi(i));
|
||||
G(i,2)=-G(i,1)*abs(theta(1));
|
||||
G(i,4)=-G(i,3)*abs(theta(2));
|
||||
G(i,6)=-G(i,5)*abs(theta(3));
|
||||
G(i,8)=-G(i,7)*abs(theta(4));
|
||||
end
|
||||
pen=Penalty*(G'*G);
|
||||
pfL=Penalty*G'*c;
|
||||
Ke=Ke+pen;
|
||||
else
|
||||
pen=zeros(8);
|
||||
pfL=zeros(8,1);
|
||||
end
|
||||
% Assemble Global Matrices
|
||||
gnum(1)=2*Element(e,1)-1;
|
||||
gnum(2)=2*Element(e,2)-1;
|
||||
gnum(3)=2*Element(e,3)-1;
|
||||
gnum(4)=2*Element(e,4)-1;
|
||||
for i=1:4;
|
||||
for j=1:4;
|
||||
K(gnum(j),gnum(i))=K(gnum(j),gnum(i))+Ke(2*j-1,2*i-1);
|
||||
K(gnum(j)+1,gnum(i))=K(gnum(j)+1,gnum(i))+Ke(2*j,2*i-1);
|
||||
K(gnum(j),gnum(i)+1)=K(gnum(j),gnum(i)+1)+Ke(2*j-1,2*i);
|
||||
K(gnum(j)+1,gnum(i)+1)=K(gnum(j)+1,gnum(i)+1)+Ke(2*j,2*i);
|
||||
M(gnum(j),gnum(i))=M(gnum(j),gnum(i))+Me(2*j-1,2*i-1);
|
||||
M(gnum(j)+1,gnum(i))=M(gnum(j)+1,gnum(i))+Me(2*j,2*i-1);
|
||||
M(gnum(j),gnum(i)+1)=M(gnum(j),gnum(i)+1)+Me(2*j-1,2*i);
|
||||
M(gnum(j)+1,gnum(i)+1)=M(gnum(j)+1,gnum(i)+1)+Me(2*j,2*i);
|
||||
end
|
||||
end
|
||||
for i=1:4;
|
||||
pforce(gnum(i))=pforce(gnum(i))+pfL(2*i-1);
|
||||
pforce(gnum(i)+1)=pforce(gnum(i)+1)+pfL(2*i);
|
||||
end
|
||||
end
|
||||
%Remove NON-ENHANCED DOFs(Reduce Matrices)
|
||||
iindex=0.;
|
||||
for i=1:ndof*numNodes;
|
||||
check=0;
|
||||
% if mod(i,2)==0 && eNodes(i)~=1
|
||||
% check=1;
|
||||
% end
|
||||
if check==0
|
||||
iindex=iindex+1;
|
||||
TR1(iindex)=Tnew(i);
|
||||
BR1(iindex)=Bound(i);
|
||||
pforceR1(iindex)=pforce(i);
|
||||
jindex=0;
|
||||
for j=1:ndof*numNodes;
|
||||
check=0;
|
||||
% if mod(j,2)==0 && eNodes(j)~=1
|
||||
% check=1;
|
||||
% end
|
||||
if check==0
|
||||
jindex=jindex+1;
|
||||
MR1(iindex,jindex)=M(i,j);
|
||||
KR1(iindex,jindex)=K(i,j);
|
||||
end
|
||||
end
|
||||
end
|
||||
end
|
||||
AR1=KR1+MR1;
|
||||
SubR1=AR1*BR1';
|
||||
RHSR1=MR1*TR1'-SubR1+pforceR1';
|
||||
% Apply Boundary Conditions
|
||||
Biindex=0.;
|
||||
for i=1:iindex;
|
||||
if BR1(i)==0.;
|
||||
Biindex=Biindex+1;
|
||||
RHSR2(Biindex)=RHSR1(i);
|
||||
jindex=0;
|
||||
for j=1:iindex;
|
||||
check=0;
|
||||
if BR1(j)==0.;
|
||||
jindex=jindex+1;
|
||||
AR2(Biindex,jindex)=AR1(i,j);
|
||||
end
|
||||
end
|
||||
end
|
||||
end
|
||||
%Solve
|
||||
Tnewr=(AR2^-1)*RHSR2';
|
||||
% Restore Matrices
|
||||
Biindex=0;
|
||||
for i=1:iindex;
|
||||
if BR1(i)==0.;
|
||||
Biindex=Biindex+1;
|
||||
TR1(i)=Tnewr(Biindex);
|
||||
end
|
||||
end
|
||||
iindex=0;
|
||||
for i=1:ndof*numNodes;
|
||||
check=0;
|
||||
% if mod(i,2)==0 && eNodes(i)~=1
|
||||
% check=1;
|
||||
% end
|
||||
if check==0
|
||||
iindex=iindex+1;
|
||||
Tnew(i)=TR1(iindex);
|
||||
end
|
||||
end
|
||||
Tnew
|
||||
end
|
||||
stored';
|
||||
269
Unpublished/XFEM/2D_Solver/FESolveX2DLS.m
Normal file
269
Unpublished/XFEM/2D_Solver/FESolveX2DLS.m
Normal file
|
|
@ -0,0 +1,269 @@
|
|||
function [] = FESolveX2DLS()
|
||||
% MATLAB based 2-D XFEM Solver
|
||||
% J. Grogan (2012)
|
||||
clear all
|
||||
% Define Mesh
|
||||
NumX=3;
|
||||
NumY=1;
|
||||
delX=1.;
|
||||
delY=1.;
|
||||
for j=1:NumY+1
|
||||
for i=1:NumX+1
|
||||
index=i+(NumX+1)*(j-1);
|
||||
Node(index,1)=single((i-1.))*delX;
|
||||
Node(index,2)=single((j-1.))*delY;
|
||||
end
|
||||
end
|
||||
numNodes=(NumX+1)*(NumY+1);
|
||||
for j=1:NumY
|
||||
for i=1:NumX
|
||||
index=i+NumX*(j-1);
|
||||
Element(index,1)=i+(NumX+1)*(j-1);
|
||||
Element(index,2)=i+(NumX+1)*(j-1)+1;
|
||||
Element(index,3)=i+(NumX+1)*(j)+1;
|
||||
Element(index,4)=i+(NumX+1)*(j);
|
||||
end
|
||||
end
|
||||
numElem=(NumX)*(NumY);
|
||||
% dofs per node
|
||||
ndof=2;
|
||||
% Define Section Properties
|
||||
rho=1.;
|
||||
% initial interface position
|
||||
dpos=0.1;
|
||||
% Initial temperatures
|
||||
Tnew=zeros(numNodes*2,1);
|
||||
Bound=zeros(numNodes*2,1);
|
||||
stored(1)=dpos;
|
||||
for e=1:numElem
|
||||
for n=1:4
|
||||
crdn=Node(Element(e,n),1);
|
||||
if crdn<=dpos
|
||||
Tnew(2*Element(e,n)-1)=1.;
|
||||
Bound(2*Element(e,n)-1)=1.;
|
||||
end
|
||||
end
|
||||
end
|
||||
% Define Time Step
|
||||
dtime=0.1;
|
||||
tsteps=20;
|
||||
time=0.;
|
||||
% penalty term
|
||||
beta=80.;
|
||||
% Loop through time steps
|
||||
for ts=1:tsteps
|
||||
% Get interface velocity
|
||||
d(1)=dpos+delX;
|
||||
d(2)=dpos+3*delX/4;
|
||||
d(3)=dpos+delX/4;
|
||||
d(4)=dpos;
|
||||
for e=1:numElem
|
||||
crdn1=Node(Element(e,1),1);
|
||||
crdn2=Node(Element(e,2),1);
|
||||
for j=1:4
|
||||
if d(j)>=crdn1 & d(j)<crdn2
|
||||
elen=abs(crdn2-crdn1);
|
||||
ajacob=elen/2.;
|
||||
point=(d(j)-crdn1)/ajacob-1.;
|
||||
theta(1)=abs(crdn1-dpos)*sign(crdn1-dpos);
|
||||
theta(2)=abs(crdn2-dpos)*sign(crdn2-dpos);
|
||||
tmp1a=Tnew(Element(e,1)*2-1);
|
||||
tmp1b=Tnew(Element(e,1)*2);
|
||||
tmp2a=Tnew(Element(e,2)*2-1);
|
||||
tmp2b=Tnew(Element(e,2)*2);
|
||||
xi=point;
|
||||
gm(1)=(1.-xi)/2.;
|
||||
gm(3)=(1.+xi)/2.;
|
||||
term=theta(1)*gm(1)+theta(2)*gm(3);
|
||||
gm(2)=gm(1)*(abs(term)-abs(theta(1)));
|
||||
gm(4)=gm(3)*(abs(term)-abs(theta(2)));
|
||||
t(j)=gm(1)*tmp1a+gm(2)*tmp1b+gm(3)*tmp2a+gm(4)*tmp2b;
|
||||
end
|
||||
end
|
||||
end
|
||||
% vel=-0.1*(0.5/delX)*(2*t(1)+t(2)-t(3)-2*t(4))
|
||||
vel=0.0;
|
||||
% Update interface position
|
||||
dpos=dpos+vel*dtime;
|
||||
stored(ts+1)=dpos;
|
||||
K=zeros(numNodes*ndof,numNodes*ndof);
|
||||
M=zeros(numNodes*ndof,numNodes*ndof);
|
||||
pforce=zeros(numNodes*ndof,1);
|
||||
% Loop Through Elements
|
||||
for e=1:numElem
|
||||
Ke=zeros(4*ndof);
|
||||
Me=zeros(4*ndof);
|
||||
for icrd=1:4;
|
||||
crdnx(icrd)=Node(Element(e,icrd),1);
|
||||
crdny(icrd)=Node(Element(e,icrd),2);
|
||||
theta(icrd)=abs(crdnx(icrd)-dpos)*sign(crdnx(icrd)-dpos);
|
||||
end
|
||||
if sign(theta(1))~=sign(theta(2))
|
||||
% enriched element
|
||||
enr=8;
|
||||
% get interface position on element
|
||||
elen=abs(crdnx(2)-crdnx(1));
|
||||
frac=abs(dpos-crdnx(1))/elen;
|
||||
len1=2.*frac;
|
||||
len2=2.*(1.-frac);
|
||||
% devide element for sub integration
|
||||
mid1=-1+len1/2.;
|
||||
mid2=1-len2/2.;
|
||||
gx(1)=mid1-(len1/2.)/sqrt(3.);
|
||||
gx(2)=mid1+(len1/2.)/sqrt(3.);
|
||||
gx(3)=mid1+(len1/2.)/sqrt(3.);
|
||||
gx(4)=mid1-(len1/2.)/sqrt(3.);
|
||||
gx(5)=mid2-(len2/2.)/sqrt(3.);
|
||||
gx(6)=mid2+(len2/2.)/sqrt(3.);
|
||||
gx(7)=mid2+(len2/2.)/sqrt(3.);
|
||||
gx(8)=mid2-(len2/2.)/sqrt(3.);
|
||||
gpos=1/sqrt(3.);
|
||||
hx(1)=-gpos;
|
||||
hx(2)=-gpos;
|
||||
hx(3)=+gpos;
|
||||
hx(4)=+gpos;
|
||||
hx(5)=-gpos;
|
||||
hx(6)=-gpos;
|
||||
hx(7)=+gpos;
|
||||
hx(8)=+gpos;
|
||||
for iw=1:4
|
||||
w(iw)=frac/2.;
|
||||
w(iw+4)=(1.-frac)/2.;
|
||||
end
|
||||
else
|
||||
% regular element - fix extra dofs
|
||||
enr=4;
|
||||
gpos=1/sqrt(3.);
|
||||
gx(1)=-gpos;
|
||||
gx(2)=gpos;
|
||||
gx(3)=gpos;
|
||||
gx(4)=-gpos;
|
||||
hx(1)=-gpos;
|
||||
hx(2)=-gpos;
|
||||
hx(3)=gpos;
|
||||
hx(4)=gpos;
|
||||
for iw=1:4
|
||||
w(iw)=1.;
|
||||
end
|
||||
end
|
||||
% Loop Through Int Points
|
||||
for i=1:enr;
|
||||
g=gx(i);
|
||||
h=hx(i);
|
||||
phi(1)=0.25*(1.-g)*(1.-h);
|
||||
phi(3)=0.25*(1.+g)*(1.-h);
|
||||
phi(5)=0.25*(1.+g)*(1.+h);
|
||||
phi(7)=0.25*(1.-g)*(1.+h);
|
||||
iLS=theta(1)*phi(1)+theta(2)*phi(3)+theta(3)*phi(5)+theta(4)*phi(7);
|
||||
if iLS<0.
|
||||
cond=0.;
|
||||
spec=0.01;
|
||||
else
|
||||
cond=1.;
|
||||
spec=1.;
|
||||
end
|
||||
for iter=1:4
|
||||
phi(2*iter)=phi(2*iter-1)*(abs(iLS)-abs(theta(iter)));
|
||||
end
|
||||
phig(1)=0.25*-(1.-h);
|
||||
phig(3)=0.25*(1.-h);
|
||||
phig(5)=0.25*(1.+h);
|
||||
phig(7)=0.25*-(1.+h);
|
||||
phih(1)=0.25*-(1.-g);
|
||||
phih(3)=0.25*-(1.+g);
|
||||
phih(5)=0.25*(1.+g);
|
||||
phih(7)=0.25*(1.-g);
|
||||
diLSg=sign(iLS)*(phig(1)*theta(1)+phig(3)*theta(2)+phig(5)*theta(3)+phig(7)*theta(4));
|
||||
diLSh=sign(iLS)*(phih(1)*theta(1)+phih(3)*theta(2)+phih(5)*theta(3)+phih(7)*theta(4));
|
||||
for iter=1:4
|
||||
phig(2*iter)=phig(2*iter-1)*(abs(iLS)-abs(theta(iter)))+phi(2*iter-1)*diLSg;
|
||||
phih(2*iter)=phih(2*iter-1)*(abs(iLS)-abs(theta(iter)))+phi(2*iter-1)*diLSh;
|
||||
end
|
||||
rjac=zeros(2,2);
|
||||
for iter=1:4
|
||||
rjac(1,1)=rjac(1,1)+phig(2*iter-1)*crdnx(iter);
|
||||
rjac(1,2)=rjac(1,2)+phig(2*iter-1)*crdny(iter);
|
||||
rjac(2,1)=rjac(2,1)+phih(2*iter-1)*crdnx(iter);
|
||||
rjac(2,2)=rjac(2,2)+phih(2*iter-1)*crdny(iter);
|
||||
end
|
||||
djac=rjac(1,1)*rjac(2,2)-rjac(1,2)*rjac(2,1);
|
||||
rjaci(1,1)= rjac(2,2)/djac;
|
||||
rjaci(2,2)= rjac(1,1)/djac;
|
||||
rjaci(1,2)=-rjac(1,2)/djac;
|
||||
rjaci(2,1)=-rjac(2,1)/djac ;
|
||||
for iter=1:8
|
||||
phix(iter)=rjaci(1,1)*phig(iter)+rjaci(1,2)*phih(iter);
|
||||
phiy(iter)=rjaci(2,1)*phig(iter)+rjaci(2,2)*phih(iter);
|
||||
end
|
||||
we=w(i)*djac;
|
||||
Ke=Ke+we*cond*(phix'*phix+phiy'*phiy);
|
||||
Me=Me+(we*rho*spec*phi'*phi)/dtime;
|
||||
end
|
||||
% Add penalty term and get temp gradient on interface
|
||||
if enr==8;
|
||||
xi=2.*frac-1;
|
||||
yi=0.;
|
||||
gm(1)=0.25*(1.-xi)*(1.-yi);
|
||||
gm(3)=0.25*(1.+xi)*(1.-yi);
|
||||
gm(5)=0.25*(1.+xi)*(1.+yi);
|
||||
gm(7)=0.25*(1.-xi)*(1.+yi);
|
||||
gm(2)=gm(1)*(-abs(theta(1)));
|
||||
gm(4)=gm(3)*(-abs(theta(2)));
|
||||
gm(6)=gm(5)*(-abs(theta(3)));
|
||||
gm(8)=gm(7)*(-abs(theta(4)));
|
||||
pen=beta*(gm'*gm);
|
||||
pfL=beta*1.*gm';
|
||||
Ke=Ke+pen;
|
||||
else
|
||||
pen=zeros(8);
|
||||
pfL=zeros(8,1);
|
||||
end
|
||||
% Assemble Global Matrices
|
||||
gnum(1)=2*Element(e,1)-1;
|
||||
gnum(2)=2*Element(e,2)-1;
|
||||
gnum(3)=2*Element(e,3)-1;
|
||||
gnum(4)=2*Element(e,4)-1;
|
||||
for i=1:4;
|
||||
for j=1:4;
|
||||
K(gnum(j),gnum(i))=K(gnum(j),gnum(i))+Ke(2*j-1,2*i-1);
|
||||
K(gnum(j)+1,gnum(i)+1)=K(gnum(j)+1,gnum(i)+1)+Ke(2*j,2*i);
|
||||
M(gnum(j),gnum(i))=M(gnum(j),gnum(i))+Me(2*j-1,2*i-1);
|
||||
M(gnum(j)+1,gnum(i)+1)=M(gnum(j)+1,gnum(i)+1)+Me(2*j,2*i);
|
||||
end
|
||||
end
|
||||
for i=1:4;
|
||||
pforce(gnum(i))=pforce(gnum(i))+pfL(2*i-1);
|
||||
pforce(gnum(i)+1)=pforce(gnum(i)+1)+pfL(2*i);
|
||||
end
|
||||
end
|
||||
%Remove inactive DOFs(Reduce Matrices)
|
||||
RHS=M*Tnew;
|
||||
A=K+M;
|
||||
Sub=A*Bound;
|
||||
iindex=0;
|
||||
for i=1:ndof*numNodes;
|
||||
if Bound(i)==0.;
|
||||
iindex=iindex+1;
|
||||
RHSred(iindex)=RHS(i)-Sub(i)+pforce(i);
|
||||
jindex=0;
|
||||
for j=1:ndof*numNodes;
|
||||
if Bound(j)==0.;
|
||||
jindex=jindex+1;
|
||||
Ared(iindex,jindex)=A(i,j);
|
||||
end
|
||||
end
|
||||
end
|
||||
end
|
||||
%Solve
|
||||
StiffI=Ared^-1;
|
||||
Tnewr=(Ared^-1)*RHSred';
|
||||
iindex=0;
|
||||
for i=1:ndof*numNodes;
|
||||
if Bound(i)==0.;
|
||||
iindex=iindex+1;
|
||||
Tnew(i)=Tnewr(iindex);
|
||||
end
|
||||
end
|
||||
Tnew
|
||||
end
|
||||
stored'
|
||||
305
Unpublished/XFEM/2D_Solver/FESolveX2Db.asv
Normal file
305
Unpublished/XFEM/2D_Solver/FESolveX2Db.asv
Normal file
|
|
@ -0,0 +1,305 @@
|
|||
function [] = FESolveX2Db()
|
||||
% MATLAB based 2-D XFEM Solver
|
||||
% J. Grogan (2012)
|
||||
clear all
|
||||
% Define Mesh
|
||||
NumX=2;
|
||||
NumY=1;
|
||||
delX=0.25;
|
||||
delY=0.25;
|
||||
for j=1:NumY+1
|
||||
for i=1:NumX+1
|
||||
index=i+(NumX+1)*(j-1);
|
||||
Node(index,1)=single((i-1.))*delX;
|
||||
Node(index,2)=single((j-1.))*delY;
|
||||
end
|
||||
end
|
||||
numNodes=(NumX+1)*(NumY+1);
|
||||
for j=1:NumY
|
||||
for i=1:NumX
|
||||
index=i+NumX*(j-1);
|
||||
Element(index,1)=i+(NumX+1)*(j-1);
|
||||
Element(index,2)=i+(NumX+1)*(j-1)+1;
|
||||
Element(index,3)=i+(NumX+1)*(j)+1;
|
||||
Element(index,4)=i+(NumX+1)*(j);
|
||||
end
|
||||
end
|
||||
numElem=(NumX)*(NumY);
|
||||
% dofs per node
|
||||
ndof=2;
|
||||
% Define Section Properties
|
||||
rho=1.;
|
||||
% initial interface position
|
||||
dpos=0.4;
|
||||
% Initial temperatures
|
||||
Tnew=zeros(numNodes*2,1);
|
||||
Bound=zeros(numNodes*2,1);
|
||||
stored(1)=dpos;
|
||||
for e=1:numElem
|
||||
for n=1:4
|
||||
crdn=Node(Element(e,n),1);
|
||||
if crdn<=dpos
|
||||
Tnew(2*Element(e,n)-1)=1.;
|
||||
end
|
||||
if crdn<0.01
|
||||
Bound(2*Element(e,n)-1)=1.;
|
||||
end
|
||||
end
|
||||
end
|
||||
% Define Time Step
|
||||
dtime=0.01;
|
||||
tsteps=1;
|
||||
time=0.;
|
||||
% penalty term
|
||||
Penalty=00.;
|
||||
% Loop through time steps
|
||||
for ts=1:tsteps
|
||||
% Get interface velocity
|
||||
d(1)=dpos+delX;
|
||||
d(2)=dpos+3*delX/4;
|
||||
d(3)=dpos+delX/4;
|
||||
d(4)=dpos;
|
||||
for e=1:numElem
|
||||
crdn1=Node(Element(e,1),1);
|
||||
crdn2=Node(Element(e,2),1);
|
||||
for j=1:4
|
||||
if d(j)>=crdn1 && d(j)<crdn2
|
||||
elen=abs(crdn2-crdn1);
|
||||
ajacob=elen/2.;
|
||||
point=(d(j)-crdn1)/ajacob-1.;
|
||||
theta(1)=abs(crdn1-dpos)*sign(crdn1-dpos);
|
||||
theta(2)=abs(crdn2-dpos)*sign(crdn2-dpos);
|
||||
tmp1a=Tnew(Element(e,1)*2-1);
|
||||
tmp1b=Tnew(Element(e,1)*2);
|
||||
tmp2a=Tnew(Element(e,2)*2-1);
|
||||
tmp2b=Tnew(Element(e,2)*2);
|
||||
xi=point;
|
||||
gm(1)=(1.-xi)/2.;
|
||||
gm(3)=(1.+xi)/2.;
|
||||
term=theta(1)*gm(1)+theta(2)*gm(3);
|
||||
gm(2)=gm(1)*(abs(term)-abs(theta(1)));
|
||||
gm(4)=gm(3)*(abs(term)-abs(theta(2)));
|
||||
t(j)=gm(1)*tmp1a+gm(2)*tmp1b+gm(3)*tmp2a+gm(4)*tmp2b;
|
||||
end
|
||||
end
|
||||
end
|
||||
% vel=-0.1*(0.5/delX)*(2*t(1)+t(2)-t(3)-2*t(4))
|
||||
vel=0.0;
|
||||
% Update interface position
|
||||
dpos=dpos+vel*dtime;
|
||||
stored(ts+1)=dpos;
|
||||
K=zeros(numNodes*ndof,numNodes*ndof);
|
||||
M=zeros(numNodes*ndof,numNodes*ndof);
|
||||
pforce=zeros(numNodes*ndof,1);
|
||||
% Loop Through Elements
|
||||
for e=1:numElem
|
||||
Ke=zeros(4*ndof);
|
||||
Me=zeros(4*ndof);
|
||||
for icrd=1:4;
|
||||
crdnx(icrd)=Node(Element(e,icrd),1);
|
||||
crdny(icrd)=Node(Element(e,icrd),2);
|
||||
theta(icrd)=abs(crdnx(icrd)-dpos)*sign(crdnx(icrd)-dpos);
|
||||
end
|
||||
if sign(theta(1))~=sign(theta(2))
|
||||
% enriched element
|
||||
enr=8;
|
||||
% get interface position on element
|
||||
elen=abs(crdnx(2)-crdnx(1));
|
||||
frac=abs(dpos-crdnx(1))/elen;
|
||||
len1=2.*frac;
|
||||
len2=2.*(1.-frac);
|
||||
% devide element for sub integration
|
||||
mid1=-1+len1/2.;
|
||||
mid2=1-len2/2.;
|
||||
gx(1)=mid1-(len1/2.)/sqrt(3.);
|
||||
gx(2)=mid1+(len1/2.)/sqrt(3.);
|
||||
gx(3)=mid1+(len1/2.)/sqrt(3.);
|
||||
gx(4)=mid1-(len1/2.)/sqrt(3.);
|
||||
gx(5)=mid2-(len2/2.)/sqrt(3.);
|
||||
gx(6)=mid2+(len2/2.)/sqrt(3.);
|
||||
gx(7)=mid2+(len2/2.)/sqrt(3.);
|
||||
gx(8)=mid2-(len2/2.)/sqrt(3.);
|
||||
gpos=1/sqrt(3.);
|
||||
hx(1)=-gpos;
|
||||
hx(2)=-gpos;
|
||||
hx(3)=+gpos;
|
||||
hx(4)=+gpos;
|
||||
hx(5)=-gpos;
|
||||
hx(6)=-gpos;
|
||||
hx(7)=+gpos;
|
||||
hx(8)=+gpos;
|
||||
for iw=1:4
|
||||
w(iw)=frac/2.;
|
||||
w(iw+4)=(1.-frac)/2.;
|
||||
end
|
||||
else
|
||||
% regular element - fix extra dofs
|
||||
enr=4;
|
||||
gpos=1/sqrt(3.);
|
||||
gx(1)=-gpos;
|
||||
gx(2)=gpos;
|
||||
gx(3)=gpos;
|
||||
gx(4)=-gpos;
|
||||
hx(1)=-gpos;
|
||||
hx(2)=-gpos;
|
||||
hx(3)=gpos;
|
||||
hx(4)=gpos;
|
||||
for iw=1:4
|
||||
w(iw)=1.;
|
||||
end
|
||||
end
|
||||
% Loop Through Int Points
|
||||
for i=1:enr;
|
||||
g=gx(i);
|
||||
h=hx(i);
|
||||
phi(1)=0.25*(1.-g)*(1.-h);
|
||||
phi(3)=0.25*(1.+g)*(1.-h);
|
||||
phi(5)=0.25*(1.+g)*(1.+h);
|
||||
phi(7)=0.25*(1.-g)*(1.+h);
|
||||
iLS=theta(1)*phi(1)+theta(2)*phi(3)+theta(3)*phi(5)+theta(4)*phi(7);
|
||||
cond=1.;
|
||||
spec=1.;
|
||||
for iter=1:4
|
||||
phi(2*iter)=phi(2*iter-1)*(abs(iLS)-abs(theta(iter)));
|
||||
end
|
||||
phig(1)=0.25*-(1.-h);
|
||||
phig(3)=0.25*(1.-h);
|
||||
phig(5)=0.25*(1.+h);
|
||||
phig(7)=0.25*-(1.+h);
|
||||
phih(1)=0.25*-(1.-g);
|
||||
phih(3)=0.25*-(1.+g);
|
||||
phih(5)=0.25*(1.+g);
|
||||
phih(7)=0.25*(1.-g);
|
||||
diLSg=sign(iLS)*(phig(1)*theta(1)+phig(3)*theta(2)+phig(5)*theta(3)+phig(7)*theta(4));
|
||||
diLSh=sign(iLS)*(phih(1)*theta(1)+phih(3)*theta(2)+phih(5)*theta(3)+phih(7)*theta(4));
|
||||
for iter=1:4
|
||||
phig(2*iter)=phig(2*iter-1)*(abs(iLS)-abs(theta(iter)))+phi(2*iter-1)*diLSg;
|
||||
phih(2*iter)=phih(2*iter-1)*(abs(iLS)-abs(theta(iter)))+phi(2*iter-1)*diLSh;
|
||||
end
|
||||
rjac=zeros(2,2);
|
||||
for iter=1:4
|
||||
rjac(1,1)=rjac(1,1)+phig(2*iter-1)*crdnx(iter);
|
||||
rjac(1,2)=rjac(1,2)+phig(2*iter-1)*crdny(iter);
|
||||
rjac(2,1)=rjac(2,1)+phih(2*iter-1)*crdnx(iter);
|
||||
rjac(2,2)=rjac(2,2)+phih(2*iter-1)*crdny(iter);
|
||||
end
|
||||
djac=rjac(1,1)*rjac(2,2)-rjac(1,2)*rjac(2,1);
|
||||
rjaci(1,1)= rjac(2,2)/djac;
|
||||
rjaci(2,2)= rjac(1,1)/djac;
|
||||
rjaci(1,2)=-rjac(1,2)/djac;
|
||||
rjaci(2,1)=-rjac(2,1)/djac ;
|
||||
for iter=1:8
|
||||
phix(iter)=rjaci(1,1)*phig(iter)+rjaci(1,2)*phih(iter);
|
||||
phiy(iter)=rjaci(2,1)*phig(iter)+rjaci(2,2)*phih(iter);
|
||||
end
|
||||
we=w(i)*djac;
|
||||
Ke=Ke+we*cond*(phix'*phix+phiy'*phiy);
|
||||
Me=Me+(we*rho*spec*phi'*phi)/dtime;
|
||||
end
|
||||
Me
|
||||
% Add penalty term and get temp gradient on interface
|
||||
if enr==8;
|
||||
count=0;
|
||||
if sign(theta(1))~=sign(theta(2))
|
||||
count=count+1;
|
||||
f=abs(theta(1))/(abs(theta(1))+abs(theta(2)));
|
||||
xi(count)=f*(crdnx(2)-crdnx(1))+crdnx(1);
|
||||
yi(count)=f*(crdny(2)-crdny(1))+crdny(1);
|
||||
gi(count)=(2.*xi(count)-(crdnx(1)+crdnx(2)))/(-crdnx(1)+crdnx(2));
|
||||
hi(count)=-1.;
|
||||
end
|
||||
if sign(theta(2))~=sign(theta(3))
|
||||
count=count+1;
|
||||
f=abs(theta(2))/(abs(theta(2))+abs(theta(3)));
|
||||
xi(count)=f*(crdnx(3)-crdnx(2))+crdnx(2);
|
||||
yi(count)=f*(crdny(3)-crdny(2))+crdny(2);
|
||||
gi(count)=1.;
|
||||
hi(count)=(2.*yi(count)-(crdny(2)+crdny(3)))/(-crdny(2)+crdny(3));
|
||||
end
|
||||
if sign(theta(3))~=sign(theta(4))
|
||||
count=count+1;
|
||||
f=abs(theta(3))/(abs(theta(3))+abs(theta(4)));
|
||||
xi(count)=f*(crdnx(4)-crdnx(3))+crdnx(3);
|
||||
yi(count)=f*(crdny(4)-crdny(3))+crdny(3);
|
||||
gi(count)=(2.*xi(count)-(crdnx(4)+crdnx(3)))/(-crdnx(4)+crdnx(3));
|
||||
hi(count)=1.;
|
||||
end
|
||||
if sign(theta(1))~=sign(theta(4))
|
||||
count=count+1;
|
||||
f=abs(theta(1))/(abs(theta(1))+abs(theta(4)));
|
||||
xi(count)=f*(crdnx(4)-crdnx(1))+crdnx(1);
|
||||
yi(count)=f*(crdny(4)-crdny(1))+crdny(1);
|
||||
gi(count)=-1.;
|
||||
hi(count)=(2.*yi(count)-(crdny(1)+crdny(4)))/(-crdny(4)+crdny(1));
|
||||
end
|
||||
c=zeros(2,1);
|
||||
c=(c+1.);
|
||||
for i=1:2;
|
||||
G(i,1)=0.25*(1.-gi(i))*(1.-hi(i));
|
||||
G(i,3)=0.25*(1.+gi(i))*(1.-hi(i));
|
||||
G(i,5)=0.25*(1.+gi(i))*(1.+hi(i));
|
||||
G(i,7)=0.25*(1.-gi(i))*(1.+hi(i));
|
||||
G(i,2)=-G(i,1)*abs(theta(1));
|
||||
G(i,4)=-G(i,3)*abs(theta(2));
|
||||
G(i,6)=-G(i,5)*abs(theta(3));
|
||||
G(i,8)=-G(i,7)*abs(theta(4));
|
||||
end
|
||||
pen=Penalty*(G'*G);
|
||||
pfL=Penalty*G'*c;
|
||||
Ke=Ke+pen;
|
||||
else
|
||||
pen=zeros(8);
|
||||
pfL=zeros(8,1);
|
||||
end
|
||||
% Assemble Global Matrices
|
||||
gnum(1)=2*Element(e,1)-1;
|
||||
gnum(2)=2*Element(e,2)-1;
|
||||
gnum(3)=2*Element(e,3)-1;
|
||||
gnum(4)=2*Element(e,4)-1;
|
||||
for i=1:4;
|
||||
for j=1:4;
|
||||
K(gnum(j),gnum(i))=K(gnum(j),gnum(i))+Ke(2*j-1,2*i-1);
|
||||
K(gnum(j)+1,gnum(i)+1)=K(gnum(j)+1,gnum(i)+1)+Ke(2*j,2*i);
|
||||
M(gnum(j),gnum(i))=M(gnum(j),gnum(i))+Me(2*j-1,2*i-1);
|
||||
M(gnum(j)+1,gnum(i))=M(gnum(j)+1,gnum(i))+Me(2*j,2*i-1);
|
||||
M(gnum(j),gnum(i)+1)=M(gnum(j),gnum(i)+1)+Me(2*j-1,2*i);
|
||||
M(gnum(j)+1,gnum(i)+1)=M(gnum(j)+1,gnum(i)+1)+Me(2*j,2*i);
|
||||
end
|
||||
end
|
||||
for i=1:4;
|
||||
pforce(gnum(i))=pforce(gnum(i))+pfL(2*i-1);
|
||||
pforce(gnum(i)+1)=pforce(gnum(i)+1)+pfL(2*i);
|
||||
end
|
||||
end
|
||||
%Remove inactive DOFs(Reduce Matrices)
|
||||
M
|
||||
A=K+M;
|
||||
Sub=A*Bound;
|
||||
M*Tnew;
|
||||
RHS=M*Tnew-Sub+pforce;
|
||||
iindex=0;
|
||||
for i=1:ndof*numNodes;
|
||||
if Bound(i)==0.;
|
||||
iindex=iindex+1;
|
||||
RHSR(iindex)=RHS(i);
|
||||
jindex=0;
|
||||
for j=1:ndof*numNodes;
|
||||
if Bound(j)==0.;
|
||||
jindex=jindex+1;
|
||||
AR(iindex,jindex)=A(i,j);
|
||||
end
|
||||
end
|
||||
end
|
||||
end
|
||||
%Solve
|
||||
Tnewr=(AR^-1)*RHSR';
|
||||
iindex=0;
|
||||
for i=1:ndof*numNodes;
|
||||
if Bound(i)==0.;
|
||||
iindex=iindex+1;
|
||||
Tnew(i)=Tnewr(iindex);
|
||||
end
|
||||
end
|
||||
Tnew
|
||||
end
|
||||
stored';
|
||||
271
Unpublished/XFEM/2D_Solver/FESolveX2Db.m
Normal file
271
Unpublished/XFEM/2D_Solver/FESolveX2Db.m
Normal file
|
|
@ -0,0 +1,271 @@
|
|||
function [] = FESolveX2Db()
|
||||
% MATLAB based 2-D XFEM Solver
|
||||
% J. Grogan (2012)
|
||||
clear all
|
||||
% Define Mesh
|
||||
NumX=4;
|
||||
NumY=1;
|
||||
delX=0.25;
|
||||
delY=0.25;
|
||||
for j=1:NumY+1
|
||||
for i=1:NumX+1
|
||||
index=i+(NumX+1)*(j-1);
|
||||
Node(index,1)=single((i-1.))*delX;
|
||||
Node(index,2)=single((j-1.))*delY;
|
||||
end
|
||||
end
|
||||
numNodes=(NumX+1)*(NumY+1);
|
||||
for j=1:NumY
|
||||
for i=1:NumX
|
||||
index=i+NumX*(j-1);
|
||||
Element(index,1)=i+(NumX+1)*(j-1);
|
||||
Element(index,2)=i+(NumX+1)*(j-1)+1;
|
||||
Element(index,3)=i+(NumX+1)*(j)+1;
|
||||
Element(index,4)=i+(NumX+1)*(j);
|
||||
end
|
||||
end
|
||||
numElem=(NumX)*(NumY);
|
||||
% dofs per node
|
||||
ndof=2;
|
||||
% Define Section Properties
|
||||
rho=1.;
|
||||
% initial interface position
|
||||
dpos=0.6;
|
||||
% Initial temperatures
|
||||
Tnew=zeros(numNodes*2,1);
|
||||
Bound=zeros(numNodes*2,1);
|
||||
for e=1:numElem
|
||||
for n=1:4
|
||||
crdn=Node(Element(e,n),1);
|
||||
if crdn<=dpos
|
||||
Tnew(2*Element(e,n)-1)=1.;
|
||||
end
|
||||
if crdn<0.01
|
||||
Bound(2*Element(e,n)-1)=1.;
|
||||
end
|
||||
end
|
||||
end
|
||||
% Define Time Step
|
||||
dtime=0.01;
|
||||
tsteps=1;
|
||||
time=0.;
|
||||
% penalty term
|
||||
Penalty=00.;
|
||||
% Loop through time steps
|
||||
for ts=1:tsteps
|
||||
K=zeros(numNodes*ndof,numNodes*ndof);
|
||||
M=zeros(numNodes*ndof,numNodes*ndof);
|
||||
pforce=zeros(numNodes*ndof,1);
|
||||
% Loop Through Elements
|
||||
for e=1:numElem
|
||||
Ke=zeros(4*ndof);
|
||||
Me=zeros(4*ndof);
|
||||
for icrd=1:4;
|
||||
crdnx(icrd)=Node(Element(e,icrd),1);
|
||||
crdny(icrd)=Node(Element(e,icrd),2);
|
||||
theta(icrd)=abs(crdnx(icrd)-dpos)*sign(crdnx(icrd)-dpos);
|
||||
end
|
||||
% if sign(theta(1))~=sign(theta(2))
|
||||
if 1==2
|
||||
% enriched element
|
||||
enr=8;
|
||||
% get interface position on element
|
||||
elen=abs(crdnx(2)-crdnx(1));
|
||||
frac=abs(dpos-crdnx(1))/elen;
|
||||
len1=2.*frac;
|
||||
len2=2.*(1.-frac);
|
||||
% devide element for sub integration
|
||||
mid1=-1+len1/2.;
|
||||
mid2=1-len2/2.;
|
||||
gx(1)=mid1-(len1/2.)/sqrt(3.);
|
||||
gx(2)=mid1+(len1/2.)/sqrt(3.);
|
||||
gx(3)=mid1+(len1/2.)/sqrt(3.);
|
||||
gx(4)=mid1-(len1/2.)/sqrt(3.);
|
||||
gx(5)=mid2-(len2/2.)/sqrt(3.);
|
||||
gx(6)=mid2+(len2/2.)/sqrt(3.);
|
||||
gx(7)=mid2+(len2/2.)/sqrt(3.);
|
||||
gx(8)=mid2-(len2/2.)/sqrt(3.);
|
||||
gpos=1/sqrt(3.);
|
||||
hx(1)=-gpos;
|
||||
hx(2)=-gpos;
|
||||
hx(3)=+gpos;
|
||||
hx(4)=+gpos;
|
||||
hx(5)=-gpos;
|
||||
hx(6)=-gpos;
|
||||
hx(7)=+gpos;
|
||||
hx(8)=+gpos;
|
||||
for iw=1:4
|
||||
w(iw)=frac/2.;
|
||||
w(iw+4)=(1.-frac)/2.;
|
||||
end
|
||||
else
|
||||
% regular element - fix extra dofs
|
||||
enr=4;
|
||||
gpos=1/sqrt(3.);
|
||||
gx(1)=-gpos;
|
||||
gx(2)=gpos;
|
||||
gx(3)=gpos;
|
||||
gx(4)=-gpos;
|
||||
hx(1)=-gpos;
|
||||
hx(2)=-gpos;
|
||||
hx(3)=gpos;
|
||||
hx(4)=gpos;
|
||||
for iw=1:4
|
||||
w(iw)=1.;
|
||||
end
|
||||
end
|
||||
% Loop Through Int Points
|
||||
for i=1:enr;
|
||||
g=gx(i);
|
||||
h=hx(i);
|
||||
phi(1)=0.25*(1.-g)*(1.-h);
|
||||
phi(3)=0.25*(1.+g)*(1.-h);
|
||||
phi(5)=0.25*(1.+g)*(1.+h);
|
||||
phi(7)=0.25*(1.-g)*(1.+h);
|
||||
iLS=theta(1)*phi(1)+theta(2)*phi(3)+theta(3)*phi(5)+theta(4)*phi(7);
|
||||
cond=1.;
|
||||
spec=1.;
|
||||
for iter=1:4
|
||||
phi(2*iter)=phi(2*iter-1)*(abs(iLS)-abs(theta(iter)));
|
||||
end
|
||||
phig(1)=0.25*-(1.-h);
|
||||
phig(3)=0.25*(1.-h);
|
||||
phig(5)=0.25*(1.+h);
|
||||
phig(7)=0.25*-(1.+h);
|
||||
phih(1)=0.25*-(1.-g);
|
||||
phih(3)=0.25*-(1.+g);
|
||||
phih(5)=0.25*(1.+g);
|
||||
phih(7)=0.25*(1.-g);
|
||||
diLSg=sign(iLS)*(phig(1)*theta(1)+phig(3)*theta(2)+phig(5)*theta(3)+phig(7)*theta(4));
|
||||
diLSh=sign(iLS)*(phih(1)*theta(1)+phih(3)*theta(2)+phih(5)*theta(3)+phih(7)*theta(4));
|
||||
for iter=1:4
|
||||
phig(2*iter)=phig(2*iter-1)*(abs(iLS)-abs(theta(iter)))+phi(2*iter-1)*diLSg;
|
||||
phih(2*iter)=phih(2*iter-1)*(abs(iLS)-abs(theta(iter)))+phi(2*iter-1)*diLSh;
|
||||
end
|
||||
rjac=zeros(2,2);
|
||||
for iter=1:4
|
||||
rjac(1,1)=rjac(1,1)+phig(2*iter-1)*crdnx(iter);
|
||||
rjac(1,2)=rjac(1,2)+phig(2*iter-1)*crdny(iter);
|
||||
rjac(2,1)=rjac(2,1)+phih(2*iter-1)*crdnx(iter);
|
||||
rjac(2,2)=rjac(2,2)+phih(2*iter-1)*crdny(iter);
|
||||
end
|
||||
djac=rjac(1,1)*rjac(2,2)-rjac(1,2)*rjac(2,1);
|
||||
rjaci(1,1)= rjac(2,2)/djac;
|
||||
rjaci(2,2)= rjac(1,1)/djac;
|
||||
rjaci(1,2)=-rjac(1,2)/djac;
|
||||
rjaci(2,1)=-rjac(2,1)/djac ;
|
||||
for iter=1:8
|
||||
phix(iter)=rjaci(1,1)*phig(iter)+rjaci(1,2)*phih(iter);
|
||||
phiy(iter)=rjaci(2,1)*phig(iter)+rjaci(2,2)*phih(iter);
|
||||
end
|
||||
we=w(i)*djac;
|
||||
B=[phix;phiy];
|
||||
% Ke=Ke+we*cond*(phix'*phix+phiy'*phiy);
|
||||
Ke=Ke+we*cond*(B'*B);
|
||||
Me=Me+(we*rho*spec*phi'*phi)/dtime;
|
||||
end
|
||||
% Add penalty term and get temp gradient on interface
|
||||
if enr==8;
|
||||
count=0;
|
||||
if sign(theta(1))~=sign(theta(2))
|
||||
count=count+1;
|
||||
f=abs(theta(1))/(abs(theta(1))+abs(theta(2)));
|
||||
xi(count)=f*(crdnx(2)-crdnx(1))+crdnx(1);
|
||||
yi(count)=f*(crdny(2)-crdny(1))+crdny(1);
|
||||
gi(count)=(2.*xi(count)-(crdnx(1)+crdnx(2)))/(-crdnx(1)+crdnx(2));
|
||||
hi(count)=-1.;
|
||||
end
|
||||
if sign(theta(2))~=sign(theta(3))
|
||||
count=count+1;
|
||||
f=abs(theta(2))/(abs(theta(2))+abs(theta(3)));
|
||||
xi(count)=f*(crdnx(3)-crdnx(2))+crdnx(2);
|
||||
yi(count)=f*(crdny(3)-crdny(2))+crdny(2);
|
||||
gi(count)=1.;
|
||||
hi(count)=(2.*yi(count)-(crdny(2)+crdny(3)))/(-crdny(2)+crdny(3));
|
||||
end
|
||||
if sign(theta(3))~=sign(theta(4))
|
||||
count=count+1;
|
||||
f=abs(theta(3))/(abs(theta(3))+abs(theta(4)));
|
||||
xi(count)=f*(crdnx(4)-crdnx(3))+crdnx(3);
|
||||
yi(count)=f*(crdny(4)-crdny(3))+crdny(3);
|
||||
gi(count)=(2.*xi(count)-(crdnx(4)+crdnx(3)))/(-crdnx(4)+crdnx(3));
|
||||
hi(count)=1.;
|
||||
end
|
||||
if sign(theta(1))~=sign(theta(4))
|
||||
count=count+1;
|
||||
f=abs(theta(1))/(abs(theta(1))+abs(theta(4)));
|
||||
xi(count)=f*(crdnx(4)-crdnx(1))+crdnx(1);
|
||||
yi(count)=f*(crdny(4)-crdny(1))+crdny(1);
|
||||
gi(count)=-1.;
|
||||
hi(count)=(2.*yi(count)-(crdny(1)+crdny(4)))/(-crdny(4)+crdny(1));
|
||||
end
|
||||
c=zeros(2,1);
|
||||
c=(c+1.);
|
||||
for i=1:2;
|
||||
G(i,1)=0.25*(1.-gi(i))*(1.-hi(i));
|
||||
G(i,3)=0.25*(1.+gi(i))*(1.-hi(i));
|
||||
G(i,5)=0.25*(1.+gi(i))*(1.+hi(i));
|
||||
G(i,7)=0.25*(1.-gi(i))*(1.+hi(i));
|
||||
G(i,2)=-G(i,1)*abs(theta(1));
|
||||
G(i,4)=-G(i,3)*abs(theta(2));
|
||||
G(i,6)=-G(i,5)*abs(theta(3));
|
||||
G(i,8)=-G(i,7)*abs(theta(4));
|
||||
end
|
||||
pen=Penalty*(G'*G);
|
||||
pfL=Penalty*G'*c;
|
||||
Ke=Ke+pen;
|
||||
else
|
||||
pen=zeros(8);
|
||||
pfL=zeros(8,1);
|
||||
end
|
||||
% Assemble Global Matrices
|
||||
gnum(1)=2*Element(e,1)-1;
|
||||
gnum(2)=2*Element(e,2)-1;
|
||||
gnum(3)=2*Element(e,3)-1;
|
||||
gnum(4)=2*Element(e,4)-1;
|
||||
for i=1:4;
|
||||
for j=1:4;
|
||||
K(gnum(j),gnum(i))=K(gnum(j),gnum(i))+Ke(2*j-1,2*i-1);
|
||||
K(gnum(j)+1,gnum(i))=K(gnum(j)+1,gnum(i))+Ke(2*j,2*i-1);
|
||||
K(gnum(j),gnum(i)+1)=K(gnum(j),gnum(i)+1)+Ke(2*j-1,2*i);
|
||||
K(gnum(j)+1,gnum(i)+1)=K(gnum(j)+1,gnum(i)+1)+Ke(2*j,2*i);
|
||||
M(gnum(j),gnum(i))=M(gnum(j),gnum(i))+Me(2*j-1,2*i-1);
|
||||
M(gnum(j)+1,gnum(i))=M(gnum(j)+1,gnum(i))+Me(2*j,2*i-1);
|
||||
M(gnum(j),gnum(i)+1)=M(gnum(j),gnum(i)+1)+Me(2*j-1,2*i);
|
||||
M(gnum(j)+1,gnum(i)+1)=M(gnum(j)+1,gnum(i)+1)+Me(2*j,2*i);
|
||||
end
|
||||
end
|
||||
for i=1:4;
|
||||
pforce(gnum(i))=pforce(gnum(i))+pfL(2*i-1);
|
||||
pforce(gnum(i)+1)=pforce(gnum(i)+1)+pfL(2*i);
|
||||
end
|
||||
end
|
||||
%Remove inactive DOFs(Reduce Matrices)
|
||||
A=K+M;
|
||||
Sub=A*Bound;
|
||||
RHS=M*Tnew-Sub+pforce;
|
||||
iindex=0;
|
||||
for i=1:ndof*numNodes;
|
||||
if Bound(i)==0.;
|
||||
iindex=iindex+1;
|
||||
RHSR(iindex)=RHS(i);
|
||||
jindex=0;
|
||||
for j=1:ndof*numNodes;
|
||||
if Bound(j)==0.;
|
||||
jindex=jindex+1;
|
||||
AR(iindex,jindex)=A(i,j);
|
||||
end
|
||||
end
|
||||
end
|
||||
end
|
||||
%Solve
|
||||
Tnewr=(AR^-1)*RHSR';
|
||||
iindex=0;
|
||||
for i=1:ndof*numNodes;
|
||||
if Bound(i)==0.;
|
||||
iindex=iindex+1;
|
||||
Tnew(i)=Tnewr(iindex);
|
||||
end
|
||||
end
|
||||
Tnew
|
||||
end
|
||||
404
Unpublished/XFEM/2D_Solver/LevelSet.f90
Normal file
404
Unpublished/XFEM/2D_Solver/LevelSet.f90
Normal file
|
|
@ -0,0 +1,404 @@
|
|||
! This Subroutine Implements the Level Set Method
|
||||
! J. Grogan - 07/10/13
|
||||
subroutine uexternaldb(lop,lrestart,time,dtime,kstep,kinc)
|
||||
include 'aba_param.inc'
|
||||
dimension time(2)
|
||||
integer Element (100,4)
|
||||
real Node(100,2),LSet(100)
|
||||
!
|
||||
if(lop==0)then
|
||||
! Get Mesh Data
|
||||
call getMesh(Element,Node,numElem,numNodes)
|
||||
! Get Initial Level Set
|
||||
call initialLSet(LSet,Node,numNodes)
|
||||
elseif(lop==1)then
|
||||
! Update Level Set
|
||||
call updateLSet(Node,numNodes,Element,numElem,dtime,LSet)
|
||||
endif
|
||||
return
|
||||
end
|
||||
! This subroutine returns the finite element mesh connectivity data
|
||||
subroutine getMesh(Element,Node,numElem,numNodes)
|
||||
include 'aba_param.inc'
|
||||
integer Element (100,4)
|
||||
real Node(100,2)
|
||||
character(256) outdir,jobname,input
|
||||
call getoutdir(outdir,lenoutdir)
|
||||
call getjobname(jobname,lenjobname)
|
||||
filename=trim(outdir)//trim(jobname)//'.inp'
|
||||
open(unit=107,file=filename,status='old')
|
||||
read(107,*)input
|
||||
do while (index(input,'*Node')==0)
|
||||
read(107,*)input
|
||||
enddo
|
||||
ierr=0
|
||||
numNodes=0
|
||||
do while (ierr==0)
|
||||
read(107,*)nodeNum,xcor,ycor,zcor
|
||||
if(ierr==0)then
|
||||
Node(nodeNum,1)=xcor
|
||||
Node(nodeNum,2)=ycor
|
||||
numNodes=numNodes+1
|
||||
endif
|
||||
enddo
|
||||
do while (index(input,'*Element')==0)
|
||||
read(107,*)input
|
||||
enddo
|
||||
numElem=0
|
||||
do while (ierr==0)
|
||||
read(107,*)elNum,n1,n2,n3,n4
|
||||
if(ierr==0)then
|
||||
Element(elNum,1)=n1
|
||||
Element(elNum,2)=n2
|
||||
Element(elNum,3)=n3
|
||||
Element(elNum,4)=n4
|
||||
numElem=numElem+1
|
||||
endif
|
||||
enddo
|
||||
close(107)
|
||||
end subroutine
|
||||
! This subroutine calculates the initial Level Set
|
||||
subroutine initialLSet(LSet,Node,numNodes)
|
||||
include 'aba_param.inc'
|
||||
real Node(100,2),LSet(100)
|
||||
!centx=4.
|
||||
!centy=4.
|
||||
!rad=2.1
|
||||
!do i=1,numNodes
|
||||
! dist=sqrt((Node(i,1)-centx)*(Node(i,1)-centx)+(Node(i,2)-centy)*(Node(i,2)-centy))
|
||||
! LSet(i)=dist-rad
|
||||
!enddo
|
||||
do i=1,numNodes
|
||||
dist=Node(i,1)-0.1
|
||||
LSet(i)=dist
|
||||
enddo
|
||||
end subroutine
|
||||
! This subroutine updates the Level Set
|
||||
subroutine updateLSet(Node,numNodes,Element,numElem,dtime,LSet)
|
||||
include 'aba_param.inc'
|
||||
integer Element(100,4),NBelem(100,4)
|
||||
real Node(100,2),NGlobal(100,2),NLocal(100,2)
|
||||
real LSet(100),LSetLocal(100),F(100),Fred(100)
|
||||
real A(100,100),Ared(100,100),RHS(100),RHSred(100)
|
||||
real M(100,100),MGL(100,100),f1(100),f2(100),f3(100)
|
||||
! parameters
|
||||
bandWidth=10.
|
||||
av_Length=1.
|
||||
h2=0.00001*av_Length
|
||||
visc=0.0005
|
||||
dt=0.01
|
||||
! explicit update of Level Set
|
||||
do istep=1:floor(dtime/dt)
|
||||
! Identify Narrow Band Elements and Get Local Level Set
|
||||
call getNarrowBand(NBelem,NBElems,NGlobal,NLocal,NBNodes,LSetLocal, &
|
||||
& bandWidth,LSet,Element,numElem,numNodes)
|
||||
! Identify Scalar Velocity on Nodes Crossed By Interface - F
|
||||
call getF(F,LSetLocal,NBElems,NBNodes,NBelem)
|
||||
! Get 'Stiffness' Matrix - A
|
||||
call getA(A,Node,NLocal,NBelem,NBNodes,NBElems,LSetLocal)
|
||||
! Apply BCs
|
||||
RHS=-matmul(A,F)
|
||||
iindex=0
|
||||
do i=1,NBNodes
|
||||
if (F(i)==0.)then
|
||||
iindex=iindex+1
|
||||
RHSred(iindex)=RHS(i)
|
||||
jindex=0
|
||||
do j=1,NBNodes
|
||||
if (F(j)==0.)then
|
||||
jindex=jindex+1;
|
||||
Ared(iindex,jindex)=A(i,j)
|
||||
endif
|
||||
enddo
|
||||
endif
|
||||
enddo
|
||||
! Solve for Fred
|
||||
Fred=(Ared^-1)*RHSred'
|
||||
! Get F
|
||||
iindex=0
|
||||
do i=1,NBNodes
|
||||
if (F(i)==0.)then
|
||||
iindex=iindex+1
|
||||
F(i)=Fred(iindex)
|
||||
endif
|
||||
enddo
|
||||
! Get Level Set Equation Terms
|
||||
call getTerms(M,MGLS,f1,f2,f3,Node,NLocal,NBelem,NBNodes,NBElems,&
|
||||
& LSetLocal,visc,h2,F)
|
||||
LSetLocal=LSetLocal-((((M+MGLS)^-1)*dt)*(f1+f2+f3))'
|
||||
! Reinitialize LS
|
||||
!call fastMarch(LSetLocal,NBelem,Node,NLocal,NBNodes)
|
||||
do i=1,NBNodes
|
||||
LSet(NLocal(i))=LSetLocal(i)
|
||||
end
|
||||
enddo
|
||||
end subroutine
|
||||
! This subroutine identifies elements in the narrow band
|
||||
subroutine getNarrowBand(NBelem,NBElems,NGlobal,NLocal,NBNodes,LSetLocal,&
|
||||
& bandWidth,LSet,Element,numElem,numNodes)
|
||||
include 'aba_param.inc'
|
||||
integer Element(100,4),NBelem(100,4)
|
||||
real Node(100,2),NGlobal(100,2),NLocal(100,2)
|
||||
real LSet(100),LSetLocal(100)
|
||||
! Identify Narrow Band Elements
|
||||
NBElems=0
|
||||
NBNodes=0
|
||||
NGlobal=0.
|
||||
do i=1,numElem
|
||||
check=0
|
||||
do iNd=1,4
|
||||
if (abs(LSet(Element(i,iNd)))<=bandWidth*(delX+delY)/2.)then
|
||||
check=1
|
||||
endif
|
||||
enddo
|
||||
! If an element is in the narrow band split it into triangles
|
||||
if (check==1)then
|
||||
for j=1,4
|
||||
if (NGlobal(Element(i,j))==0)then
|
||||
NBNodes=NBNodes+1
|
||||
NGlobal(Element(i,j))=NBNodes
|
||||
NLocal(NBNodes)=Element(i,j)
|
||||
endif
|
||||
endddo
|
||||
NBElems=NBElems+1
|
||||
NBelem(NBElems,1)=NGlobal(Element(i,1))
|
||||
NBelem(NBElems,2)=NGlobal(Element(i,2))
|
||||
NBelem(NBElems,3)=NGlobal(Element(i,3))
|
||||
NBElems=NBElems+1
|
||||
NBelem(NBElems,1)=NGlobal(Element(i,1))
|
||||
NBelem(NBElems,2)=NGlobal(Element(i,3))
|
||||
NBelem(NBElems,3)=NGlobal(Element(i,4))
|
||||
endif
|
||||
enddo
|
||||
! Get local Level Set
|
||||
do i=1,NBNodes
|
||||
LSetLocal(i)=LSet(NLocal(i))
|
||||
enddo
|
||||
end subroutine
|
||||
! This subroutine extends the interface velocity throughout the computational domain
|
||||
subroutine getF(F,LSetLocal,NBElems,NBNodes,NBelem)
|
||||
include 'aba_param.inc'
|
||||
real LSetLocal(100),F(100),L(3)
|
||||
F=0.
|
||||
do i=1,NBElems
|
||||
do j=1,3
|
||||
L(j)=sign(1.,LSetLocal(NBelem(i,j)))
|
||||
enddo
|
||||
if (L(1) /= L(2) .or. L(1) /= L(3))then
|
||||
do j=1,3
|
||||
F(NBelem(i,j))= 1.
|
||||
enddo
|
||||
endif
|
||||
enddo
|
||||
end subroutine
|
||||
! This subroutine gets the 'stiffness' matrix - A
|
||||
subroutine getA(A,Node,NLocal,NBelem,NBNodes,NBElems,LSetLocal)
|
||||
include 'aba_param.inc'
|
||||
integer NBelem(100,4)
|
||||
real Node(100,2),NLocal(100,2)
|
||||
real LSetLocal(100),A(100,100),AfL(3,3),AfLGLS(3,3)
|
||||
real gx(3),hx(3),phi(3),phig(3),phih(3),phix(3),phiy(3)
|
||||
A=0.
|
||||
do i=1,NBElems
|
||||
gx(1)=2./3.
|
||||
gx(2)=1./6.
|
||||
gx(3)=1./6.
|
||||
hx(1)=1./6.
|
||||
hx(2)=1./6.
|
||||
hx(3)=2./3.
|
||||
AfL=0.
|
||||
AfLGLS=0.
|
||||
x1=Node(NLocal(NBelem(i,1)),1)
|
||||
y1=Node(NLocal(NBelem(i,1)),2)
|
||||
x2=Node(NLocal(NBelem(i,2)),1)
|
||||
y2=Node(NLocal(NBelem(i,2)),2)
|
||||
x3=Node(NLocal(NBelem(i,3)),1)
|
||||
y3=Node(NLocal(NBelem(i,3)),2)
|
||||
do j=1,3
|
||||
g=gx(j)
|
||||
h=hx(j)
|
||||
phi(1)=1.-g-h
|
||||
phi(2)=g
|
||||
phi(3)=h
|
||||
phig(1)=-1.
|
||||
phig(2)=1.
|
||||
phig(3)=0.
|
||||
phih(1)=-1.
|
||||
phih(2)=0.
|
||||
phih(3)=1.
|
||||
djac=2.*abs(x1*(y2-y3)+x2*(y3-y1)+x3*(y1-y2))
|
||||
do k=1,3
|
||||
phix(k)=(1./djac)*((-y1+y3)*phig(k)+(y1-y2)*phih(k))
|
||||
phiy(k)=(1./djac)*((x1-x3)*phig(k)+(-x1+x2)*phih(k))
|
||||
enddo
|
||||
delphi=[phix;phiy]
|
||||
nodalLset=[LSetLocal(NBelem(i,1));LSetLocal(NBelem(i,2));LSetLocal(NBelem(i,3))]
|
||||
set=phi*nodalLset
|
||||
delset=delphi*nodalLset
|
||||
AfL=AfL+(phi'*sign(set))*(delset'*delphi)/3.
|
||||
AfLGLS=AfLGLS+(delphi'*delset)*(1./norm(delset))*(delset'*delphi)/3.
|
||||
enddo
|
||||
do k=1,3
|
||||
do j=1,3
|
||||
A(NBelem(i,j),NBelem(i,k))=A(NBelem(i,j),NBelem(i,k))+AfL(j,k)+AfLGLS(j,k)
|
||||
enddo
|
||||
enddo
|
||||
enddo
|
||||
end subroutine
|
||||
! This subroutine gets the neccessary terms for the level set equation
|
||||
subroutine getTerms(M,MGLS,f1,f2,f3,Node,NLocal,NBelem,NBNodes,NBElems,&
|
||||
& LSetLocal,visc,h2,F)
|
||||
include 'aba_param.inc'
|
||||
integer NBelem(100,4)
|
||||
real Node(100,2),NLocal(100,2),LSetLocal(100)
|
||||
real M(100,100),MGLS(100,100),f1(100),f2(100),f3(100)
|
||||
real ML(3,3),MGLSL(3,3),f1L(3),f2L(3),f3L(3)
|
||||
real gx(3),hx(3),phi(3),phig(3),phih(3),phix(3),phiy(3)
|
||||
|
||||
M=0.
|
||||
MGLS=0.
|
||||
f1=0.
|
||||
f2=0.
|
||||
f3=0.
|
||||
do i=1,NBElems
|
||||
ML=0.
|
||||
MGLSL=0.
|
||||
f1L=0.
|
||||
f2L=0.
|
||||
f3L=0.
|
||||
gx(1)=2./3.
|
||||
gx(2)=1./6.
|
||||
gx(3)=1./6.
|
||||
hx(1)=1./6.
|
||||
hx(2)=1./6.
|
||||
hx(3)=2./3.
|
||||
x1=Node(NLocal(NBelem(i,1)),1)
|
||||
y1=Node(NLocal(NBelem(i,1)),2)
|
||||
x2=Node(NLocal(NBelem(i,2)),1)
|
||||
y2=Node(NLocal(NBelem(i,2)),2)
|
||||
x3=Node(NLocal(NBelem(i,3)),1)
|
||||
y3=Node(NLocal(NBelem(i,3)),2)
|
||||
do j=1,3
|
||||
g=gx(j)
|
||||
h=hx(j)
|
||||
phi(1)=1.-g-h
|
||||
phi(2)=g
|
||||
phi(3)=h
|
||||
phig(1)=-1.
|
||||
phig(2)=1.
|
||||
phig(3)=0.
|
||||
phih(1)=-1.
|
||||
phih(2)=0.
|
||||
phih(3)=1.
|
||||
djac=abs(x1*(y2-y3)+x2*(y3-y1)+x3*(y1-y2))
|
||||
do k=1,3
|
||||
phix(k)=(1./djac)*((-y1+y3)*phig(k)+(y1-y2)*phih(k))
|
||||
phiy(k)=(1./djac)*((x1-x3)*phig(k)+(-x1+x2)*phih(k))
|
||||
end
|
||||
delphi=[phix;phiy]
|
||||
nodalLset=[LSetLocal(NBelem(i,1));LSetLocal(NBelem(i,2));LSetLocal(NBelem(i,3))]
|
||||
nodalF=[F(NBelem(i,1));F(NBelem(i,2));F(NBelem(i,3))]
|
||||
delset=delphi*nodalLset;
|
||||
Floc=phi*nodalF
|
||||
ML=ML+(phi'*phi)/3.
|
||||
MGLSL=MGLSL+((delphi'*(delset/norm(delset)))*Floc*(h2/abs(Floc)))*phi/3.
|
||||
f1L=f1L+phi'*Floc*norm(delset)/3.
|
||||
f2L=f2L+(delphi'*(delset/norm(delset))*Floc)*(h2/abs(Floc))*Floc*norm(delset)/3.
|
||||
vs=h2*((abs(visc+Floc*norm(delset)))/(norm(Floc*delset)+h2))
|
||||
f3L=f3L+vs*delphi'*delset/3.
|
||||
enddo
|
||||
do k=1,3
|
||||
do j=1,3
|
||||
M(NBelem(i,j),NBelem(i,k))=M(NBelem(i,j),NBelem(i,k))+ML(j,k)
|
||||
MGLS(NBelem(i,j),NBelem(i,k))=MGLS(NBelem(i,j),NBelem(i,k))+MGLSL(j,k)
|
||||
enddo
|
||||
f1(NBelem(i,k))=f1(NBelem(i,k))+f1L(k)
|
||||
f2(NBelem(i,k))=f2(NBelem(i,k))+f2L(k)
|
||||
f3(NBelem(i,k))=f3(NBelem(i,k))+f3L(k)
|
||||
enddo
|
||||
enddo
|
||||
end subroutine
|
||||
! This subroutine uses the fast marching method to re-initialize the level set
|
||||
call fastMarch(LSetLocal,NBelem,Node,NLocal,NBNodes)
|
||||
include 'aba_param.inc'
|
||||
integer NBelem(100,4),nstat(100)
|
||||
real Node(100,2),NLocal(100,2),LSetLocal(100),newlSet(100),L(3)
|
||||
newlSet=LSetLocal
|
||||
! Reinitialize LS
|
||||
nstat=0
|
||||
do i=1,NBElems
|
||||
do j=1,3
|
||||
L(j)=sign(1.,lSetLocal(NBelem(i,j)))
|
||||
enddo
|
||||
if (L(1) /= L(2) .or. L(1) /= L(3))then
|
||||
do j=1,3
|
||||
nstat(NBelem(i,j))=1
|
||||
enddo
|
||||
endif
|
||||
enddo
|
||||
maincheck=0
|
||||
do while(maincheck==0)
|
||||
lmin=1000.
|
||||
avlmin=1000.
|
||||
eindex=0
|
||||
nindex=0
|
||||
maincheck=1
|
||||
do i=1,NBElems
|
||||
if (nstat(NBelem(i,1))+nstat(NBelem(i,2))+nstat(NBelem(i,3))==2)then
|
||||
maincheck=0
|
||||
check=0
|
||||
ltot=0.
|
||||
do j=1,3
|
||||
if (nstat(NBelem(i,j))==0)then
|
||||
if (abs(lSetLocal(NBelem(i,j)))<=lmin)then
|
||||
check=1
|
||||
tempindex=j
|
||||
endif
|
||||
endif
|
||||
ltot=ltot+abs(lSetLocal(NBelem(i,j)))
|
||||
enddo
|
||||
if (check==1 .and. ltot/3.<=avlmin)then
|
||||
eindex=i
|
||||
nindex=tempindex
|
||||
lmin=lSetLocal(NBelem(eindex,nindex))
|
||||
avlmin=ltot/3.
|
||||
endif
|
||||
endif
|
||||
enddo
|
||||
if (maincheck==0)then
|
||||
! Find New LS for point
|
||||
xp=Node(NLocal(NBelem(eindex,nindex)),1)
|
||||
yp=Node(NLocal(NBelem(eindex,nindex)),2)
|
||||
count=0
|
||||
do i=1,3
|
||||
if (i/=nindex)then
|
||||
icount=icount+1
|
||||
x(icount)=Node(NLocal(NBelem(eindex,i)),1)
|
||||
y(icount)=Node(NLocal(NBelem(eindex,i)),2)
|
||||
lloc(icount)=newlSet(NBelem(eindex,i))
|
||||
endif
|
||||
enddo
|
||||
delxa=x(1)-xp
|
||||
delya=y(1)-yp
|
||||
delxb=x(2)-xp
|
||||
delyb=y(2)-yp
|
||||
N=[delxa delya; delxb delyb]
|
||||
M=N^-1
|
||||
A=(M(1)*M(1)+M(2)*M(2))
|
||||
B=(M(3)*M(3)+M(4)*M(4))
|
||||
C=2.*(M(1)*M(3)+M(2)*M(4))
|
||||
a=A+B+C
|
||||
b=-2.*lloc(1)*A-2.*lloc(2)*B-C*(lloc(1)+lloc(2))
|
||||
c=lloc(1)*lloc(1)*A+lloc(2)*lloc(2)*B+lloc(1)*lloc(2)*C-1.
|
||||
templ1=(-b+sqrt(b*b-4.*a*c))/(2.*a)
|
||||
templ2=(-b-sqrt(b*b-4.*a*c))/(2.*a)
|
||||
if (abs(templ1)>abs(templ2))then
|
||||
newlSet(NBelem(eindex,nindex))=templ1
|
||||
else
|
||||
newlSet(NBelem(eindex,nindex))=templ2
|
||||
endif
|
||||
nstat(NBelem(eindex,nindex))=1
|
||||
endif
|
||||
enddo
|
||||
LSetLocal=newlSet
|
||||
end subroutine
|
||||
268
Unpublished/XFEM/2D_Solver/XCOR1D.m
Normal file
268
Unpublished/XFEM/2D_Solver/XCOR1D.m
Normal file
|
|
@ -0,0 +1,268 @@
|
|||
function [] = XCOR1D()
|
||||
% MATLAB based 1-D XFEM Solver
|
||||
% J. Grogan (2012)
|
||||
clear all
|
||||
% Define Geometry
|
||||
len=1.;
|
||||
% Define Section Properties
|
||||
rho=1.;
|
||||
% Generate Mesh
|
||||
numElem=4;
|
||||
charlen=len/numElem;
|
||||
ndCoords=linspace(0,len,numElem+1);
|
||||
numNodes=size(ndCoords,2);
|
||||
indx=1:numElem;
|
||||
elemNodes(:,1)=indx;
|
||||
elemNodes(:,2)=indx+1;
|
||||
% dofs per node
|
||||
ndof=2;
|
||||
% initial interface position
|
||||
dpos=0.6;
|
||||
% Initial temperatures
|
||||
Tnew=zeros(numNodes*2,1);
|
||||
Bound=zeros(numNodes*2,1);
|
||||
%storage
|
||||
stored(1)=dpos;
|
||||
for e=1:numElem
|
||||
for n=1:2
|
||||
crdn1=ndCoords(elemNodes(e,n));
|
||||
if crdn1<=dpos
|
||||
Tnew(2*elemNodes(e,n)-1)=1.;
|
||||
end
|
||||
end
|
||||
end
|
||||
Bound(1)=1.;
|
||||
% Define Time Step
|
||||
dtime=0.01;
|
||||
tsteps=10;
|
||||
time=0.;
|
||||
% penalty term
|
||||
beta=100.;
|
||||
% Loop through time steps
|
||||
for ts=1:tsteps
|
||||
eNodes=zeros(2*numNodes,1);
|
||||
% Get interface velocity
|
||||
d(1)=dpos+charlen;
|
||||
d(2)=dpos+3*charlen/4;
|
||||
d(3)=dpos+charlen/4;
|
||||
d(4)=dpos;
|
||||
for e=1:numElem
|
||||
crdn1=ndCoords(elemNodes(e,1));
|
||||
crdn2=ndCoords(elemNodes(e,2));
|
||||
for j=1:4
|
||||
if d(j)>=crdn1 && d(j)<crdn2
|
||||
elen=abs(crdn2-crdn1);
|
||||
ajacob=elen/2.;
|
||||
point=(d(j)-crdn1)/ajacob-1.;
|
||||
theta(1)=abs(crdn1-dpos)*sign(crdn1-dpos);
|
||||
theta(2)=abs(crdn2-dpos)*sign(crdn2-dpos);
|
||||
tmp1a=Tnew(elemNodes(e,1)*2-1);
|
||||
tmp1b=Tnew(elemNodes(e,1)*2);
|
||||
tmp2a=Tnew(elemNodes(e,2)*2-1);
|
||||
tmp2b=Tnew(elemNodes(e,2)*2);
|
||||
xi=point;
|
||||
gm(1)=(1.-xi)/2.;
|
||||
gm(3)=(1.+xi)/2.;
|
||||
term=theta(1)*gm(1)+theta(2)*gm(3);
|
||||
gm(2)=gm(1)*(abs(term)-abs(theta(1)));
|
||||
gm(4)=gm(3)*(abs(term)-abs(theta(2)));
|
||||
t(j)=gm(1)*tmp1a+gm(2)*tmp1b+gm(3)*tmp2a+gm(4)*tmp2b;
|
||||
end
|
||||
end
|
||||
end
|
||||
vel=0.5*(0.5/charlen)*(2*t(1)+t(2)-t(3)-2*t(4));
|
||||
vel=0.
|
||||
% Update interface position
|
||||
dpos=dpos+vel*dtime;
|
||||
stored(ts+1)=dpos;
|
||||
K=zeros(numNodes*ndof,numNodes*ndof);
|
||||
M=zeros(numNodes*ndof,numNodes*ndof);
|
||||
pforce=zeros(numNodes*ndof,1);
|
||||
% Loop Through Elements
|
||||
for e=1:numElem
|
||||
Ke=zeros(2*ndof);
|
||||
Me=zeros(2*ndof);
|
||||
crdn1=ndCoords(elemNodes(e,1));
|
||||
crdn2=ndCoords(elemNodes(e,2));
|
||||
theta(1)=abs(crdn1-dpos)*sign(crdn1-dpos);
|
||||
theta(2)=abs(crdn2-dpos)*sign(crdn2-dpos);
|
||||
enr=2;
|
||||
elen=abs(crdn2-crdn1);
|
||||
ajacob=elen/2.;
|
||||
if sign(theta(1))~=sign(theta(2))
|
||||
% enriched element
|
||||
eNodes(2*elemNodes(e,1))=1;
|
||||
eNodes(2*elemNodes(e,2))=1;
|
||||
enr=4;
|
||||
% get interface position on element
|
||||
point=(dpos-crdn1)/ajacob-1.;
|
||||
% devide element for sub integration
|
||||
len1=abs(-point-1.);
|
||||
len2=abs(1.-point);
|
||||
mid1=-1+len1/2.;
|
||||
mid2=1-len2/2.;
|
||||
gpx(1)=-(len1/2.)/sqrt(3.)+mid1;
|
||||
gpx(2)=(len1/2.)/sqrt(3.)+mid1;
|
||||
gpx(3)=-(len2/2.)/sqrt(3.)+mid2;
|
||||
gpx(4)=(len2/2.)/sqrt(3.)+mid2;
|
||||
w(1)=(len1/2.);
|
||||
w(2)=(len1/2.);
|
||||
w(3)=(len2/2.);
|
||||
w(4)=(len2/2.);
|
||||
else
|
||||
% regular element - fix extra dofs
|
||||
gpx(1)=-1/sqrt(3.);
|
||||
gpx(2)=1/sqrt(3.);
|
||||
w(1)=1.;
|
||||
w(2)=1.;
|
||||
end
|
||||
% Loop Through Int Points
|
||||
for i=1:enr;
|
||||
c=gpx(i);
|
||||
phi(1)=(1.-c)/2.;
|
||||
phi(3)=(1.+c)/2.;
|
||||
term=theta(1)*phi(1)+theta(2)*phi(3);
|
||||
% if term<0
|
||||
% cond=0.00;
|
||||
% spec=0.001;
|
||||
% else
|
||||
cond=1.;
|
||||
spec=1.;
|
||||
% end
|
||||
if enr==4
|
||||
phi(2)=phi(1)*(abs(term)-abs(theta(1)));
|
||||
phi(4)=phi(3)*(abs(term)-abs(theta(2)));
|
||||
else
|
||||
phi(2)=0.0;
|
||||
phi(4)=0.0;
|
||||
end
|
||||
phic(1)=-0.5;
|
||||
phic(3)=0.5;
|
||||
dterm=sign(term)*(phic(1)*theta(1)+phic(3)*theta(2));
|
||||
if enr==4
|
||||
phic(2)=phic(1)*(abs(term)-abs(theta(1)))+phi(1)*dterm;
|
||||
phic(4)=phic(3)*(abs(term)-abs(theta(2)))+phi(3)*dterm;
|
||||
else
|
||||
phic(2)=0.0;
|
||||
phic(4)=0.0;
|
||||
end
|
||||
phix(1)=phic(1)/ajacob;
|
||||
phix(2)=phic(2)/ajacob;
|
||||
phix(3)=phic(3)/ajacob;
|
||||
phix(4)=phic(4)/ajacob;
|
||||
we=ajacob*w(i);
|
||||
Ke=Ke+we*cond*phix'*phix;
|
||||
Me=Me+(we*rho*spec*phi'*phi)/dtime;
|
||||
end
|
||||
if enr==5;
|
||||
Ke(1,2)=0.;
|
||||
Me(1,2)=0.;
|
||||
Ke(2,1)=0.;
|
||||
Me(2,1)=0.;
|
||||
Ke(1,4)=0.;
|
||||
Me(1,4)=0.;
|
||||
Ke(4,1)=0.;
|
||||
Me(4,1)=0.;
|
||||
Ke(3,2)=0.;
|
||||
Me(3,2)=0.;
|
||||
Ke(2,3)=0.;
|
||||
Me(2,3)=0.;
|
||||
Ke(4,3)=0.;
|
||||
Me(4,3)=0.;
|
||||
Ke(3,4)=0.;
|
||||
Me(3,4)=0.;
|
||||
end
|
||||
% Add penalty term and get temp gradient on interface
|
||||
if enr==4;
|
||||
xi=point;
|
||||
gm(1)=(1.-xi)/2.;
|
||||
gm(3)=(1.+xi)/2.;
|
||||
term=theta(1)*gm(1)+theta(2)*gm(3);
|
||||
gm(2)=gm(1)*(abs(term)-abs(theta(1)));
|
||||
gm(4)=gm(3)*(abs(term)-abs(theta(2)));
|
||||
pen=beta*(gm'*gm);
|
||||
pfL=beta*1*gm';
|
||||
Ke=Ke+pen;
|
||||
else
|
||||
pen=zeros(4);
|
||||
pfL=zeros(4,1);
|
||||
end
|
||||
% Assemble Global Matrices
|
||||
gnum=2.*elemNodes(e,1)-1.;
|
||||
for i=1:4;
|
||||
for j=1:4;
|
||||
K(gnum+j-1,gnum+i-1)=K(gnum+j-1,gnum+i-1)+Ke(j,i);
|
||||
M(gnum+j-1,gnum+i-1)=M(gnum+j-1,gnum+i-1)+Me(j,i);
|
||||
end
|
||||
pforce(gnum+i-1)=pforce(gnum+i-1)+pfL(i);
|
||||
end
|
||||
end
|
||||
%Remove NON-ENHANCED DOFs(Reduce Matrices)
|
||||
iindex=0.;
|
||||
for i=1:ndof*numNodes;
|
||||
check=0;
|
||||
if mod(i,2)==0 && eNodes(i)~=1
|
||||
check=1;
|
||||
end
|
||||
if check==0
|
||||
iindex=iindex+1;
|
||||
TR1(iindex)=Tnew(i);
|
||||
BR1(iindex)=Bound(i);
|
||||
pforceR1(iindex)=pforce(i);
|
||||
jindex=0;
|
||||
for j=1:ndof*numNodes;
|
||||
check=0;
|
||||
if mod(j,2)==0 && eNodes(j)~=1
|
||||
check=1;
|
||||
end
|
||||
if check==0
|
||||
jindex=jindex+1;
|
||||
MR1(iindex,jindex)=M(i,j);
|
||||
KR1(iindex,jindex)=K(i,j);
|
||||
end
|
||||
end
|
||||
end
|
||||
end
|
||||
AR1=KR1+MR1;
|
||||
SubR1=AR1*BR1';
|
||||
RHSR1=MR1*TR1'-SubR1+pforceR1';
|
||||
% Apply Boundary Conditions
|
||||
Biindex=0.;
|
||||
for i=1:iindex;
|
||||
if BR1(i)==0.;
|
||||
Biindex=Biindex+1;
|
||||
RHSR2(Biindex)=RHSR1(i);
|
||||
jindex=0;
|
||||
for j=1:iindex;
|
||||
check=0;
|
||||
if BR1(j)==0.;
|
||||
jindex=jindex+1;
|
||||
AR2(Biindex,jindex)=AR1(i,j);
|
||||
end
|
||||
end
|
||||
end
|
||||
end
|
||||
%Solve
|
||||
Tnewr=(AR2^-1)*RHSR2';
|
||||
% Restore Matrices
|
||||
Biindex=0;
|
||||
for i=1:iindex;
|
||||
if BR1(i)==0.;
|
||||
Biindex=Biindex+1;
|
||||
TR1(i)=Tnewr(Biindex);
|
||||
end
|
||||
end
|
||||
iindex=0;
|
||||
for i=1:ndof*numNodes;
|
||||
check=0;
|
||||
if mod(i,2)==0 && eNodes(i)~=1
|
||||
check=1;
|
||||
end
|
||||
if check==0
|
||||
iindex=iindex+1;
|
||||
Tnew(i)=TR1(iindex);
|
||||
end
|
||||
end
|
||||
Tnew
|
||||
end
|
||||
stored';
|
||||
196
Unpublished/XFEM/2D_Solver/XCOR1Db.m
Normal file
196
Unpublished/XFEM/2D_Solver/XCOR1Db.m
Normal file
|
|
@ -0,0 +1,196 @@
|
|||
function [] = XCOR1Db()
|
||||
% MATLAB based 1-D XFEM Solver
|
||||
% J. Grogan (2012)
|
||||
clear all
|
||||
% Define Geometry
|
||||
len=1.;
|
||||
% Define Section Properties
|
||||
rho=1.;
|
||||
% Generate Mesh
|
||||
numElem=4;
|
||||
charlen=len/numElem;
|
||||
ndCoords=linspace(0,len,numElem+1);
|
||||
numNodes=size(ndCoords,2);
|
||||
indx=1:numElem;
|
||||
elemNodes(:,1)=indx;
|
||||
elemNodes(:,2)=indx+1;
|
||||
% dofs per node
|
||||
ndof=2;
|
||||
% initial interface position
|
||||
dpos=0.6;
|
||||
% Initial temperatures
|
||||
Tnew=zeros(numNodes*2,1);
|
||||
Bound=zeros(numNodes*2,1);
|
||||
%storage
|
||||
stored(1)=dpos;
|
||||
for e=1:numElem
|
||||
for n=1:2
|
||||
crdn1=ndCoords(elemNodes(e,n));
|
||||
if crdn1<=dpos
|
||||
Tnew(2*elemNodes(e,n)-1)=1.;
|
||||
end
|
||||
end
|
||||
end
|
||||
Bound(1)=1.;
|
||||
% Define Time Step
|
||||
dtime=0.01;
|
||||
tsteps=10;
|
||||
time=0.;
|
||||
% penalty term
|
||||
beta=100.;
|
||||
% Loop through time steps
|
||||
for ts=1:tsteps
|
||||
% Get interface velocity
|
||||
d(1)=dpos+charlen;
|
||||
d(2)=dpos+3*charlen/4;
|
||||
d(3)=dpos+charlen/4;
|
||||
d(4)=dpos;
|
||||
for e=1:numElem
|
||||
crdn1=ndCoords(elemNodes(e,1));
|
||||
crdn2=ndCoords(elemNodes(e,2));
|
||||
for j=1:4
|
||||
if d(j)>=crdn1 && d(j)<crdn2
|
||||
elen=abs(crdn2-crdn1);
|
||||
ajacob=elen/2.;
|
||||
point=(d(j)-crdn1)/ajacob-1.;
|
||||
theta(1)=abs(crdn1-dpos)*sign(crdn1-dpos);
|
||||
theta(2)=abs(crdn2-dpos)*sign(crdn2-dpos);
|
||||
tmp1a=Tnew(elemNodes(e,1)*2-1);
|
||||
tmp1b=Tnew(elemNodes(e,1)*2);
|
||||
tmp2a=Tnew(elemNodes(e,2)*2-1);
|
||||
tmp2b=Tnew(elemNodes(e,2)*2);
|
||||
xi=point;
|
||||
gm(1)=(1.-xi)/2.;
|
||||
gm(3)=(1.+xi)/2.;
|
||||
term=theta(1)*gm(1)+theta(2)*gm(3);
|
||||
gm(2)=gm(1)*(abs(term)-abs(theta(1)));
|
||||
gm(4)=gm(3)*(abs(term)-abs(theta(2)));
|
||||
t(j)=gm(1)*tmp1a+gm(2)*tmp1b+gm(3)*tmp2a+gm(4)*tmp2b;
|
||||
end
|
||||
end
|
||||
end
|
||||
vel=0.5*(0.5/charlen)*(2*t(1)+t(2)-t(3)-2*t(4));
|
||||
vel=0.;
|
||||
% Update interface position
|
||||
dpos=dpos+vel*dtime;
|
||||
stored(ts+1)=dpos;
|
||||
K=zeros(numNodes*ndof,numNodes*ndof);
|
||||
M=zeros(numNodes*ndof,numNodes*ndof);
|
||||
pforce=zeros(numNodes*ndof,1);
|
||||
% Loop Through Elements
|
||||
for e=1:numElem
|
||||
Ke=zeros(2*ndof);
|
||||
Me=zeros(2*ndof);
|
||||
crdn1=ndCoords(elemNodes(e,1));
|
||||
crdn2=ndCoords(elemNodes(e,2));
|
||||
theta(1)=abs(crdn1-dpos)*sign(crdn1-dpos);
|
||||
theta(2)=abs(crdn2-dpos)*sign(crdn2-dpos);
|
||||
enr=2;
|
||||
elen=abs(crdn2-crdn1);
|
||||
ajacob=elen/2.;
|
||||
if sign(theta(1))~=sign(theta(2))
|
||||
% enriched element
|
||||
enr=4;
|
||||
% get interface position on element
|
||||
point=(dpos-crdn1)/ajacob-1.;
|
||||
% devide element for sub integration
|
||||
len1=abs(-point-1.);
|
||||
len2=abs(1.-point);
|
||||
mid1=-1+len1/2.;
|
||||
mid2=1-len2/2.;
|
||||
gpx(1)=-(len1/2.)/sqrt(3.)+mid1;
|
||||
gpx(2)=(len1/2.)/sqrt(3.)+mid1;
|
||||
gpx(3)=-(len2/2.)/sqrt(3.)+mid2;
|
||||
gpx(4)=(len2/2.)/sqrt(3.)+mid2;
|
||||
w(1)=(len1/2.);
|
||||
w(2)=(len1/2.);
|
||||
w(3)=(len2/2.);
|
||||
w(4)=(len2/2.);
|
||||
else
|
||||
% regular element - fix extra dofs
|
||||
gpx(1)=-1/sqrt(3.);
|
||||
gpx(2)=1/sqrt(3.);
|
||||
w(1)=1.;
|
||||
w(2)=1.;
|
||||
end
|
||||
% Loop Through Int Points
|
||||
for i=1:enr;
|
||||
c=gpx(i);
|
||||
phi(1)=(1.-c)/2.;
|
||||
phi(3)=(1.+c)/2.;
|
||||
term=theta(1)*phi(1)+theta(2)*phi(3);
|
||||
cond=1.;
|
||||
spec=1.;
|
||||
phi(2)=phi(1)*(abs(term)-abs(theta(1)));
|
||||
phi(4)=phi(3)*(abs(term)-abs(theta(2)));
|
||||
phic(1)=-0.5;
|
||||
phic(3)=0.5;
|
||||
dterm=sign(term)*(phic(1)*theta(1)+phic(3)*theta(2));
|
||||
phic(2)=phic(1)*(abs(term)-abs(theta(1)))+phi(1)*dterm;
|
||||
phic(4)=phic(3)*(abs(term)-abs(theta(2)))+phi(3)*dterm;
|
||||
phix(1)=phic(1)/ajacob;
|
||||
phix(2)=phic(2)/ajacob;
|
||||
phix(3)=phic(3)/ajacob;
|
||||
phix(4)=phic(4)/ajacob;
|
||||
we=ajacob*w(i);
|
||||
Ke=Ke+we*cond*phix'*phix
|
||||
Me=Me+(we*rho*spec*phi'*phi)/dtime;
|
||||
end
|
||||
Me
|
||||
% Add penalty term and get temp gradient on interface
|
||||
if enr==4;
|
||||
xi=point;
|
||||
gm(1)=(1.-xi)/2.;
|
||||
gm(3)=(1.+xi)/2.;
|
||||
term=theta(1)*gm(1)+theta(2)*gm(3);
|
||||
gm(2)=gm(1)*(abs(term)-abs(theta(1)));
|
||||
gm(4)=gm(3)*(abs(term)-abs(theta(2)));
|
||||
pen=beta*(gm'*gm);
|
||||
pfL=beta*1*gm';
|
||||
Ke=Ke+pen;
|
||||
else
|
||||
pen=zeros(4);
|
||||
pfL=zeros(4,1);
|
||||
end
|
||||
% Assemble Global Matrices
|
||||
gnum=2.*elemNodes(e,1)-1.;
|
||||
for i=1:4;
|
||||
for j=1:4;
|
||||
K(gnum+j-1,gnum+i-1)=K(gnum+j-1,gnum+i-1)+Ke(j,i);
|
||||
M(gnum+j-1,gnum+i-1)=M(gnum+j-1,gnum+i-1)+Me(j,i);
|
||||
end
|
||||
pforce(gnum+i-1)=pforce(gnum+i-1)+pfL(i);
|
||||
end
|
||||
end
|
||||
A=K+M;
|
||||
Sub=A*Bound;
|
||||
M*Tnew;
|
||||
RHS=M*Tnew-Sub+pforce;
|
||||
% Apply Boundary Conditions
|
||||
Biindex=0.;
|
||||
for i=1:ndof*numNodes;
|
||||
if Bound(i)==0.;
|
||||
Biindex=Biindex+1;
|
||||
RHSR(Biindex)=RHS(i);
|
||||
jindex=0;
|
||||
for j=1:ndof*numNodes;
|
||||
if Bound(j)==0.;
|
||||
jindex=jindex+1;
|
||||
AR(Biindex,jindex)=A(i,j);
|
||||
end
|
||||
end
|
||||
end
|
||||
end
|
||||
%Solve
|
||||
Tnewr=(AR^-1)*RHSR';
|
||||
% Restore Matrices
|
||||
Biindex=0;
|
||||
for i=1:ndof*numNodes;
|
||||
if Bound(i)==0.;
|
||||
Biindex=Biindex+1;
|
||||
Tnew(i)=Tnewr(Biindex);
|
||||
end
|
||||
end
|
||||
Tnew
|
||||
end
|
||||
stored';
|
||||
783
Unpublished/XFEM/2D_Solver/XCOR_2D.asv
Normal file
783
Unpublished/XFEM/2D_Solver/XCOR_2D.asv
Normal file
|
|
@ -0,0 +1,783 @@
|
|||
function []=XCOR_2D()
|
||||
clear all
|
||||
% Define Mesh
|
||||
NumX=2;
|
||||
NumY=1;
|
||||
delX=1.;
|
||||
delY=1.;
|
||||
numElem=NumX*NumY;
|
||||
numNodes=(NumX+1)*(NumY+1);
|
||||
Elength=(delX+delY)/2.;
|
||||
[Node,Element]=buildMesh(NumX,NumY,delX,delY);
|
||||
% Simulation Parameters
|
||||
rho=1.;
|
||||
Penalty=80.;
|
||||
dtImp=0.1;
|
||||
dtExp=0.01;
|
||||
tsteps=4;
|
||||
bandWidth=10.;
|
||||
epsilon=0.00001;
|
||||
visc=0.0005;
|
||||
% Get Initial Level Set
|
||||
LSetOld=initialLSet(Node,numNodes);
|
||||
% plotLSet(NumX,NumY,delX,delY,LSet);
|
||||
% Initial Conditions
|
||||
Temp=zeros(numNodes*2,1);
|
||||
for i=1:numNodes
|
||||
if LSetOld(i)<=0
|
||||
Temp(2*i-1)=1.;
|
||||
end
|
||||
end
|
||||
% Boundary Conditions
|
||||
Bound=zeros(numNodes*2,1);
|
||||
for i=1:numNodes
|
||||
if Node(i,1)<delX/10.
|
||||
Bound(2*i-1)=1.;
|
||||
end
|
||||
end
|
||||
% Loop through time steps
|
||||
for ts=1:tsteps
|
||||
% Update Level Set
|
||||
LSetNew=updateLSet(Temp,Node,numNodes,Element,numElem,dtImp,dtExp,LSetOld,...
|
||||
Elength,bandWidth,epsilon,visc);
|
||||
% Solve for Temperature
|
||||
Temp=getTemp(Node,Element,numNodes,numElem,LSetNew,Bound,Temp,Penalty,rho,dtImp,LSetOld);
|
||||
LSetOld=LSetNew;
|
||||
LSetOld'
|
||||
end
|
||||
end
|
||||
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||
% Create a linear quadrilateral FE mesh
|
||||
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||
function [Node,Element]=buildMesh(NumX,NumY,delX,delY)
|
||||
for j=1:NumY+1
|
||||
for i=1:NumX+1
|
||||
index=i+(NumX+1)*(j-1);
|
||||
Node(index,1)=single((i-1.))*delX;
|
||||
Node(index,2)=single((j-1.))*delY;
|
||||
end
|
||||
end
|
||||
for j=1:NumY
|
||||
for i=1:NumX
|
||||
index=i+NumX*(j-1);
|
||||
Element(index,1)=i+(NumX+1)*(j-1);
|
||||
Element(index,2)=i+(NumX+1)*(j-1)+1;
|
||||
Element(index,3)=i+(NumX+1)*(j)+1;
|
||||
Element(index,4)=i+(NumX+1)*(j);
|
||||
end
|
||||
end
|
||||
end
|
||||
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||
% This function updates the level set
|
||||
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||
function [LSet]=updateLSet(Temp,Node,numNodes,Element,numElem,dtImp,dtExp,LSet,...
|
||||
Elength,bandWidth,epsilon,visc)
|
||||
% parameters
|
||||
charLen=epsilon*Elength;
|
||||
for tstep=1:floor(dtImp/dtExp)
|
||||
% Identify Narrow Band Elements and Get Local Level Set
|
||||
[NBelem,NBElems,NGlobal,NLocal,NBNodes,LSetLocal]=getNarrowBand(bandWidth,...
|
||||
Elength,LSet,Element,numElem,numNodes);
|
||||
% Identify Scalar Velocity on Nodes Crossed By Interface - F
|
||||
F=getF(Temp,LSetLocal,NBElems,NBNodes,NLocal,NBelem,Node,Elength);
|
||||
% Get 'Stiffness' Matrix - A
|
||||
A=getA(Node,NLocal,NBelem,NBNodes,NBElems,LSetLocal);
|
||||
% Apply BCs
|
||||
RHS=-A*F;
|
||||
iindex=0;
|
||||
for i=1:NBNodes
|
||||
if F(i)==0.
|
||||
iindex=iindex+1;
|
||||
RHSred(iindex)=RHS(i);
|
||||
jindex=0;
|
||||
for j=1:NBNodes
|
||||
if F(j)==0.
|
||||
jindex=jindex+1;
|
||||
Ared(iindex,jindex)=A(i,j);
|
||||
end
|
||||
end
|
||||
end
|
||||
end
|
||||
if iindex>0
|
||||
% Solve for Fred
|
||||
Fred=(Ared^-1)*RHSred';
|
||||
% Get F
|
||||
iindex=0;
|
||||
for i=1:NBNodes
|
||||
if F(i)==0.
|
||||
iindex=iindex+1;
|
||||
F(i)=Fred(iindex);
|
||||
end
|
||||
end
|
||||
end
|
||||
% Get Level Set Equation Terms
|
||||
[M,MGLS,f1,f2,f3]=getTerms(Node,NLocal,NBelem,NBNodes,NBElems,LSetLocal,visc,charLen,F);
|
||||
LSetLocal=LSetLocal-((((M+MGLS)^-1)*dtExp)*(f1+f2+f3))';
|
||||
% Reinitialize LS
|
||||
%LSetLocal=fastMarch(LSetLocal,NBelem,Node,NLocal,NBNodes,NBElems);
|
||||
for i=1:NBNodes
|
||||
LSet(NLocal(i))=LSetLocal(i);
|
||||
end
|
||||
end
|
||||
end
|
||||
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||
% Find elements in narrow band and create map between
|
||||
% global node labels and those in narrow band
|
||||
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||
function [NBelem,NBElems,NGlobal,NLocal,NBNodes,LSetLocal]=getNarrowBand(bandWidth,...
|
||||
ELength,LSet,Element,numElem,numNodes)
|
||||
% Identify Narrow Band Elements
|
||||
NBElems=0;
|
||||
NBNodes=0;
|
||||
NGlobal=zeros(numNodes);
|
||||
for i=1:numElem
|
||||
check=0;
|
||||
for iNd=1:4
|
||||
if abs(LSet(Element(i,iNd)))<=bandWidth*ELength
|
||||
check=1;
|
||||
end
|
||||
end
|
||||
% If an element is in the narrow band split it into triangles
|
||||
if check==1
|
||||
for j=1:4
|
||||
if NGlobal(Element(i,j))==0
|
||||
NBNodes=NBNodes+1;
|
||||
NGlobal(Element(i,j))=NBNodes;
|
||||
NLocal(NBNodes)=Element(i,j);
|
||||
end
|
||||
end
|
||||
NBElems=NBElems+1;
|
||||
NBelem(NBElems,1)=NGlobal(Element(i,1));
|
||||
NBelem(NBElems,2)=NGlobal(Element(i,2));
|
||||
NBelem(NBElems,3)=NGlobal(Element(i,3));
|
||||
NBElems=NBElems+1;
|
||||
NBelem(NBElems,1)=NGlobal(Element(i,1));
|
||||
NBelem(NBElems,2)=NGlobal(Element(i,3));
|
||||
NBelem(NBElems,3)=NGlobal(Element(i,4));
|
||||
end
|
||||
end
|
||||
% Get local Level Set
|
||||
for i=1:NBNodes
|
||||
LSetLocal(i)=LSet(NLocal(i));
|
||||
end
|
||||
end
|
||||
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||
% Get Interface Normal Veloctiy 'F'
|
||||
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||
function F=getF(Temp,LSetLocal,NBElems,NBNodes,NLocal,NBelem,Node,ELength)
|
||||
F=zeros(NBNodes,1);
|
||||
eStat=zeros(NBElems,1);
|
||||
nData=zeros(NBNodes,2);
|
||||
for i=1:NBElems
|
||||
for j=1:3
|
||||
L(j)=LSetLocal(NBelem(i,j));
|
||||
end
|
||||
x11=Node(NLocal(NBelem(i,1)),1);
|
||||
x12=Node(NLocal(NBelem(i,2)),1);
|
||||
x13=Node(NLocal(NBelem(i,3)),1);
|
||||
y11=Node(NLocal(NBelem(i,1)),2);
|
||||
y12=Node(NLocal(NBelem(i,2)),2);
|
||||
y13=Node(NLocal(NBelem(i,3)),2);
|
||||
count=0.;
|
||||
if sign(L(1)) ~= sign(L(2))
|
||||
eStat(i)=1;
|
||||
count=count+1;
|
||||
f=abs(L(1))/(abs(L(1))+abs(L(2)));
|
||||
xi(count)=f*(x12-x11)+x11;
|
||||
yi(count)=f*(y12-y11)+y11;
|
||||
end
|
||||
if sign(L(1)) ~= sign(L(3))
|
||||
eStat(i)=1;
|
||||
count=count+1;
|
||||
f=abs(L(1))/(abs(L(1))+abs(L(3)));
|
||||
xi(count)=f*(x13-x11)+x11;
|
||||
yi(count)=f*(y13-y11)+y11 ;
|
||||
end
|
||||
if sign(L(2)) ~= sign(L(3))
|
||||
eStat(i)=1;
|
||||
count=count+1;
|
||||
f=abs(L(2))/(abs(L(2))+abs(L(3)));
|
||||
xi(count)=f*(x13-x12)+x12;
|
||||
yi(count)=f*(y13-y12)+y12 ;
|
||||
end
|
||||
if eStat(i)==1
|
||||
n=[yi(2)-yi(1); xi(1)-xi(2)];
|
||||
n=n/norm(n);
|
||||
xd(1,1)=(xi(1)+xi(2))/2.;
|
||||
xd(1,2)=(yi(1)+yi(2))/2.;
|
||||
xd(2,1)=0.1*ELength*n(1)+xd(1,1);
|
||||
xd(2,2)=0.1*ELength*n(2)+xd(1,2);
|
||||
% Check if xd2 is in element
|
||||
v0(1)=x11;
|
||||
v0(2)=y11;
|
||||
v1(1)=x12-x11;
|
||||
v1(2)=y12-y11;
|
||||
v2(1)=x13-x11;
|
||||
v2(2)=y13-y11;
|
||||
v(1)=xd(2,1);
|
||||
v(2)=xd(2,2);
|
||||
ra=((v(1)*v2(2)-v2(1)*v(2))-(v0(1)*v2(2)-v2(1)*v0(2)))/(v1(1)*v2(2)-v2(1)*v1(2));
|
||||
rb=-((v(1)*v1(2)-v1(1)*v(2))-(v0(1)*v1(2)-v1(1)*v0(2)))/(v1(1)*v2(2)-v2(1)*v1(2));
|
||||
check=0;
|
||||
if ra>0. && rb>0. && ra+rb<1.
|
||||
index=i;
|
||||
x21=x11;
|
||||
x22=x12;
|
||||
x23=x13;
|
||||
y21=y11;
|
||||
y22=y12;
|
||||
y23=y13;
|
||||
else
|
||||
for j=1:NBElems
|
||||
tx1=Node(NLocal(NBelem(j,1)),1);
|
||||
tx2=Node(NLocal(NBelem(j,2)),1);
|
||||
tx3=Node(NLocal(NBelem(j,3)),1);
|
||||
ty1=Node(NLocal(NBelem(j,1)),2);
|
||||
ty2=Node(NLocal(NBelem(j,2)),2);
|
||||
ty3=Node(NLocal(NBelem(j,3)),2);
|
||||
v0(1)=tx1;
|
||||
v0(2)=ty1;
|
||||
v1(1)=tx2-tx1;
|
||||
v1(2)=ty2-ty1;
|
||||
v2(1)=tx3-tx1;
|
||||
v2(2)=ty3-ty1;
|
||||
v(1)=xd(2,1);
|
||||
v(2)=xd(2,2);
|
||||
ra=((v(1)*v2(2)-v2(1)*v(2))-(v0(1)*v2(2)-v2(1)*v0(2)))/(v1(1)*v2(2)-v2(1)*v1(2));
|
||||
rb=-((v(1)*v1(2)-v1(1)*v(2))-(v0(1)*v1(2)-v1(1)*v0(2)))/(v1(1)*v2(2)-v2(1)*v1(2));
|
||||
if ra>0. && rb>0. && ra+rb<1.
|
||||
index=j;
|
||||
x21=tx1;
|
||||
x22=tx2;
|
||||
x23=tx3;
|
||||
y21=ty1;
|
||||
y22=ty2;
|
||||
y23=ty3;
|
||||
end
|
||||
end
|
||||
end
|
||||
Ae1=0.5*((x12*y13-x13*y12)+(y12-y13)*x11+(x13-x12)*y11);
|
||||
Ae2=0.5*((x22*y23-x23*y22)+(y22-y23)*x21+(x23-x22)*y21);
|
||||
N1=(1./(2.*Ae))*((y2-y3)*(xd(j,1)-x2)+(x3-x2)*(xd(j,2)-y2));
|
||||
N2=(1./(2.*Ae))*((y3-y1)*(xd(j,1)-x3)+(x1-x3)*(xd(j,2)-y3));
|
||||
N3=(1./(2.*Ae))*((y1-y2)*(xd(j,1)-x1)+(x2-x1)*(xd(j,2)-y1));
|
||||
T1=Temp(2*NLocal(NBelem(i,1))-1);
|
||||
T2=Temp(2*NLocal(NBelem(i,2))-1);
|
||||
T3=Temp(2*NLocal(NBelem(i,3))-1);
|
||||
a1=Temp(2*NLocal(NBelem(i,1)));
|
||||
a2=Temp(2*NLocal(NBelem(i,2)));
|
||||
a3=Temp(2*NLocal(NBelem(i,3)));
|
||||
L1=LSetLocal(NBelem(i,1));
|
||||
L2=LSetLocal(NBelem(i,2));
|
||||
L3=LSetLocal(NBelem(i,3));
|
||||
LS=abs(N1*L1+L2*N2+L3*N3);
|
||||
p1=N1*(LS-abs(L1));
|
||||
p2=N2*(LS-abs(L2));
|
||||
p3=N3*(LS-abs(L3));
|
||||
T(j)=N1*T1+N2*T2+N3*T3+p1*a1+p2*a2+p3*a3;
|
||||
end
|
||||
gradT=(T(2)-T(1))/(0.1*ELength);
|
||||
for j=1:3
|
||||
nData(NBelem(i,j),1)=nData(NBelem(i,j),1)+1.;
|
||||
nData(NBelem(i,j),2)=nData(NBelem(i,j),2)+0.1*gradT;
|
||||
end
|
||||
end
|
||||
end
|
||||
for i=1:NBNodes
|
||||
if nData(i,1)>0
|
||||
F(i)=nData(i,2)/nData(i,1);
|
||||
end
|
||||
end
|
||||
end
|
||||
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||
% Get 'Stiffness' Matrix 'A'
|
||||
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||
function [A]=getA(Node,NLocal,NBelem,NBNodes,NBElems,LSetLocal)
|
||||
A=zeros(NBNodes);
|
||||
for i=1:NBElems
|
||||
gx(1)=2./3.;
|
||||
gx(2)=1./6.;
|
||||
gx(3)=1./6.;
|
||||
hx(1)=1./6.;
|
||||
hx(2)=1./6.;
|
||||
hx(3)=2./3.;
|
||||
AfL=zeros(3);
|
||||
AfLGLS=zeros(3);
|
||||
x1=Node(NLocal(NBelem(i,1)),1);
|
||||
y1=Node(NLocal(NBelem(i,1)),2);
|
||||
x2=Node(NLocal(NBelem(i,2)),1);
|
||||
y2=Node(NLocal(NBelem(i,2)),2);
|
||||
x3=Node(NLocal(NBelem(i,3)),1);
|
||||
y3=Node(NLocal(NBelem(i,3)),2);
|
||||
for j=1:3
|
||||
g=gx(j);
|
||||
h=hx(j);
|
||||
phi(1)=1.-g-h;
|
||||
phi(2)=g;
|
||||
phi(3)=h;
|
||||
phig(1)=-1.;
|
||||
phig(2)=1.;
|
||||
phig(3)=0.;
|
||||
phih(1)=-1.;
|
||||
phih(2)=0.;
|
||||
phih(3)=1.;
|
||||
djac=2*abs(x1*(y2-y3)+x2*(y3-y1)+x3*(y1-y2));
|
||||
for k=1:3
|
||||
phix(k)=(1./djac)*((-y1+y3)*phig(k)+(y1-y2)*phih(k));
|
||||
phiy(k)=(1./djac)*((x1-x3)*phig(k)+(-x1+x2)*phih(k));
|
||||
end
|
||||
delphi=[phix;phiy];
|
||||
nodalLset=[LSetLocal(NBelem(i,1));LSetLocal(NBelem(i,2));LSetLocal(NBelem(i,3))];
|
||||
set=phi*nodalLset;
|
||||
delset=delphi*nodalLset;
|
||||
AfL=AfL+(phi'*sign(set))*(delset'*delphi)/3.;
|
||||
AfLGLS=AfLGLS+(delphi'*delset)*(1./norm(delset))*(delset'*delphi)/3.;
|
||||
end
|
||||
sum=AfL+AfLGLS;
|
||||
for k=1:3;
|
||||
for j=1:3;
|
||||
A(NBelem(i,j),NBelem(i,k))=A(NBelem(i,j),NBelem(i,k))+sum(j,k);
|
||||
end
|
||||
end
|
||||
end
|
||||
end
|
||||
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||
% Get terms for LS equation
|
||||
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||
function [M,MGLS,f1,f2,f3]=getTerms(Node,NLocal,NBelem,NBNodes,NBElems,LSetLocal,visc,charLen,F)
|
||||
M=zeros(NBNodes);
|
||||
MGLS=zeros(NBNodes);
|
||||
f1=zeros(NBNodes,1);
|
||||
f2=zeros(NBNodes,1);
|
||||
f3=zeros(NBNodes,1);
|
||||
for i=1:NBElems
|
||||
ML=zeros(3);
|
||||
MGLSL=zeros(3);
|
||||
f1L=zeros(3,1);
|
||||
f2L=zeros(3,1);
|
||||
f3L=zeros(3,1);
|
||||
gx(1)=2./3.;
|
||||
gx(2)=1./6.;
|
||||
gx(3)=1./6.;
|
||||
hx(1)=1./6.;
|
||||
hx(2)=1./6.;
|
||||
hx(3)=2./3.;
|
||||
x1=Node(NLocal(NBelem(i,1)),1);
|
||||
y1=Node(NLocal(NBelem(i,1)),2);
|
||||
x2=Node(NLocal(NBelem(i,2)),1);
|
||||
y2=Node(NLocal(NBelem(i,2)),2);
|
||||
x3=Node(NLocal(NBelem(i,3)),1);
|
||||
y3=Node(NLocal(NBelem(i,3)),2);
|
||||
for j=1:3
|
||||
g=gx(j);
|
||||
h=hx(j);
|
||||
phi(1)=1.-g-h;
|
||||
phi(2)=g;
|
||||
phi(3)=h;
|
||||
phig(1)=-1.;
|
||||
phig(2)=1.;
|
||||
phig(3)=0.;
|
||||
phih(1)=-1.;
|
||||
phih(2)=0.;
|
||||
phih(3)=1.;
|
||||
djac=abs(x1*(y2-y3)+x2*(y3-y1)+x3*(y1-y2));
|
||||
for k=1:3
|
||||
phix(k)=(1./djac)*((-y1+y3)*phig(k)+(y1-y2)*phih(k));
|
||||
phiy(k)=(1./djac)*((x1-x3)*phig(k)+(-x1+x2)*phih(k));
|
||||
end
|
||||
delphi=[phix;phiy];
|
||||
nodalLset=[LSetLocal(NBelem(i,1));LSetLocal(NBelem(i,2));LSetLocal(NBelem(i,3))];
|
||||
nodalF=[F(NBelem(i,1));F(NBelem(i,2));F(NBelem(i,3))];
|
||||
delset=delphi*nodalLset;
|
||||
Floc=phi*nodalF;
|
||||
ML=ML+(phi'*phi)/3.;
|
||||
MGLSL=MGLSL+((delphi'*(delset/norm(delset)))*Floc*(charLen/abs(Floc)))*phi/3.;
|
||||
f1L=f1L+phi'*Floc*norm(delset)/3.;
|
||||
f2L=f2L+(delphi'*(delset/norm(delset))*Floc)*(charLen/abs(Floc))*Floc*norm(delset)/3.;
|
||||
vs=charLen*((abs(visc+Floc*norm(delset)))/(norm(Floc*delset)+charLen));
|
||||
f3L=f3L+vs*delphi'*delset/3.;
|
||||
end
|
||||
for k=1:3;
|
||||
for j=1:3;
|
||||
M(NBelem(i,j),NBelem(i,k))=M(NBelem(i,j),NBelem(i,k))+ML(j,k);
|
||||
MGLS(NBelem(i,j),NBelem(i,k))=MGLS(NBelem(i,j),NBelem(i,k))+MGLSL(j,k);
|
||||
end
|
||||
f1(NBelem(i,k))=f1(NBelem(i,k))+f1L(k);
|
||||
f2(NBelem(i,k))=f2(NBelem(i,k))+f2L(k);
|
||||
f3(NBelem(i,k))=f3(NBelem(i,k))+f3L(k);
|
||||
end
|
||||
end
|
||||
end
|
||||
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||
% Use Fast March Method to Reinitialize LS
|
||||
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||
function LSetLocal=fastMarch(LSetLocal,NBelem,Node,NLocal,NBNodes,NBElems)
|
||||
newlSet=LSetLocal;
|
||||
% Reinitialize LS
|
||||
nstat=zeros(NBNodes,1);
|
||||
for i=1:NBElems
|
||||
for j=1:3
|
||||
L(j)=sign(LSetLocal(NBelem(i,j)));
|
||||
end
|
||||
if L(1) ~= L(2) || L(1) ~= L(3)
|
||||
for j=1:3
|
||||
nstat(NBelem(i,j))=1;
|
||||
end
|
||||
end
|
||||
end
|
||||
maincheck=0;
|
||||
while(maincheck==0)
|
||||
lmin=1000.;
|
||||
avlmin=1000.;
|
||||
eindex=0;
|
||||
nindex=0;
|
||||
maincheck=1;
|
||||
for i=1:NBElems
|
||||
if nstat(NBelem(i,1))+nstat(NBelem(i,2))+nstat(NBelem(i,3))==2
|
||||
maincheck=0;
|
||||
check=0;
|
||||
ltot=0.;
|
||||
for j=1:3
|
||||
if nstat(NBelem(i,j))==0
|
||||
if abs(LSetLocal(NBelem(i,j)))<=lmin
|
||||
check=1;
|
||||
tempindex=j;
|
||||
end
|
||||
end
|
||||
ltot=ltot+abs(LSetLocal(NBelem(i,j)));
|
||||
end
|
||||
if check==1 && ltot/3.<=avlmin
|
||||
eindex=i;
|
||||
nindex=tempindex;
|
||||
lmin=LSetLocal(NBelem(eindex,nindex));
|
||||
avlmin=ltot/3.;
|
||||
end
|
||||
end
|
||||
end
|
||||
if maincheck==0
|
||||
% Find New LS for point
|
||||
xp=Node(NLocal(NBelem(eindex,nindex)),1);
|
||||
yp=Node(NLocal(NBelem(eindex,nindex)),2);
|
||||
count=0;
|
||||
for i=1:3
|
||||
if i~=nindex
|
||||
count=count+1;
|
||||
x(count)=Node(NLocal(NBelem(eindex,i)),1);
|
||||
y(count)=Node(NLocal(NBelem(eindex,i)),2);
|
||||
lloc(count)=newlSet(NBelem(eindex,i));
|
||||
end
|
||||
end
|
||||
delxa=x(1)-xp;
|
||||
delya=y(1)-yp;
|
||||
delxb=x(2)-xp;
|
||||
delyb=y(2)-yp;
|
||||
N=[delxa delya; delxb delyb];
|
||||
M=N^-1;
|
||||
A=(M(1)*M(1)+M(2)*M(2));
|
||||
B=(M(3)*M(3)+M(4)*M(4));
|
||||
C=2.*(M(1)*M(3)+M(2)*M(4));
|
||||
a=A+B+C;
|
||||
b=-2.*lloc(1)*A-2.*lloc(2)*B-C*(lloc(1)+lloc(2));
|
||||
c=lloc(1)*lloc(1)*A+lloc(2)*lloc(2)*B+lloc(1)*lloc(2)*C-1.;
|
||||
templ1=(-b+sqrt(b*b-4.*a*c))/(2.*a);
|
||||
templ2=(-b-sqrt(b*b-4.*a*c))/(2.*a);
|
||||
if abs(templ1)>abs(templ2)
|
||||
newlSet(NBelem(eindex,nindex))=templ1;
|
||||
else
|
||||
newlSet(NBelem(eindex,nindex))=templ2;
|
||||
end
|
||||
nstat(NBelem(eindex,nindex))=1;
|
||||
end
|
||||
end
|
||||
LSetLocal=newlSet;
|
||||
end
|
||||
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||
% Solve Implicit Porblem to Get Temperature
|
||||
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||
function Temp=getTemp(Node,Element,numNodes,numElem,LSet,Bound,Temp,Penalty,rho,dtImp,LSetOld)
|
||||
K=zeros(numNodes*2,numNodes*2);
|
||||
M=zeros(numNodes*2,numNodes*2);
|
||||
MStar=zeros(numNodes*2,numNodes*2);
|
||||
pforce=zeros(numNodes*2,1);
|
||||
% Loop Through Elements
|
||||
for e=1:numElem
|
||||
Ke=zeros(8);
|
||||
Me=zeros(8);
|
||||
MeStar=zeros(8);
|
||||
for icrd=1:4;
|
||||
crdnx(icrd)=Node(Element(e,icrd),1);
|
||||
crdny(icrd)=Node(Element(e,icrd),2);
|
||||
theta(icrd)=LSet(Element(e,icrd));
|
||||
thetaO(icrd)=LSetOld(Element(e,icrd));
|
||||
end
|
||||
check=0;
|
||||
for i=1:3
|
||||
for j=i+1:4
|
||||
if sign(theta(1))~=sign(theta(j))
|
||||
check=1;
|
||||
end
|
||||
end
|
||||
end
|
||||
if check==1
|
||||
% possible enriched element
|
||||
npart=10;
|
||||
enr=npart*npart;
|
||||
for sdx=1:npart
|
||||
for sdy=1:npart
|
||||
midx=-1.-1./npart+(2./npart)*sdx;
|
||||
midy=-1.-1./npart+(2./npart)*sdy;
|
||||
subindex=npart*(sdy-1)+sdx;
|
||||
gpos=1./(sqrt(3.)*npart);
|
||||
gx(subindex,1)=midx-gpos;
|
||||
gx(subindex,2)=midx+gpos;
|
||||
gx(subindex,3)=midx+gpos;
|
||||
gx(subindex,4)=midx-gpos;
|
||||
hx(subindex,1)=midy-gpos;
|
||||
hx(subindex,2)=midy-gpos;
|
||||
hx(subindex,3)=midy+gpos;
|
||||
hx(subindex,4)=midy+gpos;
|
||||
end
|
||||
end
|
||||
% check if int points are on different sides of front
|
||||
check=0;
|
||||
for i=1:enr
|
||||
for j=1:4
|
||||
g=gx(i,j);
|
||||
h=hx(i,j);
|
||||
phi(1)=0.25*(1.-g)*(1.-h);
|
||||
phi(3)=0.25*(1.+g)*(1.-h);
|
||||
phi(5)=0.25*(1.+g)*(1.+h);
|
||||
phi(7)=0.25*(1.-g)*(1.+h);
|
||||
phiO=phi;
|
||||
iLS=theta(1)*phi(1)+theta(2)*phi(3)+theta(3)*phi(5)+theta(4)*phi(7);
|
||||
if i==1 && j==1
|
||||
sgn=sign(iLS);
|
||||
else
|
||||
if sign(iLS)~=sgn
|
||||
check=1;
|
||||
end
|
||||
end
|
||||
end
|
||||
end
|
||||
if check==0
|
||||
% regular element - fix extra dofs
|
||||
enr=1;
|
||||
gpos=1/sqrt(3.);
|
||||
gx(1,1)=-gpos;
|
||||
gx(1,2)=gpos;
|
||||
gx(1,3)=gpos;
|
||||
gx(1,4)=-gpos;
|
||||
hx(1,1)=-gpos;
|
||||
hx(1,2)=-gpos;
|
||||
hx(1,3)=gpos;
|
||||
hx(1,4)=gpos;
|
||||
end
|
||||
else
|
||||
% regular element - fix extra dofs
|
||||
enr=1;
|
||||
gpos=1/sqrt(3.);
|
||||
gx(1,1)=-gpos;
|
||||
gx(1,2)=gpos;
|
||||
gx(1,3)=gpos;
|
||||
gx(1,4)=-gpos;
|
||||
hx(1,1)=-gpos;
|
||||
hx(1,2)=-gpos;
|
||||
hx(1,3)=gpos;
|
||||
hx(1,4)=gpos;
|
||||
end
|
||||
for i=1:enr
|
||||
for j=1:4
|
||||
g=gx(i,j);
|
||||
h=hx(i,j);
|
||||
phi(1)=0.25*(1.-g)*(1.-h);
|
||||
phi(3)=0.25*(1.+g)*(1.-h);
|
||||
phi(5)=0.25*(1.+g)*(1.+h);
|
||||
phi(7)=0.25*(1.-g)*(1.+h);
|
||||
phiO=phi;
|
||||
iLS=theta(1)*phi(1)+theta(2)*phi(3)+theta(3)*phi(5)+theta(4)*phi(7);
|
||||
iLSO=thetaO(1)*phi(1)+thetaO(2)*phi(3)+thetaO(3)*phi(5)+thetaO(4)*phi(7);
|
||||
if iLS<0.
|
||||
cond=0.;
|
||||
spec=0.01;
|
||||
else
|
||||
cond=1.;
|
||||
spec=1.;
|
||||
end
|
||||
if iLSO<0.
|
||||
specO=0.01;
|
||||
else
|
||||
specO=1.;
|
||||
end
|
||||
for iter=1:4
|
||||
phi(2*iter)=phi(2*iter-1)*(abs(iLS)-abs(theta(iter)));
|
||||
phiO(2*iter)=phiO(2*iter-1)*(abs(iLSO)-abs(thetaO(iter)));
|
||||
end
|
||||
phig(1)=0.25*-(1.-h);
|
||||
phig(3)=0.25*(1.-h);
|
||||
phig(5)=0.25*(1.+h);
|
||||
phig(7)=0.25*-(1.+h);
|
||||
phih(1)=0.25*-(1.-g);
|
||||
phih(3)=0.25*-(1.+g);
|
||||
phih(5)=0.25*(1.+g);
|
||||
phih(7)=0.25*(1.-g);
|
||||
diLSg=sign(iLS)*(phig(1)*theta(1)+phig(3)*theta(2)+phig(5)*theta(3)+phig(7)*theta(4));
|
||||
diLSh=sign(iLS)*(phih(1)*theta(1)+phih(3)*theta(2)+phih(5)*theta(3)+phih(7)*theta(4));
|
||||
for iter=1:4
|
||||
phig(2*iter)=phig(2*iter-1)*(abs(iLS)-abs(theta(iter)))+phi(2*iter-1)*diLSg;
|
||||
phih(2*iter)=phih(2*iter-1)*(abs(iLS)-abs(theta(iter)))+phi(2*iter-1)*diLSh;
|
||||
end
|
||||
rjac=zeros(2,2);
|
||||
for iter=1:4
|
||||
rjac(1,1)=rjac(1,1)+phig(2*iter-1)*crdnx(iter);
|
||||
rjac(1,2)=rjac(1,2)+phig(2*iter-1)*crdny(iter);
|
||||
rjac(2,1)=rjac(2,1)+phih(2*iter-1)*crdnx(iter);
|
||||
rjac(2,2)=rjac(2,2)+phih(2*iter-1)*crdny(iter);
|
||||
end
|
||||
djac=rjac(1,1)*rjac(2,2)-rjac(1,2)*rjac(2,1);
|
||||
rjaci(1,1)= rjac(2,2)/djac;
|
||||
rjaci(2,2)= rjac(1,1)/djac;
|
||||
rjaci(1,2)=-rjac(1,2)/djac;
|
||||
rjaci(2,1)=-rjac(2,1)/djac ;
|
||||
for iter=1:8
|
||||
phix(iter)=rjaci(1,1)*phig(iter)+rjaci(1,2)*phih(iter);
|
||||
phiy(iter)=rjaci(2,1)*phig(iter)+rjaci(2,2)*phih(iter);
|
||||
end
|
||||
we=djac;
|
||||
Ke=Ke+(we*cond*(phix'*phix+phiy'*phiy))/double(enr);
|
||||
Me=Me+((we*rho*spec*phi'*phi)/dtImp)/double(enr);
|
||||
MeStar=MeStar+((we*rho*specO*phi'*phiO)/dtImp)/double(enr);
|
||||
end
|
||||
end
|
||||
% Add penalty term and get temp gradient on interface
|
||||
if enr>1;
|
||||
count=0;
|
||||
if sign(theta(1))~=sign(theta(2))
|
||||
count=count+1;
|
||||
f=abs(theta(1))/(abs(theta(1))+abs(theta(2)));
|
||||
xi(count)=f*(crdnx(2)-crdnx(1))+crdnx(1);
|
||||
yi(count)=f*(crdny(2)-crdny(1))+crdny(1);
|
||||
gi(count)=(2.*xi(count)-(crdnx(1)+crdnx(2)))/(-crdnx(1)+crdnx(2));
|
||||
hi(count)=-1.;
|
||||
end
|
||||
if sign(theta(2))~=sign(theta(3))
|
||||
count=count+1;
|
||||
f=abs(theta(2))/(abs(theta(2))+abs(theta(3)));
|
||||
xi(count)=f*(crdnx(3)-crdnx(2))+crdnx(2);
|
||||
yi(count)=f*(crdny(3)-crdny(2))+crdny(2);
|
||||
gi(count)=1.;
|
||||
hi(count)=(2.*yi(count)-(crdny(2)+crdny(3)))/(-crdny(2)+crdny(3));
|
||||
end
|
||||
if sign(theta(3))~=sign(theta(4))
|
||||
count=count+1;
|
||||
f=abs(theta(3))/(abs(theta(3))+abs(theta(4)));
|
||||
xi(count)=f*(crdnx(4)-crdnx(3))+crdnx(3);
|
||||
yi(count)=f*(crdny(4)-crdny(3))+crdny(3);
|
||||
gi(count)=(2.*xi(count)-(crdnx(4)+crdnx(3)))/(-crdnx(4)+crdnx(3));
|
||||
hi(count)=1.;
|
||||
end
|
||||
if sign(theta(1))~=sign(theta(4))
|
||||
count=count+1;
|
||||
f=abs(theta(1))/(abs(theta(1))+abs(theta(4)));
|
||||
xi(count)=f*(crdnx(4)-crdnx(1))+crdnx(1);
|
||||
yi(count)=f*(crdny(4)-crdny(1))+crdny(1);
|
||||
gi(count)=-1.;
|
||||
hi(count)=(2.*yi(count)-(crdny(1)+crdny(4)))/(-crdny(4)+crdny(1));
|
||||
end
|
||||
c=zeros(2,1);
|
||||
c=(c+1.);
|
||||
for i=1:2;
|
||||
G(i,1)=0.25*(1.-gi(i))*(1.-hi(i));
|
||||
G(i,3)=0.25*(1.+gi(i))*(1.-hi(i));
|
||||
G(i,5)=0.25*(1.+gi(i))*(1.+hi(i));
|
||||
G(i,7)=0.25*(1.-gi(i))*(1.+hi(i));
|
||||
G(i,2)=-G(i,1)*abs(theta(1));
|
||||
G(i,4)=-G(i,3)*abs(theta(2));
|
||||
G(i,6)=-G(i,5)*abs(theta(3));
|
||||
G(i,8)=-G(i,7)*abs(theta(4));
|
||||
end
|
||||
pen=Penalty*(G'*G);
|
||||
pfL=Penalty*G'*c;
|
||||
% pen=zeros(8);
|
||||
% pfL=zeros(8,1);
|
||||
Ke=Ke+pen;
|
||||
else
|
||||
pen=zeros(8);
|
||||
pfL=zeros(8,1);
|
||||
end
|
||||
% Assemble Global Matrices
|
||||
gnum(1)=2*Element(e,1)-1;
|
||||
gnum(2)=2*Element(e,2)-1;
|
||||
gnum(3)=2*Element(e,3)-1;
|
||||
gnum(4)=2*Element(e,4)-1;
|
||||
for i=1:4;
|
||||
for j=1:4;
|
||||
K(gnum(j),gnum(i))=K(gnum(j),gnum(i))+Ke(2*j-1,2*i-1);
|
||||
K(gnum(j)+1,gnum(i)+1)=K(gnum(j)+1,gnum(i)+1)+Ke(2*j,2*i);
|
||||
M(gnum(j),gnum(i))=M(gnum(j),gnum(i))+Me(2*j-1,2*i-1);
|
||||
M(gnum(j)+1,gnum(i)+1)=M(gnum(j)+1,gnum(i)+1)+Me(2*j,2*i);
|
||||
MStar(gnum(j),gnum(i))=MStar(gnum(j),gnum(i))+MeStar(2*j-1,2*i-1);
|
||||
MStar(gnum(j)+1,gnum(i)+1)=MStar(gnum(j)+1,gnum(i)+1)+MeStar(2*j,2*i);
|
||||
end
|
||||
end
|
||||
for i=1:4;
|
||||
pforce(gnum(i))=pforce(gnum(i))+pfL(2*i-1);
|
||||
pforce(gnum(i)+1)=pforce(gnum(i)+1)+pfL(2*i);
|
||||
end
|
||||
end
|
||||
%Remove inactive DOFs(Reduce Matrices)
|
||||
RHS=MStar*Temp;
|
||||
A=K+M;
|
||||
Sub=A*Bound;
|
||||
iindex=0;
|
||||
for i=1:2*numNodes;
|
||||
if Bound(i)==0.;
|
||||
iindex=iindex+1;
|
||||
RHSred(iindex)=RHS(i)-Sub(i)+pforce(i);
|
||||
jindex=0;
|
||||
for j=1:2*numNodes;
|
||||
if Bound(j)==0.;
|
||||
jindex=jindex+1;
|
||||
Ared(iindex,jindex)=A(i,j);
|
||||
end
|
||||
end
|
||||
end
|
||||
end
|
||||
%Solve
|
||||
Tempr=(Ared^-1)*RHSred';
|
||||
iindex=0;
|
||||
for i=1:2*numNodes;
|
||||
if Bound(i)==0.;
|
||||
iindex=iindex+1;
|
||||
Temp(i)=Tempr(iindex);
|
||||
end
|
||||
end
|
||||
Temp
|
||||
end
|
||||
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||
% Generates the initial level set
|
||||
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||
function [LSet]=initialLSet(Node,numNodes)
|
||||
%centx=4.;
|
||||
%centy=4.;
|
||||
%rad=2.1;
|
||||
%for i=1:numNodes;
|
||||
% dist=sqrt((Node(i,1)-centx)*(Node(i,1)-centx)+(Node(i,2)-centy)*(Node(i,2)-centy));
|
||||
% LSet(i)=dist-rad;
|
||||
%end
|
||||
for i=1:numNodes;
|
||||
dist=Node(i,1)-1.1;
|
||||
LSet(i)=dist;
|
||||
end
|
||||
end
|
||||
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||
% Plot the level set
|
||||
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||
function []=plotLSet(NumX,NumY,delX,delY,LSet)
|
||||
[X Y]=meshgrid(0:delX:delX*NumX,0:delY:delY*NumY);
|
||||
Z=zeros(NumX+1,NumY+1);
|
||||
for i=1:(NumX+1)*(NumY+1)
|
||||
Z(i)=LSet(i);
|
||||
end
|
||||
surf(X,Y,Z)
|
||||
end
|
||||
|
||||
801
Unpublished/XFEM/2D_Solver/XCOR_2D.m
Normal file
801
Unpublished/XFEM/2D_Solver/XCOR_2D.m
Normal file
|
|
@ -0,0 +1,801 @@
|
|||
function []=XCOR_2D()
|
||||
clear all
|
||||
% Define Mesh
|
||||
NumX=10;
|
||||
NumY=1;
|
||||
delX=1.;
|
||||
delY=1.;
|
||||
numElem=NumX*NumY;
|
||||
numNodes=(NumX+1)*(NumY+1);
|
||||
Elength=(delX+delY)/2.;
|
||||
[Node,Element]=buildMesh(NumX,NumY,delX,delY);
|
||||
% Simulation Parameters
|
||||
rho=1.;
|
||||
Penalty=200.;
|
||||
dtImp=0.01;
|
||||
dtExp=0.001;
|
||||
tsteps=10;
|
||||
bandWidth=10.;
|
||||
epsilon=0.00001;
|
||||
visc=0.0005;
|
||||
% Get Initial Level Set
|
||||
LSetOld=initialLSet(Node,numNodes);
|
||||
% plotLSet(NumX,NumY,delX,delY,LSet);
|
||||
% Initial Conditions
|
||||
Temp=zeros(numNodes*2,1);
|
||||
for i=1:numNodes
|
||||
if LSetOld(i)<=0
|
||||
Temp(2*i-1)=1.;
|
||||
end
|
||||
end
|
||||
% Boundary Conditions
|
||||
Bound=zeros(numNodes*2,1);
|
||||
for i=1:numNodes
|
||||
if Node(i,1)<delX/10.
|
||||
Bound(2*i-1)=1.;
|
||||
end
|
||||
end
|
||||
% Loop through time steps
|
||||
for ts=1:tsteps
|
||||
% Update Level Set
|
||||
LSetNew=updateLSet(Temp,Node,numNodes,Element,numElem,dtImp,dtExp,LSetOld,...
|
||||
Elength,bandWidth,epsilon,visc);
|
||||
% Solve for Temperature
|
||||
Temp=getTemp(Node,Element,numNodes,numElem,LSetNew,Bound,Temp,Penalty,rho,dtImp,LSetOld);
|
||||
LSetOld=LSetNew;
|
||||
LSetOld'
|
||||
POUT(ts)=LSetOld(1);
|
||||
end
|
||||
POUT';
|
||||
end
|
||||
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||
% Create a linear quadrilateral FE mesh
|
||||
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||
function [Node,Element]=buildMesh(NumX,NumY,delX,delY)
|
||||
for j=1:NumY+1
|
||||
for i=1:NumX+1
|
||||
index=i+(NumX+1)*(j-1);
|
||||
Node(index,1)=single((i-1.))*delX;
|
||||
Node(index,2)=single((j-1.))*delY;
|
||||
end
|
||||
end
|
||||
for j=1:NumY
|
||||
for i=1:NumX
|
||||
index=i+NumX*(j-1);
|
||||
Element(index,1)=i+(NumX+1)*(j-1);
|
||||
Element(index,2)=i+(NumX+1)*(j-1)+1;
|
||||
Element(index,3)=i+(NumX+1)*(j)+1;
|
||||
Element(index,4)=i+(NumX+1)*(j);
|
||||
end
|
||||
end
|
||||
end
|
||||
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||
% This function updates the level set
|
||||
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||
function [LSet]=updateLSet(Temp,Node,numNodes,Element,numElem,dtImp,dtExp,LSet,...
|
||||
Elength,bandWidth,epsilon,visc)
|
||||
% parameters
|
||||
charLen=epsilon*Elength;
|
||||
for tstep=1:floor(dtImp/dtExp)
|
||||
% Identify Narrow Band Elements and Get Local Level Set
|
||||
[NBelem,NBElems,NGlobal,NLocal,NBNodes,LSetLocal]=getNarrowBand(bandWidth,...
|
||||
Elength,LSet,Element,numElem,numNodes);
|
||||
% Identify Scalar Velocity on Nodes Crossed By Interface - F
|
||||
F=getF(Temp,LSetLocal,NBElems,NBNodes,NLocal,NBelem,Node,Elength);
|
||||
% Get 'Stiffness' Matrix - A
|
||||
A=getA(Node,NLocal,NBelem,NBNodes,NBElems,LSetLocal);
|
||||
% Apply BCs
|
||||
RHS=-A*F;
|
||||
iindex=0;
|
||||
for i=1:NBNodes
|
||||
if F(i)==0.
|
||||
iindex=iindex+1;
|
||||
RHSred(iindex)=RHS(i);
|
||||
jindex=0;
|
||||
for j=1:NBNodes
|
||||
if F(j)==0.
|
||||
jindex=jindex+1;
|
||||
Ared(iindex,jindex)=A(i,j);
|
||||
end
|
||||
end
|
||||
end
|
||||
end
|
||||
if iindex>0
|
||||
% Solve for Fred
|
||||
Fred=(Ared^-1)*RHSred';
|
||||
% Get F
|
||||
iindex=0;
|
||||
for i=1:NBNodes
|
||||
if F(i)==0.
|
||||
iindex=iindex+1;
|
||||
F(i)=Fred(iindex);
|
||||
end
|
||||
end
|
||||
end
|
||||
% Get Level Set Equation Terms
|
||||
[M,MGLS,f1,f2,f3]=getTerms(Node,NLocal,NBelem,NBNodes,NBElems,LSetLocal,visc,charLen,F);
|
||||
LSetLocal=LSetLocal-((((M+MGLS)^-1)*dtExp)*(f1+f2+f3))';
|
||||
% Reinitialize LS
|
||||
%LSetLocal=fastMarch(LSetLocal,NBelem,Node,NLocal,NBNodes,NBElems);
|
||||
for i=1:NBNodes
|
||||
LSet(NLocal(i))=LSetLocal(i);
|
||||
end
|
||||
end
|
||||
end
|
||||
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||
% Find elements in narrow band and create map between
|
||||
% global node labels and those in narrow band
|
||||
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||
function [NBelem,NBElems,NGlobal,NLocal,NBNodes,LSetLocal]=getNarrowBand(bandWidth,...
|
||||
ELength,LSet,Element,numElem,numNodes)
|
||||
% Identify Narrow Band Elements
|
||||
NBElems=0;
|
||||
NBNodes=0;
|
||||
NGlobal=zeros(numNodes);
|
||||
for i=1:numElem
|
||||
check=0;
|
||||
for iNd=1:4
|
||||
if abs(LSet(Element(i,iNd)))<=bandWidth*ELength
|
||||
check=1;
|
||||
end
|
||||
end
|
||||
% If an element is in the narrow band split it into triangles
|
||||
if check==1
|
||||
for j=1:4
|
||||
if NGlobal(Element(i,j))==0
|
||||
NBNodes=NBNodes+1;
|
||||
NGlobal(Element(i,j))=NBNodes;
|
||||
NLocal(NBNodes)=Element(i,j);
|
||||
end
|
||||
end
|
||||
NBElems=NBElems+1;
|
||||
NBelem(NBElems,1)=NGlobal(Element(i,1));
|
||||
NBelem(NBElems,2)=NGlobal(Element(i,2));
|
||||
NBelem(NBElems,3)=NGlobal(Element(i,3));
|
||||
NBElems=NBElems+1;
|
||||
NBelem(NBElems,1)=NGlobal(Element(i,1));
|
||||
NBelem(NBElems,2)=NGlobal(Element(i,3));
|
||||
NBelem(NBElems,3)=NGlobal(Element(i,4));
|
||||
end
|
||||
end
|
||||
% Get local Level Set
|
||||
for i=1:NBNodes
|
||||
LSetLocal(i)=LSet(NLocal(i));
|
||||
end
|
||||
end
|
||||
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||
% Get Interface Normal Veloctiy 'F'
|
||||
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||
function F=getF(Temp,LSetLocal,NBElems,NBNodes,NLocal,NBelem,Node,ELength)
|
||||
F=zeros(NBNodes,1);
|
||||
eStat=zeros(NBElems,1);
|
||||
nData=zeros(NBNodes,2);
|
||||
for i=1:NBElems
|
||||
for j=1:3
|
||||
L(j)=LSetLocal(NBelem(i,j));
|
||||
end
|
||||
x11=Node(NLocal(NBelem(i,1)),1);
|
||||
x12=Node(NLocal(NBelem(i,2)),1);
|
||||
x13=Node(NLocal(NBelem(i,3)),1);
|
||||
y11=Node(NLocal(NBelem(i,1)),2);
|
||||
y12=Node(NLocal(NBelem(i,2)),2);
|
||||
y13=Node(NLocal(NBelem(i,3)),2);
|
||||
count=0.;
|
||||
if sign(L(1)) ~= sign(L(2))
|
||||
eStat(i)=1;
|
||||
count=count+1;
|
||||
f=abs(L(1))/(abs(L(1))+abs(L(2)));
|
||||
xi(count)=f*(x12-x11)+x11;
|
||||
yi(count)=f*(y12-y11)+y11;
|
||||
end
|
||||
if sign(L(1)) ~= sign(L(3))
|
||||
eStat(i)=1;
|
||||
count=count+1;
|
||||
f=abs(L(1))/(abs(L(1))+abs(L(3)));
|
||||
xi(count)=f*(x13-x11)+x11;
|
||||
yi(count)=f*(y13-y11)+y11 ;
|
||||
end
|
||||
if sign(L(2)) ~= sign(L(3))
|
||||
eStat(i)=1;
|
||||
count=count+1;
|
||||
f=abs(L(2))/(abs(L(2))+abs(L(3)));
|
||||
xi(count)=f*(x13-x12)+x12;
|
||||
yi(count)=f*(y13-y12)+y12 ;
|
||||
end
|
||||
if eStat(i)==1
|
||||
n=[yi(2)-yi(1); xi(1)-xi(2)];
|
||||
n=n/norm(n);
|
||||
xd(1,1)=(xi(1)+xi(2))/2.;
|
||||
xd(1,2)=(yi(1)+yi(2))/2.;
|
||||
xd(2,1)=0.15*ELength*n(1)+xd(1,1);
|
||||
xd(2,2)=0.15*ELength*n(2)+xd(1,2);
|
||||
% Check if xd2 is in element
|
||||
v0(1)=x11;
|
||||
v0(2)=y11;
|
||||
v1(1)=x12-x11;
|
||||
v1(2)=y12-y11;
|
||||
v2(1)=x13-x11;
|
||||
v2(2)=y13-y11;
|
||||
v(1)=xd(2,1);
|
||||
v(2)=xd(2,2);
|
||||
ra=((v(1)*v2(2)-v2(1)*v(2))-(v0(1)*v2(2)-v2(1)*v0(2)))/(v1(1)*v2(2)-v2(1)*v1(2));
|
||||
rb=-((v(1)*v1(2)-v1(1)*v(2))-(v0(1)*v1(2)-v1(1)*v0(2)))/(v1(1)*v2(2)-v2(1)*v1(2));
|
||||
check=0;
|
||||
if ra>0. && rb>0. && ra+rb<1.
|
||||
index=i;
|
||||
x21=x11;
|
||||
x22=x12;
|
||||
x23=x13;
|
||||
y21=y11;
|
||||
y22=y12;
|
||||
y23=y13;
|
||||
else
|
||||
for j=1:NBElems
|
||||
tx1=Node(NLocal(NBelem(j,1)),1);
|
||||
tx2=Node(NLocal(NBelem(j,2)),1);
|
||||
tx3=Node(NLocal(NBelem(j,3)),1);
|
||||
ty1=Node(NLocal(NBelem(j,1)),2);
|
||||
ty2=Node(NLocal(NBelem(j,2)),2);
|
||||
ty3=Node(NLocal(NBelem(j,3)),2);
|
||||
v0(1)=tx1;
|
||||
v0(2)=ty1;
|
||||
v1(1)=tx2-tx1;
|
||||
v1(2)=ty2-ty1;
|
||||
v2(1)=tx3-tx1;
|
||||
v2(2)=ty3-ty1;
|
||||
v(1)=xd(2,1);
|
||||
v(2)=xd(2,2);
|
||||
ra=((v(1)*v2(2)-v2(1)*v(2))-(v0(1)*v2(2)-v2(1)*v0(2)))/(v1(1)*v2(2)-v2(1)*v1(2));
|
||||
rb=-((v(1)*v1(2)-v1(1)*v(2))-(v0(1)*v1(2)-v1(1)*v0(2)))/(v1(1)*v2(2)-v2(1)*v1(2));
|
||||
if ra>0. && rb>0. && ra+rb<1.
|
||||
index=j;
|
||||
x21=tx1;
|
||||
x22=tx2;
|
||||
x23=tx3;
|
||||
y21=ty1;
|
||||
y22=ty2;
|
||||
y23=ty3;
|
||||
end
|
||||
end
|
||||
end
|
||||
Ae=0.5*((x12*y13-x13*y12)+(y12-y13)*x11+(x13-x12)*y11);
|
||||
N1=(1./(2.*Ae))*((y12-y13)*(xd(1,1)-x12)+(x13-x12)*(xd(1,2)-y12));
|
||||
N2=(1./(2.*Ae))*((y13-y11)*(xd(1,1)-x13)+(x11-x13)*(xd(1,2)-y13));
|
||||
N3=(1./(2.*Ae))*((y11-y12)*(xd(1,1)-x11)+(x12-x11)*(xd(1,2)-y11));
|
||||
T1=Temp(2*NLocal(NBelem(i,1))-1);
|
||||
T2=Temp(2*NLocal(NBelem(i,2))-1);
|
||||
T3=Temp(2*NLocal(NBelem(i,3))-1);
|
||||
a1=Temp(2*NLocal(NBelem(i,1)));
|
||||
a2=Temp(2*NLocal(NBelem(i,2)));
|
||||
a3=Temp(2*NLocal(NBelem(i,3)));
|
||||
L1=LSetLocal(NBelem(i,1));
|
||||
L2=LSetLocal(NBelem(i,2));
|
||||
L3=LSetLocal(NBelem(i,3));
|
||||
LS=abs(N1*L1+L2*N2+L3*N3);
|
||||
p1=N1*(LS-abs(L1));
|
||||
p2=N2*(LS-abs(L2));
|
||||
p3=N3*(LS-abs(L3));
|
||||
T(1)=N1*T1+N2*T2+N3*T3+p1*a1+p2*a2+p3*a3;
|
||||
Ae=0.5*((x22*y23-x23*y22)+(y22-y23)*x21+(x23-x22)*y21);
|
||||
N1=(1./(2.*Ae))*((y22-y23)*(xd(2,1)-x22)+(x23-x22)*(xd(2,2)-y22));
|
||||
N2=(1./(2.*Ae))*((y23-y21)*(xd(2,1)-x23)+(x21-x23)*(xd(2,2)-y23));
|
||||
N3=(1./(2.*Ae))*((y21-y22)*(xd(2,1)-x21)+(x22-x21)*(xd(2,2)-y21));
|
||||
T1=Temp(2*NLocal(NBelem(index,1))-1);
|
||||
T2=Temp(2*NLocal(NBelem(index,2))-1);
|
||||
T3=Temp(2*NLocal(NBelem(index,3))-1);
|
||||
a1=Temp(2*NLocal(NBelem(index,1)));
|
||||
a2=Temp(2*NLocal(NBelem(index,2)));
|
||||
a3=Temp(2*NLocal(NBelem(index,3)));
|
||||
L1=LSetLocal(NBelem(index,1));
|
||||
L2=LSetLocal(NBelem(index,2));
|
||||
L3=LSetLocal(NBelem(index,3));
|
||||
LS=abs(N1*L1+L2*N2+L3*N3);
|
||||
p1=N1*(LS-abs(L1));
|
||||
p2=N2*(LS-abs(L2));
|
||||
p3=N3*(LS-abs(L3));
|
||||
T(2)=N1*T1+N2*T2+N3*T3+p1*a1+p2*a2+p3*a3
|
||||
gradT=(T(2)-T(1))/(0.15*ELength);
|
||||
for j=1:3
|
||||
nData(NBelem(i,j),1)=nData(NBelem(i,j),1)+1.;
|
||||
nData(NBelem(i,j),2)=nData(NBelem(i,j),2)+0.1*gradT;
|
||||
end
|
||||
end
|
||||
end
|
||||
for i=1:NBNodes
|
||||
if nData(i,1)>0
|
||||
F(i)=nData(i,2)/nData(i,1);
|
||||
end
|
||||
end
|
||||
end
|
||||
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||
% Get 'Stiffness' Matrix 'A'
|
||||
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||
function [A]=getA(Node,NLocal,NBelem,NBNodes,NBElems,LSetLocal)
|
||||
A=zeros(NBNodes);
|
||||
for i=1:NBElems
|
||||
gx(1)=2./3.;
|
||||
gx(2)=1./6.;
|
||||
gx(3)=1./6.;
|
||||
hx(1)=1./6.;
|
||||
hx(2)=1./6.;
|
||||
hx(3)=2./3.;
|
||||
AfL=zeros(3);
|
||||
AfLGLS=zeros(3);
|
||||
x1=Node(NLocal(NBelem(i,1)),1);
|
||||
y1=Node(NLocal(NBelem(i,1)),2);
|
||||
x2=Node(NLocal(NBelem(i,2)),1);
|
||||
y2=Node(NLocal(NBelem(i,2)),2);
|
||||
x3=Node(NLocal(NBelem(i,3)),1);
|
||||
y3=Node(NLocal(NBelem(i,3)),2);
|
||||
for j=1:3
|
||||
g=gx(j);
|
||||
h=hx(j);
|
||||
phi(1)=1.-g-h;
|
||||
phi(2)=g;
|
||||
phi(3)=h;
|
||||
phig(1)=-1.;
|
||||
phig(2)=1.;
|
||||
phig(3)=0.;
|
||||
phih(1)=-1.;
|
||||
phih(2)=0.;
|
||||
phih(3)=1.;
|
||||
djac=2*abs(x1*(y2-y3)+x2*(y3-y1)+x3*(y1-y2));
|
||||
for k=1:3
|
||||
phix(k)=(1./djac)*((-y1+y3)*phig(k)+(y1-y2)*phih(k));
|
||||
phiy(k)=(1./djac)*((x1-x3)*phig(k)+(-x1+x2)*phih(k));
|
||||
end
|
||||
delphi=[phix;phiy];
|
||||
nodalLset=[LSetLocal(NBelem(i,1));LSetLocal(NBelem(i,2));LSetLocal(NBelem(i,3))];
|
||||
set=phi*nodalLset;
|
||||
delset=delphi*nodalLset;
|
||||
AfL=AfL+(phi'*sign(set))*(delset'*delphi)/3.;
|
||||
AfLGLS=AfLGLS+(delphi'*delset)*(1./norm(delset))*(delset'*delphi)/3.;
|
||||
end
|
||||
sum=AfL+AfLGLS;
|
||||
for k=1:3;
|
||||
for j=1:3;
|
||||
A(NBelem(i,j),NBelem(i,k))=A(NBelem(i,j),NBelem(i,k))+sum(j,k);
|
||||
end
|
||||
end
|
||||
end
|
||||
end
|
||||
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||
% Get terms for LS equation
|
||||
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||
function [M,MGLS,f1,f2,f3]=getTerms(Node,NLocal,NBelem,NBNodes,NBElems,LSetLocal,visc,charLen,F)
|
||||
M=zeros(NBNodes);
|
||||
MGLS=zeros(NBNodes);
|
||||
f1=zeros(NBNodes,1);
|
||||
f2=zeros(NBNodes,1);
|
||||
f3=zeros(NBNodes,1);
|
||||
for i=1:NBElems
|
||||
ML=zeros(3);
|
||||
MGLSL=zeros(3);
|
||||
f1L=zeros(3,1);
|
||||
f2L=zeros(3,1);
|
||||
f3L=zeros(3,1);
|
||||
gx(1)=2./3.;
|
||||
gx(2)=1./6.;
|
||||
gx(3)=1./6.;
|
||||
hx(1)=1./6.;
|
||||
hx(2)=1./6.;
|
||||
hx(3)=2./3.;
|
||||
x1=Node(NLocal(NBelem(i,1)),1);
|
||||
y1=Node(NLocal(NBelem(i,1)),2);
|
||||
x2=Node(NLocal(NBelem(i,2)),1);
|
||||
y2=Node(NLocal(NBelem(i,2)),2);
|
||||
x3=Node(NLocal(NBelem(i,3)),1);
|
||||
y3=Node(NLocal(NBelem(i,3)),2);
|
||||
for j=1:3
|
||||
g=gx(j);
|
||||
h=hx(j);
|
||||
phi(1)=1.-g-h;
|
||||
phi(2)=g;
|
||||
phi(3)=h;
|
||||
phig(1)=-1.;
|
||||
phig(2)=1.;
|
||||
phig(3)=0.;
|
||||
phih(1)=-1.;
|
||||
phih(2)=0.;
|
||||
phih(3)=1.;
|
||||
djac=abs(x1*(y2-y3)+x2*(y3-y1)+x3*(y1-y2));
|
||||
for k=1:3
|
||||
phix(k)=(1./djac)*((-y1+y3)*phig(k)+(y1-y2)*phih(k));
|
||||
phiy(k)=(1./djac)*((x1-x3)*phig(k)+(-x1+x2)*phih(k));
|
||||
end
|
||||
delphi=[phix;phiy];
|
||||
nodalLset=[LSetLocal(NBelem(i,1));LSetLocal(NBelem(i,2));LSetLocal(NBelem(i,3))];
|
||||
nodalF=[F(NBelem(i,1));F(NBelem(i,2));F(NBelem(i,3))];
|
||||
delset=delphi*nodalLset;
|
||||
Floc=phi*nodalF;
|
||||
ML=ML+(phi'*phi)/3.;
|
||||
MGLSL=MGLSL+((delphi'*(delset/norm(delset)))*Floc*(charLen/abs(Floc)))*phi/3.;
|
||||
f1L=f1L+phi'*Floc*norm(delset)/3.;
|
||||
f2L=f2L+(delphi'*(delset/norm(delset))*Floc)*(charLen/abs(Floc))*Floc*norm(delset)/3.;
|
||||
vs=charLen*((abs(visc+Floc*norm(delset)))/(norm(Floc*delset)+charLen));
|
||||
f3L=f3L+vs*delphi'*delset/3.;
|
||||
end
|
||||
for k=1:3;
|
||||
for j=1:3;
|
||||
M(NBelem(i,j),NBelem(i,k))=M(NBelem(i,j),NBelem(i,k))+ML(j,k);
|
||||
MGLS(NBelem(i,j),NBelem(i,k))=MGLS(NBelem(i,j),NBelem(i,k))+MGLSL(j,k);
|
||||
end
|
||||
f1(NBelem(i,k))=f1(NBelem(i,k))+f1L(k);
|
||||
f2(NBelem(i,k))=f2(NBelem(i,k))+f2L(k);
|
||||
f3(NBelem(i,k))=f3(NBelem(i,k))+f3L(k);
|
||||
end
|
||||
end
|
||||
end
|
||||
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||
% Use Fast March Method to Reinitialize LS
|
||||
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||
function LSetLocal=fastMarch(LSetLocal,NBelem,Node,NLocal,NBNodes,NBElems)
|
||||
newlSet=LSetLocal;
|
||||
% Reinitialize LS
|
||||
nstat=zeros(NBNodes,1);
|
||||
for i=1:NBElems
|
||||
for j=1:3
|
||||
L(j)=sign(LSetLocal(NBelem(i,j)));
|
||||
end
|
||||
if L(1) ~= L(2) || L(1) ~= L(3)
|
||||
for j=1:3
|
||||
nstat(NBelem(i,j))=1;
|
||||
end
|
||||
end
|
||||
end
|
||||
maincheck=0;
|
||||
while(maincheck==0)
|
||||
lmin=1000.;
|
||||
avlmin=1000.;
|
||||
eindex=0;
|
||||
nindex=0;
|
||||
maincheck=1;
|
||||
for i=1:NBElems
|
||||
if nstat(NBelem(i,1))+nstat(NBelem(i,2))+nstat(NBelem(i,3))==2
|
||||
maincheck=0;
|
||||
check=0;
|
||||
ltot=0.;
|
||||
for j=1:3
|
||||
if nstat(NBelem(i,j))==0
|
||||
if abs(LSetLocal(NBelem(i,j)))<=lmin
|
||||
check=1;
|
||||
tempindex=j;
|
||||
end
|
||||
end
|
||||
ltot=ltot+abs(LSetLocal(NBelem(i,j)));
|
||||
end
|
||||
if check==1 && ltot/3.<=avlmin
|
||||
eindex=i;
|
||||
nindex=tempindex;
|
||||
lmin=LSetLocal(NBelem(eindex,nindex));
|
||||
avlmin=ltot/3.;
|
||||
end
|
||||
end
|
||||
end
|
||||
if maincheck==0
|
||||
% Find New LS for point
|
||||
xp=Node(NLocal(NBelem(eindex,nindex)),1);
|
||||
yp=Node(NLocal(NBelem(eindex,nindex)),2);
|
||||
count=0;
|
||||
for i=1:3
|
||||
if i~=nindex
|
||||
count=count+1;
|
||||
x(count)=Node(NLocal(NBelem(eindex,i)),1);
|
||||
y(count)=Node(NLocal(NBelem(eindex,i)),2);
|
||||
lloc(count)=newlSet(NBelem(eindex,i));
|
||||
end
|
||||
end
|
||||
delxa=x(1)-xp;
|
||||
delya=y(1)-yp;
|
||||
delxb=x(2)-xp;
|
||||
delyb=y(2)-yp;
|
||||
N=[delxa delya; delxb delyb];
|
||||
M=N^-1;
|
||||
A=(M(1)*M(1)+M(2)*M(2));
|
||||
B=(M(3)*M(3)+M(4)*M(4));
|
||||
C=2.*(M(1)*M(3)+M(2)*M(4));
|
||||
a=A+B+C;
|
||||
b=-2.*lloc(1)*A-2.*lloc(2)*B-C*(lloc(1)+lloc(2));
|
||||
c=lloc(1)*lloc(1)*A+lloc(2)*lloc(2)*B+lloc(1)*lloc(2)*C-1.;
|
||||
templ1=(-b+sqrt(b*b-4.*a*c))/(2.*a);
|
||||
templ2=(-b-sqrt(b*b-4.*a*c))/(2.*a);
|
||||
if abs(templ1)>abs(templ2)
|
||||
newlSet(NBelem(eindex,nindex))=templ1;
|
||||
else
|
||||
newlSet(NBelem(eindex,nindex))=templ2;
|
||||
end
|
||||
nstat(NBelem(eindex,nindex))=1;
|
||||
end
|
||||
end
|
||||
LSetLocal=newlSet;
|
||||
end
|
||||
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||
% Solve Implicit Porblem to Get Temperature
|
||||
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||
function Temp=getTemp(Node,Element,numNodes,numElem,LSet,Bound,Temp,Penalty,rho,dtImp,LSetOld)
|
||||
K=zeros(numNodes*2,numNodes*2);
|
||||
M=zeros(numNodes*2,numNodes*2);
|
||||
MStar=zeros(numNodes*2,numNodes*2);
|
||||
pforce=zeros(numNodes*2,1);
|
||||
% Loop Through Elements
|
||||
for e=1:numElem
|
||||
Ke=zeros(8);
|
||||
Me=zeros(8);
|
||||
MeStar=zeros(8);
|
||||
for icrd=1:4;
|
||||
crdnx(icrd)=Node(Element(e,icrd),1);
|
||||
crdny(icrd)=Node(Element(e,icrd),2);
|
||||
theta(icrd)=LSet(Element(e,icrd));
|
||||
thetaO(icrd)=LSetOld(Element(e,icrd));
|
||||
end
|
||||
check=0;
|
||||
for i=1:3
|
||||
for j=i+1:4
|
||||
if sign(theta(1))~=sign(theta(j))
|
||||
check=1;
|
||||
end
|
||||
end
|
||||
end
|
||||
if check==1
|
||||
% possible enriched element
|
||||
npart=10;
|
||||
enr=npart*npart;
|
||||
for sdx=1:npart
|
||||
for sdy=1:npart
|
||||
midx=-1.-1./npart+(2./npart)*sdx;
|
||||
midy=-1.-1./npart+(2./npart)*sdy;
|
||||
subindex=npart*(sdy-1)+sdx;
|
||||
gpos=1./(sqrt(3.)*npart);
|
||||
gx(subindex,1)=midx-gpos;
|
||||
gx(subindex,2)=midx+gpos;
|
||||
gx(subindex,3)=midx+gpos;
|
||||
gx(subindex,4)=midx-gpos;
|
||||
hx(subindex,1)=midy-gpos;
|
||||
hx(subindex,2)=midy-gpos;
|
||||
hx(subindex,3)=midy+gpos;
|
||||
hx(subindex,4)=midy+gpos;
|
||||
end
|
||||
end
|
||||
% check if int points are on different sides of front
|
||||
check=0;
|
||||
for i=1:enr
|
||||
for j=1:4
|
||||
g=gx(i,j);
|
||||
h=hx(i,j);
|
||||
phi(1)=0.25*(1.-g)*(1.-h);
|
||||
phi(3)=0.25*(1.+g)*(1.-h);
|
||||
phi(5)=0.25*(1.+g)*(1.+h);
|
||||
phi(7)=0.25*(1.-g)*(1.+h);
|
||||
phiO=phi;
|
||||
iLS=theta(1)*phi(1)+theta(2)*phi(3)+theta(3)*phi(5)+theta(4)*phi(7);
|
||||
if i==1 && j==1
|
||||
sgn=sign(iLS);
|
||||
else
|
||||
if sign(iLS)~=sgn
|
||||
check=1;
|
||||
end
|
||||
end
|
||||
end
|
||||
end
|
||||
if check==0
|
||||
% regular element - fix extra dofs
|
||||
enr=1;
|
||||
gpos=1/sqrt(3.);
|
||||
gx(1,1)=-gpos;
|
||||
gx(1,2)=gpos;
|
||||
gx(1,3)=gpos;
|
||||
gx(1,4)=-gpos;
|
||||
hx(1,1)=-gpos;
|
||||
hx(1,2)=-gpos;
|
||||
hx(1,3)=gpos;
|
||||
hx(1,4)=gpos;
|
||||
end
|
||||
else
|
||||
% regular element - fix extra dofs
|
||||
enr=1;
|
||||
gpos=1/sqrt(3.);
|
||||
gx(1,1)=-gpos;
|
||||
gx(1,2)=gpos;
|
||||
gx(1,3)=gpos;
|
||||
gx(1,4)=-gpos;
|
||||
hx(1,1)=-gpos;
|
||||
hx(1,2)=-gpos;
|
||||
hx(1,3)=gpos;
|
||||
hx(1,4)=gpos;
|
||||
end
|
||||
for i=1:enr
|
||||
for j=1:4
|
||||
g=gx(i,j);
|
||||
h=hx(i,j);
|
||||
phi(1)=0.25*(1.-g)*(1.-h);
|
||||
phi(3)=0.25*(1.+g)*(1.-h);
|
||||
phi(5)=0.25*(1.+g)*(1.+h);
|
||||
phi(7)=0.25*(1.-g)*(1.+h);
|
||||
phiO=phi;
|
||||
iLS=theta(1)*phi(1)+theta(2)*phi(3)+theta(3)*phi(5)+theta(4)*phi(7);
|
||||
iLSO=thetaO(1)*phi(1)+thetaO(2)*phi(3)+thetaO(3)*phi(5)+thetaO(4)*phi(7);
|
||||
if iLS<0.
|
||||
cond=0.;
|
||||
spec=0.01;
|
||||
else
|
||||
cond=1.;
|
||||
spec=1.;
|
||||
end
|
||||
if iLSO<0.
|
||||
specO=0.01;
|
||||
else
|
||||
specO=1.;
|
||||
end
|
||||
for iter=1:4
|
||||
phi(2*iter)=phi(2*iter-1)*(abs(iLS)-abs(theta(iter)));
|
||||
phiO(2*iter)=phiO(2*iter-1)*(abs(iLSO)-abs(thetaO(iter)));
|
||||
end
|
||||
phig(1)=0.25*-(1.-h);
|
||||
phig(3)=0.25*(1.-h);
|
||||
phig(5)=0.25*(1.+h);
|
||||
phig(7)=0.25*-(1.+h);
|
||||
phih(1)=0.25*-(1.-g);
|
||||
phih(3)=0.25*-(1.+g);
|
||||
phih(5)=0.25*(1.+g);
|
||||
phih(7)=0.25*(1.-g);
|
||||
diLSg=sign(iLS)*(phig(1)*theta(1)+phig(3)*theta(2)+phig(5)*theta(3)+phig(7)*theta(4));
|
||||
diLSh=sign(iLS)*(phih(1)*theta(1)+phih(3)*theta(2)+phih(5)*theta(3)+phih(7)*theta(4));
|
||||
for iter=1:4
|
||||
phig(2*iter)=phig(2*iter-1)*(abs(iLS)-abs(theta(iter)))+phi(2*iter-1)*diLSg;
|
||||
phih(2*iter)=phih(2*iter-1)*(abs(iLS)-abs(theta(iter)))+phi(2*iter-1)*diLSh;
|
||||
end
|
||||
rjac=zeros(2,2);
|
||||
for iter=1:4
|
||||
rjac(1,1)=rjac(1,1)+phig(2*iter-1)*crdnx(iter);
|
||||
rjac(1,2)=rjac(1,2)+phig(2*iter-1)*crdny(iter);
|
||||
rjac(2,1)=rjac(2,1)+phih(2*iter-1)*crdnx(iter);
|
||||
rjac(2,2)=rjac(2,2)+phih(2*iter-1)*crdny(iter);
|
||||
end
|
||||
djac=rjac(1,1)*rjac(2,2)-rjac(1,2)*rjac(2,1);
|
||||
rjaci(1,1)= rjac(2,2)/djac;
|
||||
rjaci(2,2)= rjac(1,1)/djac;
|
||||
rjaci(1,2)=-rjac(1,2)/djac;
|
||||
rjaci(2,1)=-rjac(2,1)/djac ;
|
||||
for iter=1:8
|
||||
phix(iter)=rjaci(1,1)*phig(iter)+rjaci(1,2)*phih(iter);
|
||||
phiy(iter)=rjaci(2,1)*phig(iter)+rjaci(2,2)*phih(iter);
|
||||
end
|
||||
we=djac;
|
||||
Ke=Ke+(we*cond*(phix'*phix+phiy'*phiy))/double(enr);
|
||||
Me=Me+((we*rho*spec*phi'*phi)/dtImp)/double(enr);
|
||||
MeStar=MeStar+((we*rho*specO*phi'*phiO)/dtImp)/double(enr);
|
||||
end
|
||||
end
|
||||
% Add penalty term and get temp gradient on interface
|
||||
if enr>1;
|
||||
count=0;
|
||||
if sign(theta(1))~=sign(theta(2))
|
||||
count=count+1;
|
||||
f=abs(theta(1))/(abs(theta(1))+abs(theta(2)));
|
||||
xi(count)=f*(crdnx(2)-crdnx(1))+crdnx(1);
|
||||
yi(count)=f*(crdny(2)-crdny(1))+crdny(1);
|
||||
gi(count)=(2.*xi(count)-(crdnx(1)+crdnx(2)))/(-crdnx(1)+crdnx(2));
|
||||
hi(count)=-1.;
|
||||
end
|
||||
if sign(theta(2))~=sign(theta(3))
|
||||
count=count+1;
|
||||
f=abs(theta(2))/(abs(theta(2))+abs(theta(3)));
|
||||
xi(count)=f*(crdnx(3)-crdnx(2))+crdnx(2);
|
||||
yi(count)=f*(crdny(3)-crdny(2))+crdny(2);
|
||||
gi(count)=1.;
|
||||
hi(count)=(2.*yi(count)-(crdny(2)+crdny(3)))/(-crdny(2)+crdny(3));
|
||||
end
|
||||
if sign(theta(3))~=sign(theta(4))
|
||||
count=count+1;
|
||||
f=abs(theta(3))/(abs(theta(3))+abs(theta(4)));
|
||||
xi(count)=f*(crdnx(4)-crdnx(3))+crdnx(3);
|
||||
yi(count)=f*(crdny(4)-crdny(3))+crdny(3);
|
||||
gi(count)=(2.*xi(count)-(crdnx(4)+crdnx(3)))/(-crdnx(4)+crdnx(3));
|
||||
hi(count)=1.;
|
||||
end
|
||||
if sign(theta(1))~=sign(theta(4))
|
||||
count=count+1;
|
||||
f=abs(theta(1))/(abs(theta(1))+abs(theta(4)));
|
||||
xi(count)=f*(crdnx(4)-crdnx(1))+crdnx(1);
|
||||
yi(count)=f*(crdny(4)-crdny(1))+crdny(1);
|
||||
gi(count)=-1.;
|
||||
hi(count)=(2.*yi(count)-(crdny(1)+crdny(4)))/(-crdny(4)+crdny(1));
|
||||
end
|
||||
c=zeros(2,1);
|
||||
c=(c+1.);
|
||||
for i=1:2;
|
||||
G(i,1)=0.25*(1.-gi(i))*(1.-hi(i));
|
||||
G(i,3)=0.25*(1.+gi(i))*(1.-hi(i));
|
||||
G(i,5)=0.25*(1.+gi(i))*(1.+hi(i));
|
||||
G(i,7)=0.25*(1.-gi(i))*(1.+hi(i));
|
||||
G(i,2)=-G(i,1)*abs(theta(1));
|
||||
G(i,4)=-G(i,3)*abs(theta(2));
|
||||
G(i,6)=-G(i,5)*abs(theta(3));
|
||||
G(i,8)=-G(i,7)*abs(theta(4));
|
||||
end
|
||||
pen=Penalty*(G'*G);
|
||||
pfL=Penalty*G'*c;
|
||||
% pen=zeros(8);
|
||||
% pfL=zeros(8,1);
|
||||
Ke=Ke+pen;
|
||||
else
|
||||
pen=zeros(8);
|
||||
pfL=zeros(8,1);
|
||||
end
|
||||
% Assemble Global Matrices
|
||||
gnum(1)=2*Element(e,1)-1;
|
||||
gnum(2)=2*Element(e,2)-1;
|
||||
gnum(3)=2*Element(e,3)-1;
|
||||
gnum(4)=2*Element(e,4)-1;
|
||||
for i=1:4;
|
||||
for j=1:4;
|
||||
K(gnum(j),gnum(i))=K(gnum(j),gnum(i))+Ke(2*j-1,2*i-1);
|
||||
K(gnum(j)+1,gnum(i)+1)=K(gnum(j)+1,gnum(i)+1)+Ke(2*j,2*i);
|
||||
M(gnum(j),gnum(i))=M(gnum(j),gnum(i))+Me(2*j-1,2*i-1);
|
||||
M(gnum(j)+1,gnum(i)+1)=M(gnum(j)+1,gnum(i)+1)+Me(2*j,2*i);
|
||||
MStar(gnum(j),gnum(i))=MStar(gnum(j),gnum(i))+MeStar(2*j-1,2*i-1);
|
||||
MStar(gnum(j)+1,gnum(i)+1)=MStar(gnum(j)+1,gnum(i)+1)+MeStar(2*j,2*i);
|
||||
end
|
||||
end
|
||||
for i=1:4;
|
||||
pforce(gnum(i))=pforce(gnum(i))+pfL(2*i-1);
|
||||
pforce(gnum(i)+1)=pforce(gnum(i)+1)+pfL(2*i);
|
||||
end
|
||||
end
|
||||
%Remove inactive DOFs(Reduce Matrices)
|
||||
RHS=MStar*Temp;
|
||||
A=K+M;
|
||||
Sub=A*Bound;
|
||||
iindex=0;
|
||||
for i=1:2*numNodes;
|
||||
if Bound(i)==0.;
|
||||
iindex=iindex+1;
|
||||
RHSred(iindex)=RHS(i)-Sub(i)+pforce(i);
|
||||
jindex=0;
|
||||
for j=1:2*numNodes;
|
||||
if Bound(j)==0.;
|
||||
jindex=jindex+1;
|
||||
Ared(iindex,jindex)=A(i,j);
|
||||
end
|
||||
end
|
||||
end
|
||||
end
|
||||
%Solve
|
||||
Tempr=(Ared^-1)*RHSred';
|
||||
iindex=0;
|
||||
for i=1:2*numNodes;
|
||||
if Bound(i)==0.;
|
||||
iindex=iindex+1;
|
||||
Temp(i)=Tempr(iindex);
|
||||
end
|
||||
end
|
||||
Temp
|
||||
end
|
||||
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||
% Generates the initial level set
|
||||
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||
function [LSet]=initialLSet(Node,numNodes)
|
||||
%centx=4.;
|
||||
%centy=4.;
|
||||
%rad=2.1;
|
||||
%for i=1:numNodes;
|
||||
% dist=sqrt((Node(i,1)-centx)*(Node(i,1)-centx)+(Node(i,2)-centy)*(Node(i,2)-centy));
|
||||
% LSet(i)=dist-rad;
|
||||
%end
|
||||
for i=1:numNodes;
|
||||
dist=Node(i,1)-4.6;
|
||||
LSet(i)=dist;
|
||||
end
|
||||
end
|
||||
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||
% Plot the level set
|
||||
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||
function []=plotLSet(NumX,NumY,delX,delY,LSet)
|
||||
[X Y]=meshgrid(0:delX:delX*NumX,0:delY:delY*NumY);
|
||||
Z=zeros(NumX+1,NumY+1);
|
||||
for i=1:(NumX+1)*(NumY+1)
|
||||
Z(i)=LSet(i);
|
||||
end
|
||||
surf(X,Y,Z)
|
||||
end
|
||||
|
||||
62
Unpublished/XFEM/2D_Solver/uelmatinp.inp
Normal file
62
Unpublished/XFEM/2D_Solver/uelmatinp.inp
Normal file
|
|
@ -0,0 +1,62 @@
|
|||
*HEADING
|
||||
Test for passing abaqus material to UELMAT: transient heat transfer
|
||||
*RESTART,WRITE,NUMBER INTERVAL=10
|
||||
*PREPRINT,MODEL=YES
|
||||
*PART,NAME=part1
|
||||
*NODE,NSET=NALL
|
||||
1,0,0,0
|
||||
2,1,0,0
|
||||
3,0,1,0
|
||||
4,1,1,0
|
||||
5,0,2,0
|
||||
6,1,2,0
|
||||
*NSET,NSET=Left
|
||||
1,3,5
|
||||
*NSET,NSET=Right
|
||||
2,4,6
|
||||
*USER ELEMENT, TYPE=U1, NODES=4, COORDINATES=2,
|
||||
INTEGRATION=4,TENSOR=TWOD
|
||||
11,
|
||||
*ELEMENT,TYPE=U1,ELSET=SOLID
|
||||
1, 1,2,4,3
|
||||
2, 3,4,6,5
|
||||
*END PART
|
||||
*ASSEMBLY,NAME=A1
|
||||
*INSTANCE,NAME=I1,PART=PART1
|
||||
*END INSTANCE
|
||||
*Nset, nset=Set-6, instance=I1
|
||||
1,3,5
|
||||
*Nset, nset=Set-7, instance=I1
|
||||
2,4,6
|
||||
*END ASSEMBLY
|
||||
*UEL PROPERTY, ELSET=I1.SOLID, MATERIAL=MAT_THERM
|
||||
**************************************
|
||||
***************************************
|
||||
*MATERIAL,NAME=MAT_THERM
|
||||
*CONDUCTIVITY
|
||||
1.0,
|
||||
*SPECIFIC HEAT
|
||||
1.,
|
||||
*DENSITY
|
||||
1.,
|
||||
*Initial Conditions, type=TEMPERATURE
|
||||
Set-6, 1.,0.
|
||||
*Initial Conditions, type=TEMPERATURE
|
||||
Set-7, 0.,0.
|
||||
*STEP
|
||||
*HEAT TRANSFER, DELTMX=1.
|
||||
0.1,1.0,,0.1
|
||||
**
|
||||
*BOUNDARY
|
||||
Set-6,11,11,1.
|
||||
*OUTPUT,FIELD,freq=1
|
||||
*ELEMENT OUTPUT,ELSET=I1.SOLID
|
||||
HFL,
|
||||
*NODE OUTPUT,NSET=I1.NALL
|
||||
NT,
|
||||
*OUTPUT,HISTORY
|
||||
*ELEMENT OUTPUT,ELSET=I1.SOLID
|
||||
HFL,
|
||||
*NODE OUTPUT,NSET=I1.NALL
|
||||
NT11,
|
||||
*END STEP
|
||||
546
Unpublished/XFEM/AbaqusUEL/2D_Test1.for
Normal file
546
Unpublished/XFEM/AbaqusUEL/2D_Test1.for
Normal file
|
|
@ -0,0 +1,546 @@
|
|||
C
|
||||
C User element accessing Abaqus materials
|
||||
C Heat Transfer -- conduction
|
||||
C
|
||||
c*****************************************************************
|
||||
subroutine uelmat(rhs, amatrx, svars, energy, ndofel, nrhs,
|
||||
1 nsvars, props, nprops, coords, mcrd, nnode, u, du, v, a, jtype,
|
||||
2 time, dtime, kstep, kinc, jelem, params, ndload, jdltyp, adlmag,
|
||||
3 predef, npredf, lflags, mlvarx, ddlmag, mdload, pnewdt, jprops,
|
||||
4 njpro, period, materiallib)
|
||||
c
|
||||
include 'aba_param.inc'
|
||||
C
|
||||
dimension rhs(mlvarx,*), amatrx(ndofel, ndofel), props(*),
|
||||
1 svars(*), energy(*), coords(mcrd, nnode), u(ndofel),
|
||||
2 du(mlvarx,*), v(ndofel), a(ndofel), time(2), params(*),
|
||||
3 jdltyp(mdload,*), adlmag(mdload,*), ddlmag(mdload,*),
|
||||
4 predef(2, npredf, nnode), lflags(*), jprops(*)
|
||||
c
|
||||
c local arrays
|
||||
c
|
||||
parameter (zero=0.d0, one=1.d0)
|
||||
|
||||
parameter (ndim=2, ndof=1, ninpt=4, nnodemax=4)
|
||||
c
|
||||
c ndim ... number of spatial dimensions
|
||||
c ndof ... number of degrees of freedom per node
|
||||
c ninpt ... number of integration points
|
||||
c
|
||||
dimension stiff(ndof*nnodemax,ndof*nnodemax),
|
||||
1 force(ndof*nnodemax), shape(nnodemax), dshape(ndim,nnodemax),
|
||||
2 xjaci(ndim,ndim), bmat(nnodemax*ndim), wght(ninpt)
|
||||
|
||||
dimension coords_ip(3),dfgrd0(3,3),dfgrd1(3,3),
|
||||
1 drot(3,3)
|
||||
dimension coords_new(mcrd,nnodemax)
|
||||
c
|
||||
dimension predef_loc(npredf),dpredef_loc(npredf),xx1(3,3),
|
||||
1 xx1Old(3,3)
|
||||
dimension xjaci_new(ndim,ndim),bmat_new(nnodemax*ndim)
|
||||
dimension dtemdx(ndim),rhoUdotdg(3),flux(ndim),dfdt(ndim),
|
||||
1 dfdg(ndim,ndim)
|
||||
c
|
||||
data wght /one, one, one, one/
|
||||
|
||||
c
|
||||
c********************************************************************
|
||||
c
|
||||
c U1 = first-order, plane strain, full integration
|
||||
c
|
||||
c********************************************************************
|
||||
if (lflags(3).eq.4) goto 999
|
||||
c
|
||||
c Preliminaries
|
||||
c
|
||||
pnewdtLocal = pnewdt
|
||||
if(jtype .ne. 1) then
|
||||
write(7,*)'Incorrect element type'
|
||||
call xit
|
||||
endif
|
||||
c
|
||||
c initialize rhs and lhs
|
||||
c
|
||||
do k1=1, ndof*nnode
|
||||
rhs(k1, 1)= zero
|
||||
do k2=1, ndof*nnode
|
||||
amatrx(k1, k2)= zero
|
||||
end do
|
||||
end do
|
||||
c
|
||||
do k1=1,nnode
|
||||
do k2=1,mcrd
|
||||
kk = (k1-1)*mcrd + k2
|
||||
coords_new(k2,k1) = coords(k2,k1) + u(kk)
|
||||
end do
|
||||
end do
|
||||
|
||||
c
|
||||
c loop over integration points
|
||||
c
|
||||
do kintk = 1, ninpt
|
||||
c
|
||||
c initialization
|
||||
c
|
||||
rho = zero
|
||||
rhoUdot = zero
|
||||
rhoUdotdt = zero
|
||||
rhoUdotdg = zero
|
||||
do i=1, 3
|
||||
rhoUdotdg(i) = zero
|
||||
end do
|
||||
do i=1, ndim
|
||||
flux(i) = zero
|
||||
dfdt(i) = zero
|
||||
end do
|
||||
do i=1, ndim
|
||||
do j=1, ndim
|
||||
dfdg(i,j) = zero
|
||||
end do
|
||||
end do
|
||||
c
|
||||
c evaluate shape functions and derivatives
|
||||
c
|
||||
call shapefcn(kintk,ninpt,nnode,ndim,shape,dshape)
|
||||
c
|
||||
c compute coordinates at the integration point
|
||||
c
|
||||
do k1=1, 3
|
||||
coords_ip(k1) = zero
|
||||
end do
|
||||
do k1=1,nnode
|
||||
do k2=1,mcrd
|
||||
coords_ip(k2)=coords_ip(k2)+shape(k1)*coords(k2,k1)
|
||||
end do
|
||||
end do
|
||||
c
|
||||
if(npredf.gt.0) then
|
||||
call tempfv(kintk,ninpt,nnode,ndim,shape,predef,
|
||||
* npredf,predef_loc,dpredef_loc)
|
||||
end if
|
||||
c
|
||||
c form B-matrix
|
||||
c
|
||||
djac = one
|
||||
djac_new = one
|
||||
call jacobian(jelem,mcrd,ndim,nnode,coords,dshape,
|
||||
1 djac,xjaci,pnewdt,coords_new,xjaci_new,djac_new)
|
||||
c
|
||||
if (pnewdt .lt. pnewdtLocal) pnewdtLocal = pnewdt
|
||||
c
|
||||
call bmatrix(xjaci,dshape,nnode,ndim,bmat,xjaci_new,
|
||||
1 bmat_new)
|
||||
c
|
||||
c compute temp. and temp. gradient
|
||||
c
|
||||
temp = zero
|
||||
dtemp = zero
|
||||
call settemp(ndofel,ndof,ndim,nnode,mlvarx,bmat,du,
|
||||
* dstran,u,xx1,xx1Old,temp,dtemp,dtemdx,shape)
|
||||
c
|
||||
c get Abaqus material
|
||||
c
|
||||
rpl = zero
|
||||
drpldt = zero
|
||||
celent = one
|
||||
call material_lib_ht(materiallib,rhoUdot,rhoUdotdt,rhoUdotdg,
|
||||
* flux,dfdt,dfdg,rpl,drpldt,kintk,djac,predef_loc,
|
||||
* dpredef_loc,npredf,temp,dtemp,dtemdx,celent,coords_ip)
|
||||
c
|
||||
c
|
||||
c form stiffness matrix and internal force vector
|
||||
c
|
||||
call rhsjacobian(nnode,ndim,ndof,
|
||||
1 wght(kintk),djac,rhoUdot,rhoUdotdt,rhoUdotdg,flux,
|
||||
2 dfdt,dfdg,shape,bmat,stiff,force,dtime,lflags)
|
||||
|
||||
c
|
||||
c assemble rhs and lhs
|
||||
c
|
||||
do k1=1, ndof*nnode
|
||||
rhs(k1, 1) = rhs(k1, 1) - force(k1)
|
||||
do k2=1, ndof*nnode
|
||||
amatrx(k1, k2) = amatrx(k1, k2) + stiff(k1,k2)
|
||||
end do
|
||||
end do
|
||||
end do ! end loop on material integration points
|
||||
pnewdt = pnewdtLocal
|
||||
c
|
||||
999 continue
|
||||
c
|
||||
return
|
||||
end
|
||||
c*****************************************************************
|
||||
c
|
||||
c Compute shape fuctions
|
||||
c
|
||||
subroutine shapefcn(kintk,ninpt,nnode,ndim,dN,dNdz)
|
||||
c
|
||||
include 'aba_param.inc'
|
||||
c
|
||||
parameter (dmone=-1.0d0,one=1.0d0,four=4.0d0,eight=8.0d0,
|
||||
1 gaussCoord=0.577350269d0)
|
||||
parameter (maxElemNode=8,maxDof=3,i2d4node=24,i3d8node=38)
|
||||
dimension dN(*),dNdz(ndim,*),coord24(2,4),coord38(3,8)
|
||||
c
|
||||
data coord24 /dmone, dmone,
|
||||
2 one, dmone,
|
||||
3 one, one,
|
||||
4 dmone, one/
|
||||
c
|
||||
data coord38 /dmone, dmone, dmone,
|
||||
2 one, dmone, dmone,
|
||||
3 one, one, dmone,
|
||||
4 dmone, one, dmone,
|
||||
5 dmone, dmone, one,
|
||||
6 one, dmone, one,
|
||||
7 one, one, one,
|
||||
8 dmone, one, one/
|
||||
C
|
||||
iCode = 0
|
||||
if (ninpt.eq.4.and.nnode.eq.4.and.ndim.eq.2) then
|
||||
iCode = 24
|
||||
else if (ninpt.eq.8.and.nnode.eq.8.and.ndim.eq.3) then
|
||||
iCode = 38
|
||||
else
|
||||
write (6,*) '***ERROR: The shape fuctions cannot be found'
|
||||
end if
|
||||
C
|
||||
C 3D 8-nodes
|
||||
C
|
||||
if (iCode.eq.i3d8node) then
|
||||
c
|
||||
c determine (g,h,r)
|
||||
c
|
||||
g = coord38(1,kintk)*gaussCoord
|
||||
h = coord38(2,kintk)*gaussCoord
|
||||
r = coord38(3,kintk)*gaussCoord
|
||||
c
|
||||
c shape functions
|
||||
dN(1) = (one - g)*(one - h)*(one - r)/eight
|
||||
dN(2) = (one + g)*(one - h)*(one - r)/eight
|
||||
dN(3) = (one + g)*(one + h)*(one - r)/eight
|
||||
dN(4) = (one - g)*(one + h)*(one - r)/eight
|
||||
dN(5) = (one - g)*(one - h)*(one + r)/eight
|
||||
dN(6) = (one + g)*(one - h)*(one + r)/eight
|
||||
dN(7) = (one + g)*(one + h)*(one + r)/eight
|
||||
dN(8) = (one - g)*(one + h)*(one + r)/eight
|
||||
c
|
||||
c derivative d(Ni)/d(g)
|
||||
dNdz(1,1) = -(one - h)*(one - r)/eight
|
||||
dNdz(1,2) = (one - h)*(one - r)/eight
|
||||
dNdz(1,3) = (one + h)*(one - r)/eight
|
||||
dNdz(1,4) = -(one + h)*(one - r)/eight
|
||||
dNdz(1,5) = -(one - h)*(one + r)/eight
|
||||
dNdz(1,6) = (one - h)*(one + r)/eight
|
||||
dNdz(1,7) = (one + h)*(one + r)/eight
|
||||
dNdz(1,8) = -(one + h)*(one + r)/eight
|
||||
c
|
||||
c derivative d(Ni)/d(h)
|
||||
dNdz(2,1) = -(one - g)*(one - r)/eight
|
||||
dNdz(2,2) = -(one + g)*(one - r)/eight
|
||||
dNdz(2,3) = (one + g)*(one - r)/eight
|
||||
dNdz(2,4) = (one - g)*(one - r)/eight
|
||||
dNdz(2,5) = -(one - g)*(one + r)/eight
|
||||
dNdz(2,6) = -(one + g)*(one + r)/eight
|
||||
dNdz(2,7) = (one + g)*(one + r)/eight
|
||||
dNdz(2,8) = (one - g)*(one + r)/eight
|
||||
c
|
||||
c derivative d(Ni)/d(r)
|
||||
dNdz(3,1) = -(one - g)*(one - h)/eight
|
||||
dNdz(3,2) = -(one + g)*(one - h)/eight
|
||||
dNdz(3,3) = -(one + g)*(one + h)/eight
|
||||
dNdz(3,4) = -(one - g)*(one + h)/eight
|
||||
dNdz(3,5) = (one - g)*(one - h)/eight
|
||||
dNdz(3,6) = (one + g)*(one - h)/eight
|
||||
dNdz(3,7) = (one + g)*(one + h)/eight
|
||||
dNdz(3,8) = (one - g)*(one + h)/eight
|
||||
C
|
||||
C 2D 4-nodes
|
||||
C
|
||||
else if (iCode.eq.i2d4node) then
|
||||
c
|
||||
c determine (g,h)
|
||||
c
|
||||
g = coord24(1,kintk)*gaussCoord
|
||||
h = coord24(2,kintk)*gaussCoord
|
||||
c
|
||||
c shape functions
|
||||
dN(1) = (one - g)*(one - h)/four;
|
||||
dN(2) = (one + g)*(one - h)/four;
|
||||
dN(3) = (one + g)*(one + h)/four;
|
||||
dN(4) = (one - g)*(one + h)/four;
|
||||
c
|
||||
c derivative d(Ni)/d(g)
|
||||
dNdz(1,1) = -(one - h)/four;
|
||||
dNdz(1,2) = (one - h)/four;
|
||||
dNdz(1,3) = (one + h)/four;
|
||||
dNdz(1,4) = -(one + h)/four;
|
||||
c
|
||||
c derivative d(Ni)/d(h)
|
||||
dNdz(2,1) = -(one - g)/four;
|
||||
dNdz(2,2) = -(one + g)/four;
|
||||
dNdz(2,3) = (one + g)/four;
|
||||
dNdz(2,4) = (one - g)/four;
|
||||
end if
|
||||
c
|
||||
return
|
||||
end
|
||||
c*****************************************************************
|
||||
c Get local predefined fileds
|
||||
c
|
||||
subroutine tempfv(kintk,ninpt,nnode,ndim,shape,predef,
|
||||
* npredf,predef_loc,dpredef_loc)
|
||||
c
|
||||
include 'aba_param.inc'
|
||||
c
|
||||
dimension shape(nnode),predef(2,npredf,nnode)
|
||||
dimension predef_loc(npredf),dpredef_loc(npredf)
|
||||
parameter (zero=0.d0)
|
||||
c
|
||||
do k1=1,npredf
|
||||
predef_loc(k1) = zero
|
||||
dpredef_loc(k1) = zero
|
||||
do k2=1,nnode
|
||||
predef_loc(k1) = predef_loc(k1)+
|
||||
& (predef(1,k1,k2)-predef(2,k1,k2))*shape(k2)
|
||||
dpredef_loc(k1) = dpredef_loc(k1)+predef(2,k1,k2)*shape(k2)
|
||||
end do
|
||||
end do
|
||||
c
|
||||
return
|
||||
end
|
||||
|
||||
c*****************************************************************
|
||||
c Compute jacobian matrix
|
||||
c
|
||||
subroutine jacobian(jelem,mcrd,ndim,nnode,
|
||||
1 coords,dshape,djac,xjaci,pnewdt,coords_new,xjaci_new,
|
||||
2 djac_new)
|
||||
c
|
||||
c Notation: ndim ....... element dimension
|
||||
c nnode ..... number of nodes
|
||||
c coords ..... coordinates of nodes
|
||||
c dshape ..... derivs of shape fcn
|
||||
c djac ....... determinant of Jacobian
|
||||
c xjaci ...... inverse of Jacobian matrix
|
||||
c
|
||||
c
|
||||
include 'aba_param.inc'
|
||||
parameter(zero=0.d0, fourth=0.25d0, maxDof=3)
|
||||
|
||||
dimension xjac(maxDof,maxDof), xjaci(ndim,*), coords(mcrd,*)
|
||||
dimension dshape(ndim,*),coords_new(mcrd,*)
|
||||
dimension xjac_new(maxDof,maxDof), xjaci_new(ndim,*)
|
||||
|
||||
c
|
||||
do i = 1, ndim
|
||||
do j = 1, ndim
|
||||
xjac(i,j) = zero
|
||||
xjaci(i,j) = zero
|
||||
xjac_new(i,j) = zero
|
||||
xjaci_new(i,j) = zero
|
||||
end do
|
||||
end do
|
||||
c
|
||||
do inod= 1, nnode
|
||||
do idim = 1, ndim
|
||||
do jdim = 1, ndim
|
||||
xjac(idim,jdim) = xjac(idim,jdim) +
|
||||
1 dshape(jdim,inod)*coords(idim,inod)
|
||||
end do
|
||||
end do
|
||||
end do
|
||||
C
|
||||
C ndim == 3
|
||||
C
|
||||
if (ndim.eq.3) then
|
||||
djac = xjac(1,1)*xjac(2,2)*xjac(3,3) +
|
||||
& xjac(2,1)*xjac(3,2)*xjac(1,3) +
|
||||
& xjac(3,1)*xjac(2,3)*xjac(1,2) -
|
||||
& xjac(3,1)*xjac(2,2)*xjac(1,3) -
|
||||
& xjac(2,1)*xjac(1,2)*xjac(3,3) -
|
||||
& xjac(1,1)*xjac(2,3)*xjac(3,2)
|
||||
if (djac .gt. zero) then
|
||||
! jacobian is positive - o.k.
|
||||
xjaci(1,1) = (xjac(2,2)*xjac(3,3)-xjac(2,3)*xjac(3,2))/djac
|
||||
xjaci(1,2) = (xjac(1,3)*xjac(3,2)-xjac(1,2)*xjac(3,3))/djac
|
||||
xjaci(1,3) = (xjac(1,2)*xjac(2,3)-xjac(1,3)*xjac(2,2))/djac
|
||||
!
|
||||
xjaci(2,1) = (xjac(2,3)*xjac(3,1)-xjac(2,1)*xjac(3,3))/djac
|
||||
xjaci(2,2) = (xjac(1,1)*xjac(3,3)-xjac(1,3)*xjac(3,1))/djac
|
||||
xjaci(2,3) = (xjac(1,3)*xjac(2,1)-xjac(1,1)*xjac(2,3))/djac
|
||||
!
|
||||
xjaci(3,1) = (xjac(2,1)*xjac(3,2)-xjac(2,2)*xjac(3,1))/djac
|
||||
xjaci(3,2) = (xjac(1,2)*xjac(3,1)-xjac(1,1)*xjac(3,2))/djac
|
||||
xjaci(3,3) = (xjac(1,1)*xjac(2,2)-xjac(1,2)*xjac(2,1))/djac
|
||||
else
|
||||
! negative or zero jacobian
|
||||
write(7,*)'WARNING: element',jelem,'has neg.
|
||||
1 Jacobian'
|
||||
pnewdt = fourth
|
||||
endif
|
||||
C
|
||||
C ndim == 2
|
||||
C
|
||||
else if (ndim.eq.2) then
|
||||
djac = xjac(1,1)*xjac(2,2) - xjac(1,2)*xjac(2,1)
|
||||
djac_new = xjac_new(1,1)*xjac_new(2,2)
|
||||
* - xjac_new(1,2)*xjac_new(2,1)
|
||||
if (djac .gt. zero) then
|
||||
! jacobian is positive - o.k.
|
||||
xjaci(1,1) = xjac(2,2)/djac
|
||||
xjaci(2,2) = xjac(1,1)/djac
|
||||
xjaci(1,2) = -xjac(1,2)/djac
|
||||
xjaci(2,1) = -xjac(2,1)/djac
|
||||
else
|
||||
! negative or zero jacobian
|
||||
write(7,*)'WARNING: element',jelem,'has neg.
|
||||
1 Jacobian'
|
||||
pnewdt = fourth
|
||||
endif
|
||||
end if
|
||||
|
||||
return
|
||||
end
|
||||
c*****************************************************************
|
||||
c
|
||||
c Compute the B matrix
|
||||
c
|
||||
subroutine bmatrix(xjaci,dshape,nnode,ndim,bmat,
|
||||
* xjaci_new,bmat_new)
|
||||
c
|
||||
c Notation:
|
||||
c bmat(i) .....dN1/dx, dN1/dy, dN2/dx, dN2/dy..
|
||||
c xjaci ...... inverse Jabobian matrix
|
||||
c dshape ......derivative of shape functions
|
||||
c
|
||||
include 'aba_param.inc'
|
||||
c
|
||||
parameter (zero=0.d0)
|
||||
dimension bmat(*), dshape(ndim,*)
|
||||
dimension xjaci(ndim,*)
|
||||
dimension xjaci_new(ndim,*),bmat_new(*)
|
||||
|
||||
|
||||
do i = 1, nnode*ndim
|
||||
bmat(i) = zero
|
||||
bmat_new(i) = zero
|
||||
end do
|
||||
|
||||
do inod = 1, nnode
|
||||
do ider = 1, ndim
|
||||
do idim = 1, ndim
|
||||
irow = idim + (inod - 1)*ndim
|
||||
bmat(irow) = bmat(irow) +
|
||||
1 xjaci(idim,ider)*dshape(ider,inod)
|
||||
|
||||
end do
|
||||
end do
|
||||
end do
|
||||
|
||||
return
|
||||
end
|
||||
c*****************************************************************
|
||||
c
|
||||
c Set temperatures
|
||||
c
|
||||
subroutine settemp(ndofel,ndof,ndim,nnode,
|
||||
1 mlvarx,bmat,du,dstran,u,xx1,xx1Old,temp,dtemp,dtemdx,dN)
|
||||
c
|
||||
c
|
||||
c
|
||||
include 'aba_param.inc'
|
||||
parameter(zero=0.d0, one=1.d0)
|
||||
|
||||
dimension dstran(*), bmat(ndim,*),
|
||||
1 du(mlvarx, *), xdu(3), xx1(3,*),
|
||||
2 u(ndofel), utmp(3),
|
||||
3 utmpOld(3),xx1Old(3,*),eps(3,3),dInvFold(3,3)
|
||||
dimension dtemdx(*),dN(*)
|
||||
C
|
||||
c
|
||||
c****************************************************************
|
||||
c Compute temp, dtemp, and temp gradient at the material point
|
||||
c****************************************************************
|
||||
c
|
||||
|
||||
temp = zero
|
||||
dtemp = zero
|
||||
do iNode=1, nnode
|
||||
temp = temp + dN(iNode)*u(iNode)
|
||||
dtemp = dtemp + dN(iNode)*du(iNode,1)
|
||||
end do
|
||||
do iDof = 1, ndim
|
||||
dtemdx(iDof) = zero
|
||||
do iNode=1, nnode
|
||||
dtemdx(iDof) = dtemdx(iDof) + bmat(idof,iNode)*u(iNode)
|
||||
end do
|
||||
end do
|
||||
c
|
||||
return
|
||||
end
|
||||
c*****************************************************************
|
||||
c
|
||||
c Compute element jacobian and nodal forces
|
||||
c
|
||||
subroutine rhsjacobian(nnode,ndim,ndof,
|
||||
1 weight,djac,rhoUdot,rhoUdotdt,rhoUdotdg,flux,dfdt,
|
||||
2 dfdg,dN,bmat,stiff,force,dtime,lflags)
|
||||
c
|
||||
c Stiffness matrix and internal force contributions at
|
||||
c material integration point
|
||||
c
|
||||
include 'aba_param.inc'
|
||||
|
||||
parameter(zero=0.d0,maxDof=3)
|
||||
|
||||
dimension stiff(ndof*nnode,*)
|
||||
dimension force(*)
|
||||
dimension flux(*),dfdt(*),dfdg(ndim,*),rhoUdotdg(*)
|
||||
dimension dN(*),bmat(ndim,*),lflags(*)
|
||||
|
||||
do i = 1, ndof*nnode
|
||||
force(i) = zero
|
||||
do j = 1, ndof*nnode
|
||||
stiff(j,i) = zero
|
||||
end do
|
||||
end do
|
||||
|
||||
dvol=weight*djac
|
||||
do nodj=1, nnode
|
||||
if (lflags(1).eq.32.or.lflags(1).eq.33)
|
||||
& force(nodj) = dN(nodj)*rhoUdot*dvol
|
||||
ccc force(nodj) = dN(nodj)*(rhoUdot-rpl)*dvol
|
||||
do jDof=1, ndim
|
||||
force(nodj) = force(nodj)+bmat(jDof,nodj)*flux(jDof)*dvol
|
||||
do nodi=1, nnode
|
||||
ccc stiff(nodj,nodi) = stiff(nodj,nodi) +
|
||||
ccc * bmat(jDof,nodj)*dN(nodi)*dfdt(jDof)*dvol
|
||||
do iDof=1, ndim
|
||||
stiff(nodj,nodi) = stiff(nodj,nodi) +
|
||||
* bmat(jDof,nodj)*bmat(iDof,nodi)*dfdg(jDof,iDof)*dvol
|
||||
end do
|
||||
end do
|
||||
end do
|
||||
end do
|
||||
do nodj=1, nnode
|
||||
do nodi=1, nnode
|
||||
do iDof=1, ndim
|
||||
ccc stiff(nodj,nodi) = stiff(nodj,nodi) +
|
||||
ccc * dN(nodj)*bmat(iDof,nodi)*rhoUdotdg(iDof)*dvol
|
||||
end do
|
||||
end do
|
||||
end do
|
||||
c
|
||||
if (lflags(1).eq.32.or.lflags(1).eq.33) then
|
||||
do nodj=1, nnode
|
||||
do nodi=1, nnode
|
||||
stiff(nodj,nodi) = stiff(nodj,nodi) +
|
||||
* rhoUdotdt*dN(nodj)*dN(nodi)*dvol/dtime
|
||||
end do
|
||||
end do
|
||||
end if
|
||||
c
|
||||
return
|
||||
end
|
||||
108
Unpublished/XFEM/AbaqusUEL/2D_Test2.for
Normal file
108
Unpublished/XFEM/AbaqusUEL/2D_Test2.for
Normal file
|
|
@ -0,0 +1,108 @@
|
|||
subroutine uel(rhs,amatrx,svars,energy,ndofel,nrhs,nsvars,props,
|
||||
1 nprops,coords,mcrd,nnode,u,du,v,a,jtype,time,dtime,kstep,kinc,
|
||||
2 jelem,params,ndload,jdltyp,adlmag,predef,npredf,lflags,
|
||||
3 mlvarx,ddlmag,mdload,pnewdt,jprops,njprop,period)
|
||||
c
|
||||
include 'aba_param.inc'
|
||||
c
|
||||
dimension rhs(mlvarx,*),amatrx(ndofel,ndofel),svars(nsvars),
|
||||
1 energy(8),props(*),coords(mcrd,nnode),dndg(4),dndh(4),
|
||||
2 u(ndofel),du(mlvarx,*),v(ndofel),a(ndofel),time(2),
|
||||
3 params(3),jdltyp(mdload,*),adlmag(mdload,*),
|
||||
4 ddlmag(mdload,*),predef(2,npredf,nnode),lflags(*),jprops(*)
|
||||
c
|
||||
dimension gx(4),hx(4),gwei(4),dN(4),phix(8),phiy(8)
|
||||
c
|
||||
parameter(zero=0.d0,one=1.d0)
|
||||
C MATERIAL PROPERTY DEFINITION
|
||||
thick = 1.
|
||||
rho = 1.
|
||||
spec = 1.
|
||||
conduc = 1.
|
||||
C INITIALIZATION (NRHS=1)
|
||||
do k1=1,ndofel
|
||||
rhs(k1,nrhs)=zero
|
||||
do k2=1,ndofel
|
||||
amatrx(k2,k1)=zero
|
||||
enddo
|
||||
enddo
|
||||
if (lflags(1).eq.33) then
|
||||
gpos=1./sqrt(3.)
|
||||
gx(1)=-gpos
|
||||
gx(2)=gpos
|
||||
gx(3)=gpos
|
||||
gx(4)=-gpos
|
||||
hx(1)=-gpos
|
||||
hx(2)=-gpos
|
||||
hx(3)=gpos
|
||||
hx(4)=gpos
|
||||
do i=1,4
|
||||
gwei(i)=1.
|
||||
enddo
|
||||
c assemble amatrx and rhs
|
||||
do k=1,4
|
||||
c loop through gauss pts
|
||||
g=gx(k)
|
||||
h=hx(k)
|
||||
c shape functions
|
||||
dN(1) = (one - g)*(one - h)/4.
|
||||
dN(2) = (one + g)*(one - h)/4.
|
||||
dN(3) = (one + g)*(one + h)/4.
|
||||
dN(4) = (one - g)*(one + h)/4.
|
||||
c derivative d(Ni)/d(g)
|
||||
dNdg(1) = -(one - h)/4.
|
||||
dNdg(2) = (one - h)/4.
|
||||
dNdg(3) = (one + h)/4.
|
||||
dNdg(4) = -(one + h)/4.
|
||||
c derivative d(Ni)/d(h)
|
||||
dNdh(1) = -(one - g)/4.
|
||||
dNdh(2) = -(one + g)/4.
|
||||
dNdh(3) = (one + g)/4.
|
||||
dNdh(4) = (one - g)/4.
|
||||
c derivative dx/dg,dx/dh,dy/dg,dy/dh
|
||||
dxdg=zero
|
||||
dxdh=zero
|
||||
dydg=zero
|
||||
dydh=zero
|
||||
do i=1,4
|
||||
dxdg=dxdg+coords(1,i)*dNdg(i)
|
||||
dxdh=dxdh+coords(1,i)*dNdh(i)
|
||||
dydg=dydg+coords(2,i)*dNdg(i)
|
||||
dydh=dydh+coords(2,i)*dNdh(i)
|
||||
enddo
|
||||
c calculation of jacobian
|
||||
ajacob=(dxdg*dydh-dxdh*dydg)
|
||||
c derivative dn/dx,dn/dy
|
||||
do i=1,4
|
||||
phix(i)=(dNdg(i)*dydh-dNdh(i)*dydg)/ajacob
|
||||
phiy(i)=(dNdh(i)*dxdg-dNdg(i)*dxdh)/ajacob
|
||||
enddo
|
||||
dtdx=zero
|
||||
dtdy=zero
|
||||
t =zero
|
||||
told=zero
|
||||
do i=1,4
|
||||
dtdx=u(i)*phix(i)+dtdx
|
||||
dtdy=u(i)*phiy(i)+dtdy
|
||||
t=u(i)*dn(i)+t
|
||||
told=(u(i)-du(i,nrhs))*dn(i)+told
|
||||
end do
|
||||
cond=1.
|
||||
dcdt=zero
|
||||
dtdt=(t-told)/dtime
|
||||
we=gwei(k)*ajacob
|
||||
do ki=1,4
|
||||
c loop over nodes
|
||||
rhs(ki,nrhs) = rhs(ki,nrhs) -
|
||||
1 we*(dN(ki)*rho*spec*dtdt +
|
||||
2 cond*(phix(ki)*dtdx + phiy(ki)*dtdy))
|
||||
do kj=1,4
|
||||
amatrx(ki,kj)= amatrx(ki,kj) +
|
||||
1 we*(dn(ki)*dn(kj)*rho*spec/dtime +
|
||||
1 cond*(phix(ki)*phix(kj) + phiy(ki)*phiy(kj)))
|
||||
end do
|
||||
end do
|
||||
enddo
|
||||
end if
|
||||
return
|
||||
end
|
||||
260
Unpublished/XFEM/AbaqusUEL/2D_XCor.for
Normal file
260
Unpublished/XFEM/AbaqusUEL/2D_XCor.for
Normal file
|
|
@ -0,0 +1,260 @@
|
|||
c 2D XFEM Corrosion Element
|
||||
|
||||
subroutine uel(rhs,amatrx,svars,energy,ndofel,nrhs,nsvars,props,
|
||||
1 nprops,coords,mcrd,nnode,u,du,v,a,jtype,time,dtime,kstep,kinc,
|
||||
2 jelem,params,ndload,jdltyp,adlmag,predef,npredf,lflags,
|
||||
3 mlvarx,ddlmag,mdload,pnewdt,jprops,njprop,period)
|
||||
c
|
||||
include 'aba_param.inc'
|
||||
c
|
||||
dimension rhs(mlvarx,*),amatrx(ndofel,ndofel),svars(nsvars),
|
||||
1 energy(8),props(*),coords(mcrd,nnode),
|
||||
2 u(ndofel),du(mlvarx,*),v(ndofel),a(ndofel),time(2),
|
||||
3 params(3),jdltyp(mdload,*),adlmag(mdload,*),
|
||||
4 ddlmag(mdload,*),predef(2,npredf,nnode),lflags(*),jprops(*)
|
||||
c
|
||||
dimension phig(8),phih(8),phi(8),phix(8),phiy(8)
|
||||
dimension crdnx(4),crdny(4),dndg(4),dndh(4)
|
||||
dimension theta(4),rjac(2,2),rjaci(2,2)
|
||||
dimension gx(100,4),hx(100,4),xi(2),yi(2),gi(2),hi(2)
|
||||
dimension c(2),gp(2,8),gm2(8,8)
|
||||
c
|
||||
parameter(zero=0.d0,one=1.d0)
|
||||
c material property definition
|
||||
thick = 1.
|
||||
rho = 1.
|
||||
beta=0.
|
||||
dpos=0.6
|
||||
c initialization (nrhs=1)
|
||||
do k1=1,ndofel
|
||||
rhs(k1,nrhs)=zero
|
||||
do k2=1,ndofel
|
||||
amatrx(k2,k1)=zero
|
||||
enddo
|
||||
enddo
|
||||
if (lflags(1).eq.33) then
|
||||
do icrd=1,4
|
||||
crdnx(icrd)=coords(1,icrd)
|
||||
crdny(icrd)=coords(2,icrd)
|
||||
theta(icrd)=abs(crdnx(icrd)-dpos)*
|
||||
1 sign(1.,crdnx(icrd)-dpos)
|
||||
enddo
|
||||
c if (sign(1.,theta(1))/=sign(1.,theta(2)))then
|
||||
if (2==1)then
|
||||
c possible enriched element
|
||||
npart=10
|
||||
rpart=float(npart)
|
||||
ienr=npart*npart
|
||||
do isdx=1,npart
|
||||
do isdy=1,npart
|
||||
rmidx=-1.-1./rpart+(2./rpart)*float(isdx)
|
||||
rmidy=-1.-1./rpart+(2./rpart)*float(isdy)
|
||||
isubindex=npart*(isdy-1)+isdx
|
||||
gpos=1./(sqrt(3.)*rpart)
|
||||
gx(isubindex,1)=rmidx-gpos
|
||||
gx(isubindex,2)=rmidx+gpos
|
||||
gx(isubindex,3)=rmidx+gpos
|
||||
gx(isubindex,4)=rmidx-gpos
|
||||
hx(isubindex,1)=rmidy-gpos
|
||||
hx(isubindex,2)=rmidy-gpos
|
||||
hx(isubindex,3)=rmidy+gpos
|
||||
hx(isubindex,4)=rmidy+gpos
|
||||
enddo
|
||||
enddo
|
||||
c check if int points are on different sides of front
|
||||
icheck=0
|
||||
do i=1,ienr
|
||||
do j=1,4
|
||||
g=gx(i,j)
|
||||
h=hx(i,j)
|
||||
phi(1)=0.25*(1.-g)*(1.-h)
|
||||
phi(3)=0.25*(1.+g)*(1.-h)
|
||||
phi(5)=0.25*(1.+g)*(1.+h)
|
||||
phi(7)=0.25*(1.-g)*(1.+h)
|
||||
rLS=theta(1)*phi(1)+theta(2)*phi(3)
|
||||
1 +theta(3)*phi(5)+theta(4)*phi(7)
|
||||
if (i==1 .and. j==1)then
|
||||
sgn=sign(1.,rLS)
|
||||
else
|
||||
if (sign(1.,rLS)/=sgn)then
|
||||
icheck=1
|
||||
endif
|
||||
endif
|
||||
enddo
|
||||
enddo
|
||||
if (icheck==0)then
|
||||
c regular element - fix extra dofs
|
||||
ienr=1
|
||||
gpos=1/sqrt(3.)
|
||||
gx(1,1)=-gpos
|
||||
gx(1,2)=gpos
|
||||
gx(1,3)=gpos
|
||||
gx(1,4)=-gpos
|
||||
hx(1,1)=-gpos
|
||||
hx(1,2)=-gpos
|
||||
hx(1,3)=gpos
|
||||
hx(1,4)=gpos
|
||||
endif
|
||||
else
|
||||
c Normal Shp Funs
|
||||
ienr=1
|
||||
gpos=1/sqrt(3.)
|
||||
gx(1,1)=-gpos
|
||||
gx(1,2)=gpos
|
||||
gx(1,3)=gpos
|
||||
gx(1,4)=-gpos
|
||||
hx(1,1)=-gpos
|
||||
hx(1,2)=-gpos
|
||||
hx(1,3)=gpos
|
||||
hx(1,4)=gpos
|
||||
endif
|
||||
c assemble amatrx and rhs
|
||||
do i=1,ienr
|
||||
do j=1,4
|
||||
g=gx(i,j)
|
||||
h=hx(i,j)
|
||||
phi(1)=0.25*(1.-g)*(1.-h)
|
||||
phi(3)=0.25*(1.+g)*(1.-h)
|
||||
phi(5)=0.25*(1.+g)*(1.+h)
|
||||
phi(7)=0.25*(1.-g)*(1.+h)
|
||||
rLS=theta(1)*phi(1)+theta(2)*phi(3)
|
||||
1 +theta(3)*phi(5)+theta(4)*phi(7)
|
||||
cond=1.
|
||||
spec=1.
|
||||
do iter=1,4
|
||||
phi(2*iter)=phi(2*iter-1)*
|
||||
1 (abs(rLS)-abs(theta(iter)))
|
||||
enddo
|
||||
phig(1)=0.25*-(1.-h)
|
||||
phig(3)=0.25*(1.-h)
|
||||
phig(5)=0.25*(1.+h)
|
||||
phig(7)=0.25*-(1.+h)
|
||||
phih(1)=0.25*-(1.-g)
|
||||
phih(3)=0.25*-(1.+g)
|
||||
phih(5)=0.25*(1.+g)
|
||||
phih(7)=0.25*(1.-g)
|
||||
diLSg=sign(1.,rLS)*(phig(1)*theta(1)+phig(3)*
|
||||
1 theta(2)+phig(5)*theta(3)+phig(7)*theta(4))
|
||||
diLSh=sign(1.,rLS)*(phih(1)*theta(1)+phih(3)*
|
||||
1 theta(2)+phih(5)*theta(3)+phih(7)*theta(4))
|
||||
do iter=1,4
|
||||
phig(2*iter)=phig(2*iter-1)*(abs(rLS)-
|
||||
1 abs(theta(iter)))+phi(2*iter-1)*diLSg
|
||||
phih(2*iter)=phih(2*iter-1)*(abs(rLS)-
|
||||
1 abs(theta(iter)))+phi(2*iter-1)*diLSh
|
||||
enddo
|
||||
rjac=zero
|
||||
do iter=1,4
|
||||
rjac(1,1)=rjac(1,1)+phig(2*iter-1)*crdnx(iter)
|
||||
rjac(1,2)=rjac(1,2)+phig(2*iter-1)*crdny(iter)
|
||||
rjac(2,1)=rjac(2,1)+phih(2*iter-1)*crdnx(iter)
|
||||
rjac(2,2)=rjac(2,2)+phih(2*iter-1)*crdny(iter)
|
||||
enddo
|
||||
djac=rjac(1,1)*rjac(2,2)-rjac(1,2)*rjac(2,1)
|
||||
rjaci(1,1)= rjac(2,2)/djac
|
||||
rjaci(2,2)= rjac(1,1)/djac
|
||||
rjaci(1,2)=-rjac(1,2)/djac
|
||||
rjaci(2,1)=-rjac(2,1)/djac
|
||||
do iter=1,8
|
||||
phix(iter)=rjaci(1,1)*phig(iter)+
|
||||
1 rjaci(1,2)*phih(iter)
|
||||
phiy(iter)=rjaci(2,1)*phig(iter)+
|
||||
1 rjaci(2,2)*phih(iter)
|
||||
enddo
|
||||
dtdx=zero
|
||||
dtdy=zero
|
||||
t =zero
|
||||
told=zero
|
||||
do iter=1,8
|
||||
dtdx=u(iter)*phix(iter)+dtdx
|
||||
dtdy=u(iter)*phiy(iter)+dtdy
|
||||
t=u(iter)*phi(iter)+t
|
||||
told=(u(iter)-du(iter,nrhs))*phi(iter)+told
|
||||
end do
|
||||
dtdt=(t-told)/dtime
|
||||
we=djac
|
||||
do ki=1,8
|
||||
c loop over nodes
|
||||
rhs(ki,nrhs) = rhs(ki,nrhs) -
|
||||
1 (we/float(ienr))*(phi(ki)*rho*spec*dtdt+
|
||||
2 cond*(phix(ki)*dtdx + phiy(ki)*dtdy))
|
||||
do kj=1,8
|
||||
amatrx(ki,kj)=amatrx(ki,kj)+(we/float(ienr))
|
||||
1 *(phi(ki)*phi(kj)*rho*spec/dtime+cond
|
||||
2 *(phix(ki)*phix(kj)+phiy(ki)*phiy(kj)))
|
||||
end do
|
||||
end do
|
||||
enddo
|
||||
enddo
|
||||
c if interface is in the element a penalty term is needed
|
||||
if(ienr>1)then
|
||||
icount=0
|
||||
if (sign(1.,theta(1))/=sign(1.,theta(2)))then
|
||||
icount=icount+1
|
||||
f=abs(theta(1))/(abs(theta(1))+abs(theta(2)))
|
||||
xi(icount)=f*(crdnx(2)-crdnx(1))+crdnx(1)
|
||||
yi(icount)=f*(crdny(2)-crdny(1))+crdny(1)
|
||||
gi(icount)=(2.*xi(icount)-(crdnx(1)+crdnx(2)))
|
||||
1 /(-crdnx(1)+crdnx(2))
|
||||
hi(icount)=-1.
|
||||
endif
|
||||
if (sign(1.,theta(2))/=sign(1.,theta(3)))then
|
||||
icount=icount+1
|
||||
f=abs(theta(2))/(abs(theta(2))+abs(theta(3)))
|
||||
xi(icount)=f*(crdnx(3)-crdnx(2))+crdnx(2)
|
||||
yi(icount)=f*(crdny(3)-crdny(2))+crdny(2)
|
||||
gi(icount)=1.
|
||||
hi(icount)=(2.*yi(icount)-(crdny(2)+crdny(3)))
|
||||
1 /(-crdny(2)+crdny(3))
|
||||
endif
|
||||
if (sign(1.,theta(3))/=sign(1.,theta(4)))then
|
||||
icount=icount+1
|
||||
f=abs(theta(3))/(abs(theta(3))+abs(theta(4)))
|
||||
xi(icount)=f*(crdnx(4)-crdnx(3))+crdnx(3)
|
||||
yi(icount)=f*(crdny(4)-crdny(3))+crdny(3)
|
||||
gi(icount)=(2.*xi(icount)-(crdnx(4)+crdnx(3)))
|
||||
1 /(-crdnx(4)+crdnx(3))
|
||||
hi(icount)=1.
|
||||
endif
|
||||
if (sign(1.,theta(1))/=sign(1.,theta(4)))then
|
||||
icount=icount+1
|
||||
f=abs(theta(1))/(abs(theta(1))+abs(theta(4)))
|
||||
xi(icount)=f*(crdnx(4)-crdnx(1))+crdnx(1)
|
||||
yi(icount)=f*(crdny(4)-crdny(1))+crdny(1)
|
||||
gi(icount)=-1.
|
||||
hi(icount)=(2.*yi(icount)-(crdny(1)+crdny(4)))
|
||||
1 /(-crdny(4)+crdny(1))
|
||||
endif
|
||||
c(1)=1.
|
||||
c(2)=1.
|
||||
do iter=1,2
|
||||
Gp(iter,1)=0.25*(1.-gi(iter))*(1.-hi(iter))
|
||||
Gp(iter,3)=0.25*(1.+gi(iter))*(1.-hi(iter))
|
||||
Gp(iter,5)=0.25*(1.+gi(iter))*(1.+hi(iter))
|
||||
Gp(iter,7)=0.25*(1.-gi(iter))*(1.+hi(iter))
|
||||
Gp(iter,2)=-Gp(iter,1)*abs(theta(1))
|
||||
Gp(iter,4)=-Gp(iter,3)*abs(theta(2))
|
||||
Gp(iter,6)=-Gp(iter,5)*abs(theta(3))
|
||||
Gp(iter,8)=-Gp(iter,7)*abs(theta(4))
|
||||
enddo
|
||||
do i=1,8
|
||||
rhs(i,nrhs)=rhs(i,nrhs)+
|
||||
1 beta*(Gp(1,i)*c(1)+Gp(2,i)*c(2))
|
||||
enddo
|
||||
c find GtG
|
||||
gm2=0.
|
||||
do i=1,8
|
||||
do j=1,8
|
||||
gm2(i,j)=gp(1,i)*gp(1,j)+gp(2,i)*gp(2,j)
|
||||
enddo
|
||||
enddo
|
||||
c add penalty stiffness
|
||||
do i=1,8
|
||||
do j=1,8
|
||||
amatrx(i,j)=amatrx(i,j)+beta*gm2(i,j)
|
||||
enddo
|
||||
enddo
|
||||
endif
|
||||
end if
|
||||
return
|
||||
end
|
||||
260
Unpublished/XFEM/AbaqusUEL/2D_XCorS.f
Normal file
260
Unpublished/XFEM/AbaqusUEL/2D_XCorS.f
Normal file
|
|
@ -0,0 +1,260 @@
|
|||
c 2D XFEM Corrosion Element
|
||||
|
||||
subroutine uel(rhs,amatrx,svars,energy,ndofel,nrhs,nsvars,props,
|
||||
1 nprops,coords,mcrd,nnode,u,du,v,a,jtype,time,dtime,kstep,kinc,
|
||||
2 jelem,params,ndload,jdltyp,adlmag,predef,npredf,lflags,
|
||||
3 mlvarx,ddlmag,mdload,pnewdt,jprops,njprop,period)
|
||||
c
|
||||
include 'aba_param.inc'
|
||||
c
|
||||
dimension rhs(mlvarx,*),amatrx(ndofel,ndofel),svars(nsvars),
|
||||
1 energy(8),props(*),coords(mcrd,nnode),
|
||||
2 u(ndofel),du(mlvarx,*),v(ndofel),a(ndofel),time(2),
|
||||
3 params(3),jdltyp(mdload,*),adlmag(mdload,*),
|
||||
4 ddlmag(mdload,*),predef(2,npredf,nnode),lflags(*),jprops(*)
|
||||
c
|
||||
dimension phig(8),phih(8),phi(8),phix(8),phiy(8)
|
||||
dimension crdnx(4),crdny(4),dndg(4),dndh(4)
|
||||
dimension theta(4),rjac(2,2),rjaci(2,2)
|
||||
dimension gx(100,4),hx(100,4),xi(2),yi(2),gi(2),hi(2)
|
||||
dimension c(2),gp(2,8),gm2(8,8)
|
||||
c
|
||||
parameter(zero=0.d0,one=1.d0)
|
||||
c material property definition
|
||||
thick = 1.
|
||||
rho = 1.
|
||||
beta=0.
|
||||
dpos=0.6
|
||||
c initialization (nrhs=1)
|
||||
do k1=1,ndofel
|
||||
rhs(k1,nrhs)=zero
|
||||
do k2=1,ndofel
|
||||
amatrx(k2,k1)=zero
|
||||
enddo
|
||||
enddo
|
||||
if (lflags(1).eq.33) then
|
||||
do icrd=1,4
|
||||
crdnx(icrd)=coords(1,icrd)
|
||||
crdny(icrd)=coords(2,icrd)
|
||||
theta(icrd)=abs(crdnx(icrd)-dpos)*
|
||||
1 sign(1.,crdnx(icrd)-dpos)
|
||||
enddo
|
||||
c if (sign(1.,theta(1))/=sign(1.,theta(2)))then
|
||||
if (2==1)then
|
||||
c possible enriched element
|
||||
npart=10
|
||||
rpart=float(npart)
|
||||
ienr=npart*npart
|
||||
do isdx=1,npart
|
||||
do isdy=1,npart
|
||||
rmidx=-1.-1./rpart+(2./rpart)*float(isdx)
|
||||
rmidy=-1.-1./rpart+(2./rpart)*float(isdy)
|
||||
isubindex=npart*(isdy-1)+isdx
|
||||
gpos=1./(sqrt(3.)*rpart)
|
||||
gx(isubindex,1)=rmidx-gpos
|
||||
gx(isubindex,2)=rmidx+gpos
|
||||
gx(isubindex,3)=rmidx+gpos
|
||||
gx(isubindex,4)=rmidx-gpos
|
||||
hx(isubindex,1)=rmidy-gpos
|
||||
hx(isubindex,2)=rmidy-gpos
|
||||
hx(isubindex,3)=rmidy+gpos
|
||||
hx(isubindex,4)=rmidy+gpos
|
||||
enddo
|
||||
enddo
|
||||
c check if int points are on different sides of front
|
||||
icheck=0
|
||||
do i=1,ienr
|
||||
do j=1,4
|
||||
g=gx(i,j)
|
||||
h=hx(i,j)
|
||||
phi(1)=0.25*(1.-g)*(1.-h)
|
||||
phi(3)=0.25*(1.+g)*(1.-h)
|
||||
phi(5)=0.25*(1.+g)*(1.+h)
|
||||
phi(7)=0.25*(1.-g)*(1.+h)
|
||||
rLS=theta(1)*phi(1)+theta(2)*phi(3)
|
||||
1 +theta(3)*phi(5)+theta(4)*phi(7)
|
||||
if (i==1 .and. j==1)then
|
||||
sgn=sign(1.,rLS)
|
||||
else
|
||||
if (sign(1.,rLS)/=sgn)then
|
||||
icheck=1
|
||||
endif
|
||||
endif
|
||||
enddo
|
||||
enddo
|
||||
if (check==0)then
|
||||
c regular element - fix extra dofs
|
||||
ienr=1
|
||||
gpos=1/sqrt(3.)
|
||||
gx(1,1)=-gpos
|
||||
gx(1,2)=gpos
|
||||
gx(1,3)=gpos
|
||||
gx(1,4)=-gpos
|
||||
hx(1,1)=-gpos
|
||||
hx(1,2)=-gpos
|
||||
hx(1,3)=gpos
|
||||
hx(1,4)=gpos
|
||||
endif
|
||||
else
|
||||
c Normal Shp Funs
|
||||
ienr=1
|
||||
gpos=1/sqrt(3.)
|
||||
gx(1,1)=-gpos
|
||||
gx(1,2)=gpos
|
||||
gx(1,3)=gpos
|
||||
gx(1,4)=-gpos
|
||||
hx(1,1)=-gpos
|
||||
hx(1,2)=-gpos
|
||||
hx(1,3)=gpos
|
||||
hx(1,4)=gpos
|
||||
endif
|
||||
c assemble amatrx and rhs
|
||||
do i=1,ienr
|
||||
do j=1,4
|
||||
g=gx(i,j)
|
||||
h=hx(i,j)
|
||||
phi(1)=0.25*(1.-g)*(1.-h)
|
||||
phi(3)=0.25*(1.+g)*(1.-h)
|
||||
phi(5)=0.25*(1.+g)*(1.+h)
|
||||
phi(7)=0.25*(1.-g)*(1.+h)
|
||||
rLS=theta(1)*phi(1)+theta(2)*phi(3)
|
||||
1 +theta(3)*phi(5)+theta(4)*phi(7)
|
||||
cond=1.
|
||||
spec=1.
|
||||
do iter=1,4
|
||||
phi(2*iter)=phi(2*iter-1)*
|
||||
1 (abs(rLS)-abs(theta(iter)))
|
||||
enddo
|
||||
phig(1)=0.25*-(1.-h)
|
||||
phig(3)=0.25*(1.-h)
|
||||
phig(5)=0.25*(1.+h)
|
||||
phig(7)=0.25*-(1.+h)
|
||||
phih(1)=0.25*-(1.-g)
|
||||
phih(3)=0.25*-(1.+g)
|
||||
phih(5)=0.25*(1.+g)
|
||||
phih(7)=0.25*(1.-g)
|
||||
diLSg=sign(1.,rLS)*(phig(1)*theta(1)+phig(3)*
|
||||
1 theta(2)+phig(5)*theta(3)+phig(7)*theta(4))
|
||||
diLSh=sign(1.,rLS)*(phih(1)*theta(1)+phih(3)*
|
||||
1 theta(2)+phih(5)*theta(3)+phih(7)*theta(4))
|
||||
do iter=1,4
|
||||
phig(2*iter)=phig(2*iter-1)*(abs(rLS)-
|
||||
1 abs(theta(iter)))+phi(2*iter-1)*diLSg
|
||||
phih(2*iter)=phih(2*iter-1)*(abs(rLS)-
|
||||
1 abs(theta(iter)))+phi(2*iter-1)*diLSh
|
||||
enddo
|
||||
rjac=zero
|
||||
do iter=1,4
|
||||
rjac(1,1)=rjac(1,1)+phig(2*iter-1)*crdnx(iter)
|
||||
rjac(1,2)=rjac(1,2)+phig(2*iter-1)*crdny(iter)
|
||||
rjac(2,1)=rjac(2,1)+phih(2*iter-1)*crdnx(iter)
|
||||
rjac(2,2)=rjac(2,2)+phih(2*iter-1)*crdny(iter)
|
||||
enddo
|
||||
djac=rjac(1,1)*rjac(2,2)-rjac(1,2)*rjac(2,1)
|
||||
rjaci(1,1)= rjac(2,2)/djac
|
||||
rjaci(2,2)= rjac(1,1)/djac
|
||||
rjaci(1,2)=-rjac(1,2)/djac
|
||||
rjaci(2,1)=-rjac(2,1)/djac
|
||||
do iter=1,8
|
||||
phix(iter)=rjaci(1,1)*phig(iter)+
|
||||
1 rjaci(1,2)*phih(iter)
|
||||
phiy(iter)=rjaci(2,1)*phig(iter)+
|
||||
1 rjaci(2,2)*phih(iter)
|
||||
enddo
|
||||
dtdx=zero
|
||||
dtdy=zero
|
||||
t =zero
|
||||
told=zero
|
||||
do iter=1,8
|
||||
dtdx=u(iter)*phix(iter)+dtdx
|
||||
dtdy=u(iter)*phiy(iter)+dtdy
|
||||
t=u(iter)*phi(iter)+t
|
||||
told=(u(iter)-du(iter,nrhs))*phi(iter)+told
|
||||
end do
|
||||
dtdt=(t-told)/dtime
|
||||
we=djac
|
||||
do ki=1,8
|
||||
c loop over nodes
|
||||
rhs(ki,nrhs) = rhs(ki,nrhs) -
|
||||
1 (we/float(ienr))*(phi(ki)*rho*spec*dtdt+
|
||||
2 cond*(phix(ki)*dtdx + phiy(ki)*dtdy))
|
||||
do kj=1,8
|
||||
amatrx(ki,kj)=amatrx(ki,kj)+(we/float(ienr))
|
||||
1 *(phi(ki)*phi(kj)*rho*spec/dtime+cond
|
||||
2 *(phix(ki)*phix(kj)+phiy(ki)*phiy(kj)))
|
||||
end do
|
||||
end do
|
||||
enddo
|
||||
enddo
|
||||
c if interface is in the element a penalty term is needed
|
||||
if(ienr>1)then
|
||||
icount=0
|
||||
if (sign(1.,theta(1))/=sign(1.,theta(2)))then
|
||||
icount=icount+1
|
||||
f=abs(theta(1))/(abs(theta(1))+abs(theta(2)))
|
||||
xi(icount)=f*(crdnx(2)-crdnx(1))+crdnx(1)
|
||||
yi(icount)=f*(crdny(2)-crdny(1))+crdny(1)
|
||||
gi(icount)=(2.*xi(icount)-(crdnx(1)+crdnx(2)))
|
||||
1 /(-crdnx(1)+crdnx(2))
|
||||
hi(icount)=-1.
|
||||
endif
|
||||
if (sign(1.,theta(2))/=sign(1.,theta(3)))then
|
||||
icount=icount+1
|
||||
f=abs(theta(2))/(abs(theta(2))+abs(theta(3)))
|
||||
xi(icount)=f*(crdnx(3)-crdnx(2))+crdnx(2)
|
||||
yi(icount)=f*(crdny(3)-crdny(2))+crdny(2)
|
||||
gi(icount)=1.
|
||||
hi(icount)=(2.*yi(icount)-(crdny(2)+crdny(3)))
|
||||
1 /(-crdny(2)+crdny(3))
|
||||
endif
|
||||
if (sign(1.,theta(3))/=sign(1.,theta(4)))then
|
||||
icount=icount+1
|
||||
f=abs(theta(3))/(abs(theta(3))+abs(theta(4)))
|
||||
xi(icount)=f*(crdnx(4)-crdnx(3))+crdnx(3)
|
||||
yi(icount)=f*(crdny(4)-crdny(3))+crdny(3)
|
||||
gi(icount)=(2.*xi(icount)-(crdnx(4)+crdnx(3)))
|
||||
1 /(-crdnx(4)+crdnx(3))
|
||||
hi(icount)=1.
|
||||
endif
|
||||
if (sign(1.,theta(1))/=sign(1.,theta(4)))then
|
||||
icount=icount+1
|
||||
f=abs(theta(1))/(abs(theta(1))+abs(theta(4)))
|
||||
xi(icount)=f*(crdnx(4)-crdnx(1))+crdnx(1)
|
||||
yi(icount)=f*(crdny(4)-crdny(1))+crdny(1)
|
||||
gi(icount)=-1.
|
||||
hi(icount)=(2.*yi(icount)-(crdny(1)+crdny(4)))
|
||||
1 /(-crdny(4)+crdny(1))
|
||||
endif
|
||||
c(1)=1.
|
||||
c(2)=1.
|
||||
do iter=1,2
|
||||
Gp(iter,1)=0.25*(1.-gi(iter))*(1.-hi(iter))
|
||||
Gp(iter,3)=0.25*(1.+gi(iter))*(1.-hi(iter))
|
||||
Gp(iter,5)=0.25*(1.+gi(iter))*(1.+hi(iter))
|
||||
Gp(iter,7)=0.25*(1.-gi(iter))*(1.+hi(iter))
|
||||
Gp(iter,2)=-Gp(iter,1)*abs(theta(1))
|
||||
Gp(iter,4)=-Gp(iter,3)*abs(theta(2))
|
||||
Gp(iter,6)=-Gp(iter,5)*abs(theta(3))
|
||||
Gp(iter,8)=-Gp(iter,7)*abs(theta(4))
|
||||
enddo
|
||||
do i=1,8
|
||||
rhs(i,nrhs)=rhs(i,nrhs)+
|
||||
1 beta*(Gp(1,i)*c(1)+Gp(2,i)*c(2))
|
||||
enddo
|
||||
c find GtG
|
||||
gm2=0.
|
||||
do i=1,8
|
||||
do j=1,8
|
||||
gm2(i,j)=gp(1,i)*gp(1,j)+gp(2,i)*gp(2,j)
|
||||
enddo
|
||||
enddo
|
||||
c add penalty stiffness
|
||||
do i=1,8
|
||||
do j=1,8
|
||||
amatrx(i,j)=amatrx(i,j)+beta*gm2(i,j)
|
||||
enddo
|
||||
enddo
|
||||
endif
|
||||
end if
|
||||
return
|
||||
end
|
||||
113
Unpublished/XFEM/AbaqusUEL/2D_XCorS.for
Normal file
113
Unpublished/XFEM/AbaqusUEL/2D_XCorS.for
Normal file
|
|
@ -0,0 +1,113 @@
|
|||
c 2D XFEM Corrosion Element
|
||||
|
||||
subroutine uel(rhs,amatrx,svars,energy,ndofel,nrhs,nsvars,props,
|
||||
1 nprops,coords,mcrd,nnode,u,du,v,a,jtype,time,dtime,kstep,kinc,
|
||||
2 jelem,params,ndload,jdltyp,adlmag,predef,npredf,lflags,
|
||||
3 mlvarx,ddlmag,mdload,pnewdt,jprops,njprop,period)
|
||||
c
|
||||
include 'aba_param.inc'
|
||||
c
|
||||
dimension rhs(mlvarx,*),amatrx(ndofel,ndofel),svars(nsvars),
|
||||
1 energy(8),props(*),coords(mcrd,nnode),
|
||||
2 u(ndofel),du(mlvarx,*),v(ndofel),a(ndofel),time(2),
|
||||
3 params(3),jdltyp(mdload,*),adlmag(mdload,*),
|
||||
4 ddlmag(mdload,*),predef(2,npredf,nnode),lflags(*),jprops(*)
|
||||
c
|
||||
dimension phig(8),phih(8),phi(8),phix(8),phiy(8)
|
||||
dimension crdnx(4),crdny(4),dndg(4),dndh(4)
|
||||
dimension theta(4),rjac(2,2),rjaci(2,2)
|
||||
dimension gx(100,4),hx(100,4),xi(2),yi(2),gi(2),hi(2)
|
||||
dimension c(2),gp(2,8),gm2(8,8)
|
||||
c
|
||||
parameter(zero=0.d0,one=1.d0)
|
||||
c material property definition
|
||||
thick = 1.
|
||||
rho = 1.
|
||||
c initialization (nrhs=1)
|
||||
do k1=1,ndofel
|
||||
rhs(k1,nrhs)=zero
|
||||
do k2=1,ndofel
|
||||
amatrx(k2,k1)=zero
|
||||
enddo
|
||||
enddo
|
||||
if (lflags(1).eq.33) then
|
||||
do icrd=1,4
|
||||
crdnx(icrd)=coords(1,icrd)
|
||||
crdny(icrd)=coords(2,icrd)
|
||||
enddo
|
||||
c Normal Shp Funs
|
||||
ienr=1
|
||||
gpos=1/sqrt(3.)
|
||||
gx(1,1)=-gpos
|
||||
gx(1,2)=gpos
|
||||
gx(1,3)=gpos
|
||||
gx(1,4)=-gpos
|
||||
hx(1,1)=-gpos
|
||||
hx(1,2)=-gpos
|
||||
hx(1,3)=gpos
|
||||
hx(1,4)=gpos
|
||||
c assemble amatrx and rhs
|
||||
do i=1,ienr
|
||||
do j=1,4
|
||||
g=gx(i,j)
|
||||
h=hx(i,j)
|
||||
phi(1)=0.25*(1.-g)*(1.-h)
|
||||
phi(2)=0.25*(1.+g)*(1.-h)
|
||||
phi(3)=0.25*(1.+g)*(1.+h)
|
||||
phi(4)=0.25*(1.-g)*(1.+h)
|
||||
cond=1.
|
||||
spec=1.
|
||||
phig(1)=0.25*-(1.-h)
|
||||
phig(2)=0.25*(1.-h)
|
||||
phig(3)=0.25*(1.+h)
|
||||
phig(4)=0.25*-(1.+h)
|
||||
phih(1)=0.25*-(1.-g)
|
||||
phih(2)=0.25*-(1.+g)
|
||||
phih(3)=0.25*(1.+g)
|
||||
phih(4)=0.25*(1.-g)
|
||||
rjac=zero
|
||||
do iter=1,4
|
||||
rjac(1,1)=rjac(1,1)+phig(iter)*crdnx(iter)
|
||||
rjac(1,2)=rjac(1,2)+phig(iter)*crdny(iter)
|
||||
rjac(2,1)=rjac(2,1)+phih(iter)*crdnx(iter)
|
||||
rjac(2,2)=rjac(2,2)+phih(iter)*crdny(iter)
|
||||
enddo
|
||||
djac=rjac(1,1)*rjac(2,2)-rjac(1,2)*rjac(2,1)
|
||||
rjaci(1,1)= rjac(2,2)/djac
|
||||
rjaci(2,2)= rjac(1,1)/djac
|
||||
rjaci(1,2)=-rjac(1,2)/djac
|
||||
rjaci(2,1)=-rjac(2,1)/djac
|
||||
do iter=1,4
|
||||
phix(iter)=rjaci(1,1)*phig(iter)+
|
||||
1 rjaci(1,2)*phih(iter)
|
||||
phiy(iter)=rjaci(2,1)*phig(iter)+
|
||||
1 rjaci(2,2)*phih(iter)
|
||||
enddo
|
||||
dtdx=zero
|
||||
dtdy=zero
|
||||
t =zero
|
||||
told=zero
|
||||
do iter=1,4
|
||||
dtdx=u(iter)*phix(iter)+dtdx
|
||||
dtdy=u(iter)*phiy(iter)+dtdy
|
||||
t=u(iter)*phi(iter)+t
|
||||
told=(u(iter)-du(iter,nrhs))*phi(iter)+told
|
||||
end do
|
||||
dtdt=(t-told)/dtime
|
||||
we=djac
|
||||
do ki=1,4
|
||||
c loop over nodes
|
||||
rhs(ki,nrhs) = rhs(ki,nrhs) -
|
||||
1 (we/float(ienr))*(phi(ki)*rho*spec*dtdt+
|
||||
2 cond*(phix(ki)*dtdx + phiy(ki)*dtdy))
|
||||
do kj=1,4
|
||||
amatrx(ki,kj)=amatrx(ki,kj)+(we/float(ienr))
|
||||
1 *(phi(ki)*phi(kj)*rho*spec/dtime+cond
|
||||
2 *(phix(ki)*phix(kj)+phiy(ki)*phiy(kj)))
|
||||
end do
|
||||
end do
|
||||
enddo
|
||||
enddo
|
||||
end if
|
||||
return
|
||||
end
|
||||
84
Unpublished/XFEM/AbaqusUEL/AbInp.inp
Normal file
84
Unpublished/XFEM/AbaqusUEL/AbInp.inp
Normal file
|
|
@ -0,0 +1,84 @@
|
|||
*Heading
|
||||
** Job name: Job-1 Model name: Model-1
|
||||
** Generated by: Abaqus/CAE 6.12-1
|
||||
*Preprint, echo=NO, model=NO, history=NO, contact=NO
|
||||
**
|
||||
** PARTS
|
||||
**
|
||||
*Part, name=Part-1
|
||||
*Node
|
||||
1, 0., 0., 0.
|
||||
2, 0.25, 0., 0.
|
||||
3, 0.5, 0., 0.
|
||||
4, 0.75, 0., 0.
|
||||
5, 1., 0., 0.
|
||||
6, 0., 0.25, 0.
|
||||
7, 0.25, 0.25, 0.
|
||||
8, 0.5, 0.25, 0.
|
||||
9, 0.75, 0.25, 0.
|
||||
10, 1., 0.25, 0.
|
||||
*USER ELEMENT,NODES=4,TYPE=U1,PROP=1,COORDINATES=2,VAR=2,unsymm
|
||||
11,
|
||||
*Element, type=U1,ELSET=UEL
|
||||
1, 1, 2,7,6
|
||||
2, 2, 3,8,7
|
||||
3, 3, 4,9,8
|
||||
4, 4, 5,10,9
|
||||
*UEL Property, Elset=UEL
|
||||
1.
|
||||
*End Part
|
||||
**
|
||||
**
|
||||
** ASSEMBLY
|
||||
**
|
||||
*Assembly, name=Assembly
|
||||
**
|
||||
*Instance, name=Part-1-1, part=Part-1
|
||||
*End Instance
|
||||
**
|
||||
*Nset, nset=_PickedSet16, internal, instance=Part-1-1
|
||||
1,2,3,6,7,8
|
||||
*Nset, nset=_PickedSet17, internal, instance=Part-1-1
|
||||
4,5,9,10
|
||||
*Nset, nset=Set-6, instance=Part-1-1
|
||||
1,6
|
||||
*End Assembly
|
||||
**
|
||||
** MATERIALS
|
||||
**
|
||||
*Material, name=Material-1
|
||||
*Conductivity
|
||||
1.,
|
||||
*Density
|
||||
1.,
|
||||
*Specific Heat
|
||||
1.,
|
||||
** ----------------------------------------------------------------
|
||||
**
|
||||
** Name: Predefined Field-1 Type: Temperature
|
||||
*Initial Conditions, type=TEMPERATURE
|
||||
_PickedSet16, 1.,0.
|
||||
** Name: Predefined Field-2 Type: Temperature
|
||||
*Initial Conditions, type=TEMPERATURE
|
||||
_PickedSet17, 0.,0.
|
||||
** STEP: Step-1
|
||||
**
|
||||
*Step, name=Step-1
|
||||
*Heat Transfer, end=PERIOD, deltmx=100.
|
||||
0.01, 0.1, 1e-09, 0.01,
|
||||
**
|
||||
** BOUNDARY CONDITIONS
|
||||
**
|
||||
** Name: BC-1 Type: Temperature
|
||||
*Boundary
|
||||
Set-6, 11, 11, 1.
|
||||
**
|
||||
** OUTPUT REQUESTS
|
||||
**
|
||||
*Restart, write, frequency=0
|
||||
**
|
||||
** FIELD OUTPUT: F-Output-1
|
||||
**
|
||||
*Output, field, variable=PRESELECT
|
||||
*Output, history, frequency=0
|
||||
*End Step
|
||||
79
Unpublished/XFEM/AbaqusUEL/AbInp1d.inp
Normal file
79
Unpublished/XFEM/AbaqusUEL/AbInp1d.inp
Normal file
|
|
@ -0,0 +1,79 @@
|
|||
*Heading
|
||||
** Job name: Job-1 Model name: Model-1
|
||||
** Generated by: Abaqus/CAE 6.12-1
|
||||
*Preprint, echo=NO, model=NO, history=NO, contact=NO
|
||||
**
|
||||
** PARTS
|
||||
**
|
||||
*Part, name=Part-1
|
||||
*Node
|
||||
1, 0., 0., 0.
|
||||
2, 0.25, 0., 0.
|
||||
3, 0.5, 0., 0.
|
||||
4, 0.75, 0., 0.
|
||||
5, 1., 0., 0.
|
||||
*USER ELEMENT,NODES=2,TYPE=U1,PROP=1,COORDINATES=1,VAR=2,unsymm
|
||||
11,12
|
||||
*Element, type=U1,ELSET=UEL
|
||||
1, 1, 2,
|
||||
2, 2, 3,
|
||||
3, 3,4
|
||||
4, 4,5
|
||||
*UEL Property, Elset=UEL
|
||||
1.
|
||||
*End Part
|
||||
**
|
||||
**
|
||||
** ASSEMBLY
|
||||
**
|
||||
*Assembly, name=Assembly
|
||||
**
|
||||
*Instance, name=Part-1-1, part=Part-1
|
||||
*End Instance
|
||||
**
|
||||
*Nset, nset=_PickedSet16, internal, instance=Part-1-1
|
||||
1,2,3
|
||||
*Nset, nset=_PickedSet17, internal, instance=Part-1-1
|
||||
4,5,6
|
||||
*Nset, nset=Set-6, instance=Part-1-1
|
||||
1,
|
||||
*End Assembly
|
||||
**
|
||||
** MATERIALS
|
||||
**
|
||||
*Material, name=Material-1
|
||||
*Conductivity
|
||||
1.,
|
||||
*Density
|
||||
1.,
|
||||
*Specific Heat
|
||||
1.,
|
||||
** ----------------------------------------------------------------
|
||||
**
|
||||
** Name: Predefined Field-1 Type: Temperature
|
||||
*Initial Conditions, type=TEMPERATURE
|
||||
_PickedSet16, 1.,0.
|
||||
** Name: Predefined Field-2 Type: Temperature
|
||||
*Initial Conditions, type=TEMPERATURE
|
||||
_PickedSet17, 0.,0.
|
||||
** STEP: Step-1
|
||||
**
|
||||
*Step, name=Step-1
|
||||
*Heat Transfer, end=PERIOD, deltmx=100.
|
||||
0.01, 0.1, 1e-09, 0.01,
|
||||
**
|
||||
** BOUNDARY CONDITIONS
|
||||
**
|
||||
** Name: BC-1 Type: Temperature
|
||||
*Boundary
|
||||
Set-6, 11, 11, 1.
|
||||
**
|
||||
** OUTPUT REQUESTS
|
||||
**
|
||||
*Restart, write, frequency=0
|
||||
**
|
||||
** FIELD OUTPUT: F-Output-1
|
||||
**
|
||||
*Output, field, variable=PRESELECT
|
||||
*Output, history, frequency=0
|
||||
*End Step
|
||||
237
Unpublished/XFEM/AbaqusUEL/JQuad.for
Normal file
237
Unpublished/XFEM/AbaqusUEL/JQuad.for
Normal file
|
|
@ -0,0 +1,237 @@
|
|||
c***********************************************************
|
||||
subroutine uelmat(rhs,amatrx,svars,energy,ndofel,nrhs,
|
||||
1 nsvars,props,nprops,coords,mcrd,nnode,u,du,
|
||||
2 v,a,jtype,time,dtime,kstep,kinc,jelem,params,
|
||||
3 ndload,jdltyp,adlmag,predef,npredf,lflags,mlvarx,
|
||||
4 ddlmag,mdload,pnewdt,jprops,njpro,period,
|
||||
5 materiallib)
|
||||
c
|
||||
include 'aba_param.inc'
|
||||
C
|
||||
dimension rhs(mlvarx,*), amatrx(ndofel, ndofel), props(*),
|
||||
1 svars(*), energy(*), coords(mcrd, nnode), u(ndofel),
|
||||
2 du(mlvarx,*), v(ndofel), a(ndofel), time(2), params(*),
|
||||
3 jdltyp(mdload,*), adlmag(mdload,*), ddlmag(mdload,*),
|
||||
4 predef(2, npredf, nnode), lflags(*), jprops(*)
|
||||
parameter (zero=0.d0, dmone=-1.0d0, one=1.d0, four=4.0d0,
|
||||
1 fourth=0.25d0,gaussCoord=0.577350269d0)
|
||||
parameter (ndim=2, ndof=2, nshr=1,nnodemax=4,
|
||||
1 ntens=4, ninpt=4, nsvint=4)
|
||||
c
|
||||
dimension stiff(ndof*nnodemax,ndof*nnodemax),
|
||||
1 force(ndof*nnodemax), shape(nnodemax), dshape(ndim,nnodemax),
|
||||
2 xjac(ndim,ndim),xjaci(ndim,ndim), bmat(nnodemax*ndim),
|
||||
3 statevLocal(nsvint),stress(ntens), ddsdde(ntens, ntens),
|
||||
4 stran(ntens), dstran(ntens), wght(ninpt)
|
||||
c
|
||||
dimension predef_loc(npredf),dpredef_loc(npredf),
|
||||
1 defGrad(3,3),utmp(3),xdu(3),stiff_p(3,3),force_p(3)
|
||||
dimension coord24(2,4),coords_ip(3)
|
||||
data coord24 /dmone, dmone,
|
||||
2 one, dmone,
|
||||
3 one, one,
|
||||
4 dmone, one/
|
||||
c
|
||||
data wght /one, one, one, one/
|
||||
c*************************************************************
|
||||
c U1 = first-order, plane strain, full integration
|
||||
c*************************************************************
|
||||
c define mass matrix as identity at start of analysis
|
||||
if (lflags(3).eq.4) then
|
||||
amatrx = zero
|
||||
do i=1, ndofel
|
||||
amatrx(i,i) = one
|
||||
end do
|
||||
goto 999
|
||||
end if
|
||||
c properties
|
||||
thickness = 0.1d0
|
||||
c initialize rhs and k
|
||||
rhs = zero
|
||||
amatrx = zero
|
||||
c loop over integration points
|
||||
do kintk = 1, ninpt
|
||||
c determine gauss point in local sys (g,h)
|
||||
c takes form: [4 3]
|
||||
c [1 2]
|
||||
g = coord24(1,kintk)*gaussCoord
|
||||
h = coord24(2,kintk)*gaussCoord
|
||||
c shape functions
|
||||
shape(1) = (one - g)*(one - h)/four
|
||||
shape(2) = (one + g)*(one - h)/four
|
||||
shape(3) = (one + g)*(one + h)/four
|
||||
shape(4) = (one - g)*(one + h)/four
|
||||
c derivative d(Ni)/d(g)
|
||||
dshape(1,1) = -(one - h)/four
|
||||
dshape(1,2) = (one - h)/four
|
||||
dshape(1,3) = (one + h)/four
|
||||
dshape(1,4) = -(one + h)/four
|
||||
c derivative d(Ni)/d(h)
|
||||
dshape(2,1) = -(one - g)/four
|
||||
dshape(2,2) = -(one + g)/four
|
||||
dshape(2,3) = (one + g)/four
|
||||
dshape(2,4) = (one - g)/four
|
||||
c compute global coordinates of the ip
|
||||
coords_ip = zero
|
||||
do k1=1,nnode
|
||||
do k2=1,mcrd
|
||||
coords_ip(k2)=coords_ip(k2)+shape(k1)*coords(k2,k1)
|
||||
end do
|
||||
end do
|
||||
c form b-matrix
|
||||
djac = one
|
||||
xjac = zero
|
||||
xjaci = zero
|
||||
c Get Jacobian
|
||||
do inod= 1, nnode
|
||||
do idim = 1, ndim
|
||||
do jdim = 1, ndim
|
||||
xjac(jdim,idim) = xjac(jdim,idim) +
|
||||
1 dshape(jdim,inod)*coords(idim,inod)
|
||||
end do
|
||||
end do
|
||||
end do
|
||||
c Get Det of Jacobian
|
||||
djac = xjac(1,1)*xjac(2,2) - xjac(1,2)*xjac(2,1)
|
||||
if (djac .gt. zero) then
|
||||
! jacobian is positive - invert it
|
||||
xjaci(1,1) = xjac(2,2)/djac
|
||||
xjaci(2,2) = xjac(1,1)/djac
|
||||
xjaci(1,2) = -xjac(1,2)/djac
|
||||
xjaci(2,1) = -xjac(2,1)/djac
|
||||
else
|
||||
! negative or zero jacobian - reduce time inc.
|
||||
write(7,*)'WARNING: element',jelem,'has neg. Jacobian'
|
||||
pnewdt = fourth
|
||||
endif
|
||||
if (pnewdt .lt. pnewdtLocal) pnewdtLocal = pnewdt
|
||||
c Build B matrix
|
||||
bmat = zero
|
||||
do inod = 1, nnode
|
||||
do ider = 1, ndim
|
||||
do idim = 1, ndim
|
||||
irow = idim + (inod - 1)*ndim
|
||||
bmat(irow) = bmat(irow) +
|
||||
1 xjaci(idim,ider)*dshape(ider,inod)
|
||||
end do
|
||||
end do
|
||||
end do
|
||||
c get strain inc
|
||||
dstran(i) = zero
|
||||
c set deformation gradient to Identity matrix
|
||||
defGrad = zero
|
||||
do k1=1,3
|
||||
defGrad(k1,k1) = one
|
||||
end do
|
||||
c compute incremental strains
|
||||
do nodi = 1, nnode
|
||||
incr_row = (nodi - 1)*ndof
|
||||
do i = 1, ndof
|
||||
xdu(i)= du(i + incr_row,1)
|
||||
utmp(i) = u(i + incr_row)
|
||||
end do
|
||||
dNidx = bmat(1+(nodi-1)*ndim)
|
||||
dNidy = bmat(2+(nodi-1)*ndim)
|
||||
dstran(1) = dstran(1)+dNidx*xdu(1)
|
||||
dstran(2) = dstran(2)+dNidy*xdu(2)
|
||||
dstran(4) = dstran(4)+dNidy*xdu(1)+dNidx*xdu(2)
|
||||
c deformation gradient (prob not required for umat)
|
||||
defGrad(1,1) = defGrad(1,1) + dNidx*utmp(1)
|
||||
defGrad(1,2) = defGrad(1,2) + dNidy*utmp(1)
|
||||
defGrad(2,1) = defGrad(2,1) + dNidx*utmp(2)
|
||||
defGrad(2,2) = defGrad(2,2) + dNidy*utmp(2)
|
||||
end do
|
||||
c call constitutive routine
|
||||
isvinc= (kintk-1)*nsvint
|
||||
c prepare arrays for entry into material routines
|
||||
do i = 1, nsvint
|
||||
statevLocal(i)=svars(i+isvinc)
|
||||
end do
|
||||
c state variables
|
||||
do k1=1,ntens
|
||||
stran(k1) = statevLocal(k1)
|
||||
stress(k1) = zero
|
||||
end do
|
||||
do i=1, ntens
|
||||
do j=1, ntens
|
||||
ddsdde(i,j) = zero
|
||||
end do
|
||||
ddsdde(i,j) = one
|
||||
enddo
|
||||
c compute characteristic element length
|
||||
celent = sqrt(djac*dble(ninpt))
|
||||
dvmat = djac*thickness
|
||||
c
|
||||
dvdv0 = one
|
||||
call material_lib_mech(materiallib,stress,ddsdde,
|
||||
1 stran,dstran,kintk,dvdv0,dvmat,defGrad,
|
||||
2 predef_loc,dpredef_loc,npredf,celent,coords_ip)
|
||||
c
|
||||
do k1=1,ntens
|
||||
statevLocal(k1) = stran(k1) + dstran(k1)
|
||||
end do
|
||||
isvinc= (kintk-1)*nsvint
|
||||
c update element state variables
|
||||
do i = 1, nsvint
|
||||
svars(i+isvinc)=statevLocal(i)
|
||||
end do
|
||||
c form stiffness matrix and internal force vector
|
||||
dNjdx = zero
|
||||
dNjdy = zero
|
||||
force = zero
|
||||
stiff = zero
|
||||
dvol= wght(kintk)*djac
|
||||
do nodj = 1, nnode
|
||||
incr_col = (nodj - 1)*ndof
|
||||
dNjdx = bmat(1+(nodj-1)*ndim)
|
||||
dNjdy = bmat(2+(nodj-1)*ndim)
|
||||
force_p(1) = dNjdx*stress(1) + dNjdy*stress(4)
|
||||
force_p(2) = dNjdy*stress(2) + dNjdx*stress(4)
|
||||
do jdof = 1, ndof
|
||||
jcol = jdof + incr_col
|
||||
force(jcol) = force(jcol)+force_p(jdof)*dvol
|
||||
end do
|
||||
do nodi = 1, nnode
|
||||
incr_row = (nodi -1)*ndof
|
||||
dNidx = bmat(1+(nodi-1)*ndim)
|
||||
dNidy = bmat(2+(nodi-1)*ndim)
|
||||
stiff_p(1,1) = dNidx*ddsdde(1,1)*dNjdx
|
||||
& + dNidy*ddsdde(4,4)*dNjdy
|
||||
& + dNidx*ddsdde(1,4)*dNjdy
|
||||
& + dNidy*ddsdde(4,1)*dNjdx
|
||||
stiff_p(1,2) = dNidx*ddsdde(1,2)*dNjdy
|
||||
& + dNidy*ddsdde(4,4)*dNjdx
|
||||
& + dNidx*ddsdde(1,4)*dNjdx
|
||||
& + dNidy*ddsdde(4,2)*dNjdy
|
||||
stiff_p(2,1) = dNidy*ddsdde(2,1)*dNjdx
|
||||
& + dNidx*ddsdde(4,4)*dNjdy
|
||||
& + dNidy*ddsdde(2,4)*dNjdy
|
||||
& + dNidx*ddsdde(4,1)*dNjdx
|
||||
stiff_p(2,2) = dNidy*ddsdde(2,2)*dNjdy
|
||||
& + dNidx*ddsdde(4,4)*dNjdx
|
||||
& + dNidy*ddsdde(2,4)*dNjdx
|
||||
& + dNidx*ddsdde(4,2)*dNjdy
|
||||
do jdof = 1, ndof
|
||||
icol = jdof + incr_col
|
||||
do idof = 1, ndof
|
||||
irow = idof + incr_row
|
||||
stiff(irow,icol) = stiff(irow,icol) +
|
||||
& stiff_p(idof,jdof)*dvol
|
||||
end do
|
||||
end do
|
||||
end do
|
||||
end do
|
||||
c assemble rhs and lhs
|
||||
do k1=1, ndof*nnode
|
||||
rhs(k1, 1) = rhs(k1, 1) - force(k1)
|
||||
do k2=1, ndof*nnode
|
||||
amatrx(k1, k2) = amatrx(k1, k2) + stiff(k1,k2)
|
||||
end do
|
||||
end do
|
||||
end do ! end loop on material integration points
|
||||
pnewdt = pnewdtLocal
|
||||
c
|
||||
999 continue
|
||||
c
|
||||
return
|
||||
end
|
||||
293
Unpublished/XFEM/AbaqusUEL/JQuadX.for
Normal file
293
Unpublished/XFEM/AbaqusUEL/JQuadX.for
Normal file
|
|
@ -0,0 +1,293 @@
|
|||
c User subroutine UEL XFEM
|
||||
subroutine uel(rhs,amatrx,svars,energy,ndofel,nrhs,nsvars,
|
||||
1 props,nprops,coords,mcrd,nnode,u,du,v,a,jtype,time,dtime,
|
||||
1 kstep,kinc,jelem,params,ndload,jdltyp,adlmag,predef,npredf,
|
||||
1 lflags,mlvarx,ddlmag,mdload,pnewdt,jprops,njprop,period)
|
||||
c
|
||||
include 'aba_param.inc'
|
||||
c ABAQUS defined variables:
|
||||
dimension rhs(mlvarx,*), amatrx(ndofel,ndofel), props(*),
|
||||
1 svars(nsvars), energy(8), coords(mcrd,nnode), u(ndofel),
|
||||
1 du(mlvarx,*), v(ndofel), a(ndofel), time(2), params(*),
|
||||
1 jdltyp(mdload,*), adlmag(mdload,*), ddlmag(mdload,*),
|
||||
1 predef(2,npredf,nnode), lflags(*), jprops(*)
|
||||
c
|
||||
character*256 outdir
|
||||
integer lenoutdir
|
||||
integer i,j,k,pss,orderq(3),gint,flag,dimens
|
||||
integer ncracks,maxncp,nelmx,nnodx,typexe(nnode),ix(nnode)
|
||||
integer,parameter :: mpg=1650
|
||||
integer,allocatable:: typex(:,:),ncp(:)
|
||||
real*8 e, nu
|
||||
real*8 f(ndofel)
|
||||
real*8 sg(3,mpg),xypg(2,mpg),xe(8),ye(8),xyc0(2),xycprev(2)
|
||||
real*8, allocatable:: xyc(:,:,:),dist(:,:),elemgg(:,:)
|
||||
real*8, allocatable:: batg(:,:),dbatg(:,:),jatg(:)
|
||||
c
|
||||
c Read real and integer properties set at the ABAQUS input file
|
||||
e = props(1)
|
||||
nu = props(2)
|
||||
pss = jprops(1)
|
||||
orderq(1) = jprops(2)
|
||||
orderq(2) = jprops(3)
|
||||
orderq(3) = jprops(4)
|
||||
dimens = jprops(5)
|
||||
c Read the working directory
|
||||
call getoutdir(outdir,lenoutdir)
|
||||
c read number of cracks, max number of crack path points,
|
||||
c number of enriched elements and enriched nodes.
|
||||
open(68,file=outdir(1:lenoutdir)//’\files\gginfox’)
|
||||
read(68,*) ncracks,maxncp,nelmx,nnodx
|
||||
close(68)
|
||||
c Allocate dimensions
|
||||
allocate (typex(nnodx,2), ncp(ncracks))
|
||||
allocate (xyc(ncracks,maxncp,2), dist(nnodx,3), elemgg(nelmx,10))
|
||||
c read coordinates of path points for each crack
|
||||
open(68,file=outdir(1:lenoutdir)//’\files\ggxyc’)
|
||||
do i=1,ncracks
|
||||
read(68,*) ncp(i)
|
||||
do j=1,ncp(i)
|
||||
read(68,*) (xyc(i,j,k),k=1,2)
|
||||
end do
|
||||
end do
|
||||
close(68)
|
||||
c Read list of enriched nodes, type of enrichment and distances
|
||||
open(68,file=outdir(1:lenoutdir)//’\files\ggnodex’)
|
||||
do i=1,nnodx
|
||||
read(68,*) (typex(i,j),j=1,2),(dist(i,j),j=2,3)
|
||||
dist(i,1)=typex(i,1)
|
||||
end do
|
||||
close(68)
|
||||
c read list of enriched elements, type of enrichment and intersection points
|
||||
open(68,file=outdir(1:lenoutdir)//’\files\ggelemx’)
|
||||
do i=1,nelmx
|
||||
read(68,*) (elemgg(i,j),j=1,10)
|
||||
end do
|
||||
close(68)
|
||||
c call initializing routines for matrix and vectors
|
||||
call initializem(rhs,ndofel,nrhs)
|
||||
call initializem(amatrx,ndofel,ndofel)
|
||||
call initializev(energy,8)
|
||||
call initializev(svars,nsvars)
|
||||
c verification of element type (type=12 for enriched element)
|
||||
if (jtype.eq.12) then
|
||||
c **************************************
|
||||
c * 4 node enriched element with *
|
||||
c * up to 12 dof/node for x-fem *
|
||||
c **************************************
|
||||
if (lflags(1).eq.71) then
|
||||
c coupled thermal-stress, steady state analysis
|
||||
if (lflags(3).eq.1) then
|
||||
c Routine that defines the location of integration points according to
|
||||
c the appropriate subdivision. This enables to know the total number of
|
||||
c integration points for the current element, stored in gint, and whether
|
||||
c the element is subdivided for integration (flag=1) or not.
|
||||
CALL int2d_X(JELEM,NelmX,ElemGG,MCRD,NNODE,COORDS,orderQ,
|
||||
1 NCracks,maxNCP,NCP,XYC,gint,sg,Xe,Ye,flag,mpg,xypg,
|
||||
1 XYC0,XYCPrev)
|
||||
c Allocate dimensions once the total number of integration points gint is known
|
||||
allocate(batg(3*gint,ndofel),dbatg(3*gint,ndofel),jatg(gint))
|
||||
call initializem(batg,3*gint,ndofel)
|
||||
call initializem(dbatg,3*gint,ndofel)
|
||||
call initializev(jatg,gint)
|
||||
c Search of the enrichment type for the nodes of the current element.
|
||||
c The keys to the enrichment types are stored in the element vector TypeXe
|
||||
call typexelement(outdir,lenoutdir,jelem,nnode,nelmx,ix,typexe)
|
||||
c element stiffness matrix computation, stored in amatrx
|
||||
call k_u12(e,nu,amatrx,ndofel,nnode,dimens,mcrd,
|
||||
coords,pss,nnodx,ix,typexe,dist,xyc0,xycprev,
|
||||
gint,sg,xe,ye,flag,batg,dbatg,jatg)
|
||||
c Routine that multiplies AMATRX times U to obtain the force vector F
|
||||
c at the end of the current increment
|
||||
call mult_v(amatrx,ndofel,ndofel,u,f,ndofel)
|
||||
c compute the residual force vector
|
||||
do i=1,ndofel
|
||||
rhs(i,1) = rhs(i,1) - f(i)
|
||||
end do
|
||||
c Compute stresses at Gauss points for post-processing purposes
|
||||
c Store them as SVARS for output to the results file (.fil)
|
||||
call svars_u12(jtype,jelem,svars,nsvars,u,ndofel,batg,
|
||||
1 dbatg,jatg,gint,mpg,xypg)
|
||||
end if
|
||||
end if
|
||||
end if
|
||||
return
|
||||
end
|
||||
C Element stiffness matrix. Subroutine: K U12
|
||||
subroutine k_u12(e,nu,amatrx,ndofel,nnode,dimens,mcrd,
|
||||
1 COORDS,PSS,NnodX,ix,TypeXe,Dist,XYC0,XYCPrev,
|
||||
1 gint,sg,Xe,Ye,flag,BatG,DBatG,JatG)
|
||||
implicit none
|
||||
integer ndofel,nnode,dimens,mcrd,pss,nnodx,gint,flag,pos
|
||||
integer l,i,j,kk,typexe(nnode),ix(nnode)
|
||||
real*8 e,nu,dist(nnodx,3),sg(3,*)
|
||||
real*8 amatrx(ndofel,ndofel),xyc0(2),xycprev(2)
|
||||
real*8 xe(2*nnode),ye(2*nnode),coords(mcrd,nnode),xl(dimens,nnode)
|
||||
real*8 xsj(gint),shp(3,4)
|
||||
real*8 dnf(nnode,2,4),fnode(nnode,4),h,hnode(nnode)
|
||||
real*8 b(3,ndofel), db(3,ndofel), bt(ndofel,3), d(3,3)
|
||||
real*8 batg(3*gint,ndofel),dbatg(3*gint,ndofel),jatg(gint)
|
||||
logical nodetype1,nodetype2
|
||||
c NOTES:
|
||||
c Routine shapef2D is called to compute standard shape functions,
|
||||
c derivatives and jacobian at integration points. This routine outputs:
|
||||
c shp(3,*) - Shape functions and derivatives at point
|
||||
c shp(1,i) = dN_i/dx = dN_i/dx1
|
||||
c shp(2,i) = dN_i/dy = dN_i/dx2
|
||||
c shp(3,i) = N_i
|
||||
c xsj - Jacobian determinant at point
|
||||
c Local coordinates of integration points are passed in sg(1,*), sg(2,*)
|
||||
c Integration weights are passed in sg(3,*)
|
||||
c Initialize AMATRX and logical variables
|
||||
call initializem(amatrx,ndofel,ndofel)
|
||||
NodeType1=.false.
|
||||
NodeType2=.false.
|
||||
c Reduce info passed thru COORDS (3D) to xl (2D)
|
||||
do i=1,dimens
|
||||
do j=1,nnode
|
||||
xl(i,j)=coords(i,j)
|
||||
end do
|
||||
end do
|
||||
c Define constitutive stress-strain elastic matrix
|
||||
call calc_d(pss,d,e,nu)
|
||||
c Specify the type of nodal enrichment
|
||||
do i=1,nnode
|
||||
if (typexe(i).eq.1) then
|
||||
nodetype1=.true.
|
||||
elseif (typexe(i).eq.2) then
|
||||
nodetype2=.true.
|
||||
end if
|
||||
end do
|
||||
c Numerical integration loop over gint integration points
|
||||
DO l = 1,gint
|
||||
c Compute shape functions, derivatives and jacobian at integration point
|
||||
call shapef2d(sg(1,l),xl,shp,xsj(l),dimens,nnode,ix,.false.)
|
||||
if (flag.eq.1) then !element is subdivided for integration
|
||||
xsj(l) = sg(3,l) !the integration weight includes the jacobian
|
||||
else !element is not subdivided. standard integration
|
||||
xsj(l) = xsj(l)*sg(3,l)
|
||||
endif
|
||||
c Value of the Heaviside function at integration point
|
||||
c (This call is also used to store the values of H
|
||||
c at nodes of the element for modified enrichment)
|
||||
if (nodetype1) then
|
||||
call heaviside(nnodx,dist,nnode,ix,shp,h,hnode)
|
||||
endif
|
||||
c Derivatives of shape functions Ni times enrichment functions Fj at integration point
|
||||
c (This call is also used to compute the derivatives of shape functions Ni times
|
||||
c enrichment functions Fj at nodes of the element for modified enrichment)
|
||||
if (nodetype2) then
|
||||
call fcracktip(xyc0,xycprev,shp,xe,ye,dnf,fnode)
|
||||
endif
|
||||
c STIFFNESS MATRIX COMPUTATION:
|
||||
c Assembly of element matrix B (denoted as B) at integration point
|
||||
call initializem(b,3,ndofel)
|
||||
pos=1
|
||||
c loop over nodes
|
||||
do i= 1,nnode
|
||||
c Contribution to B of derivatives of standard shape functions
|
||||
B(1,Pos) = shp(1,i)
|
||||
B(2,Pos+1)= shp(2,i)
|
||||
B(3,Pos) = shp(2,i)
|
||||
B(3,Pos+1)= shp(1,i)
|
||||
c Contribution to B of derivatives of shape functions times Heaviside function
|
||||
if (typexe(i).eq.1) then
|
||||
b(1,2+pos) = shp(1,i)*(h-hnode(i))
|
||||
b(2,3+pos) = shp(2,i)*(h-hnode(i))
|
||||
b(3,2+pos) = shp(2,i)*(h-hnode(i))
|
||||
b(3,3+pos) = shp(1,i)*(h-hnode(i))
|
||||
c Contribution to B of derivatives of shape functions times crack tip functions
|
||||
elseif(typexe(i).eq.2) then
|
||||
do kk= 1,4
|
||||
b(1,2*kk+2+pos)= dnf(i,1,kk)-shp(1,i)*fnode(i,kk)
|
||||
b(2,2*kk+3+pos)= dnf(i,2,kk)-shp(2,i)*fnode(i,kk)
|
||||
b(3,2*kk+2+pos)= dnf(i,2,kk)-shp(2,i)*fnode(i,kk)
|
||||
b(3,2*kk+3+pos)= dnf(i,1,kk)-shp(1,i)*fnode(i,kk)
|
||||
end do
|
||||
end if
|
||||
Pos=Pos+12 !Each node has 12 dof
|
||||
end do ! i = end loop over element nodes
|
||||
db=matmul(d,b) ! matrix d*b
|
||||
bt=transpose(b) ! b transpose
|
||||
c Integration of BT*D*B
|
||||
amatrx= amatrx + matmul(bt,db)*xsj(l)
|
||||
c store information at each integration point for further post-processing
|
||||
do i=1,3
|
||||
do j=1,ndofel
|
||||
batg(3*(l-1)+i,j)=b(i,j)
|
||||
dbatg(3*(l-1)+i,j)=db(i,j)
|
||||
end do
|
||||
end do
|
||||
jatg(l)=xsj(l)
|
||||
end do ! l = end loop for each integration point
|
||||
return
|
||||
end
|
||||
c
|
||||
SUBROUTINE SVARS_U12(JTYPE,JELEM,SVARS,NSVARS,U,Dof,BatG,DBatG,
|
||||
* JatG,gint,mpg,xypg)
|
||||
c Calculates and/or stores the following magnitudes at the element integration points,
|
||||
c storing them in SVARS: strains, stresses, strain energy density, dv/dx, du/dy, jacobian,
|
||||
c dNi/dx, dNi/dy, global coordinates of integration points.
|
||||
IMPLICIT NONE
|
||||
INTEGER i,j,k,NSVARS, Dof, gint, JTYPE,JELEM,mpg
|
||||
REAL*8 SVARS(NSVARS), U(Dof),BatG(3*gint,Dof),DBatG(3*gint,Dof)
|
||||
REAL*8 JatG(gint),B(3,Dof),DB(3,Dof),Bdvdx(3,Dof),Bdudy(3,Dof)
|
||||
REAL*8 EPS(3),SIG(3),W,dvdx(3),dudy(3),JAC,xypg(2,mpg)
|
||||
c &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&
|
||||
39
|
||||
c &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&
|
||||
c First value stored in SVARS is the total number of integration points
|
||||
c of the enriched element
|
||||
SVARS(1)=gint
|
||||
DO i=1,gint
|
||||
JAC=JatG(i)
|
||||
DO k=1,3
|
||||
DO j=1,Dof
|
||||
B(k,j)=BatG(3*(i-1)+k,j)
|
||||
Bdvdx(k,j)=B(k,j) ! For computation of dv/dx
|
||||
Bdudy(k,j)=B(k,j) ! For computation of du/dy
|
||||
DB(k,j)=DBatG(3*(i-1)+k,j)
|
||||
END DO
|
||||
END DO
|
||||
CALL MULT_V(B,3,Dof,U,EPS,3) ! Compute strains EPS
|
||||
CALL MULT_V(DB,3,Dof,U,SIG,3) ! Compute stresses SIG
|
||||
W=0.5d0*(EPS(1)*SIG(1)+EPS(2)*SIG(2)+EPS(3)*SIG(3))
|
||||
c Computation of dv/dx & du/dy
|
||||
c Set to zero positions in the 3rd row of B associated with dN/dy
|
||||
DO j=1,Dof,2
|
||||
Bdvdx(3,j)=0.0d0
|
||||
END DO
|
||||
CALL MULT_V(Bdvdx,3,Dof,U,dvdx,3) !compute dv/dx, stored in dvdx(3)
|
||||
c Set to zero positions in the 3rd row of B associated with dN/dx
|
||||
DO j=2,Dof,2
|
||||
Bdudy(3,j)=0.0d0
|
||||
END DO
|
||||
CALL MULT_V(Bdudy,3,Dof,U,dudy,3) !compute du/dy, stored in dudy(3)
|
||||
c Store in SVARS the following information at integration points
|
||||
SVARS(1+20*(i-1)+1)=EPS(1)
|
||||
SVARS(1+20*(i-1)+2)=EPS(2)
|
||||
SVARS(1+20*(i-1)+3)=EPS(3)
|
||||
SVARS(1+20*(i-1)+4)=SIG(1)
|
||||
SVARS(1+20*(i-1)+5)=SIG(2)
|
||||
SVARS(1+20*(i-1)+6)=SIG(3)
|
||||
SVARS(1+20*(i-1)+7)=W
|
||||
SVARS(1+20*(i-1)+8)=dvdx(3)
|
||||
SVARS(1+20*(i-1)+9)=dudy(3)
|
||||
SVARS(1+20*(i-1)+10)=JAC ! Jacobian includes integration weight
|
||||
c Store in SVARS the shape functions derivatives dNi/dx, dNi/dy for external computation
|
||||
c of dq/dx, dq/dy (used in domain interaction integrals).
|
||||
c (we take them from the positions associated with the standard dofs)
|
||||
SVARS(1+20*(i-1)+11)=B(1,1)
|
||||
SVARS(1+20*(i-1)+12)=B(1,13)
|
||||
SVARS(1+20*(i-1)+13)=B(1,25)
|
||||
SVARS(1+20*(i-1)+14)=B(1,37)
|
||||
SVARS(1+20*(i-1)+15)=B(2,2)
|
||||
SVARS(1+20*(i-1)+16)=B(2,14)
|
||||
SVARS(1+20*(i-1)+17)=B(2,26)
|
||||
SVARS(1+20*(i-1)+18)=B(2,38)
|
||||
Store in SVARS the global coordinates of integration points
|
||||
SVARS(1+20*(i-1)+19)=xypg(1,i)
|
||||
SVARS(1+20*(i-1)+20)=xypg(2,i)
|
||||
END DO !i loop over all integration points of the element
|
||||
RETURN
|
||||
END
|
||||
70
Unpublished/XFEM/AbaqusUEL/JTruss.for
Normal file
70
Unpublished/XFEM/AbaqusUEL/JTruss.for
Normal file
|
|
@ -0,0 +1,70 @@
|
|||
subroutine uel(rhs,amatrx,svars,energy,ndofel,nrhs,nsvars,
|
||||
1 props,nprops,coords,mcrd,nnode,u,du,v,a,jtype,time,
|
||||
2 dtime,kstep,kinc,jelem,params,ndload,jdltyp,adlmag,
|
||||
3 predef,npredf,lflags,mlvarx,ddlmag,mdload,pnewdt,
|
||||
4 jprops,njprop,period)
|
||||
c
|
||||
include 'aba_param.inc'
|
||||
parameter ( zero = 0.d0, half = 0.5d0, one = 1.d0 )
|
||||
c
|
||||
c This is a linear truss element for Abaqus/Standard
|
||||
c general static analysis in 1D space (aligned to x-axis) only.
|
||||
dimension rhs(mlvarx,*),amatrx(ndofel,ndofel),
|
||||
1 svars(nsvars),energy(8),props(*),coords(mcrd,nnode),
|
||||
2 u(ndofel),du(mlvarx,*),v(ndofel),a(ndofel),time(2),
|
||||
3 params(3),jdltyp(mdload,*),adlmag(mdload,*),
|
||||
4 ddlmag(mdload,*),predef(2,npredf,nnode),lflags(*),
|
||||
5 jprops(*)
|
||||
c
|
||||
c assign section properties
|
||||
area = props(1)
|
||||
e = props(2)
|
||||
anu = props(3)
|
||||
rho = props(4)
|
||||
c calculate stiffness and mass
|
||||
alen = abs(coords(1,2)-coords(1,1))
|
||||
ak = area*e/alen
|
||||
am = half*area*rho*alen
|
||||
c Initialize Arrays
|
||||
rhs = zero
|
||||
amatrx = zero
|
||||
if (lflags(3).eq.1) then
|
||||
C Stiffness and Force
|
||||
C Get Stiffness Matrix
|
||||
amatrx(1,1) = ak
|
||||
amatrx(4,4) = ak
|
||||
amatrx(1,4) = -ak
|
||||
amatrx(4,1) = -ak
|
||||
c Get Internal Contrib to Residual Force
|
||||
rhs(1,1) = -ak*(u(1)-u(4))
|
||||
rhs(4,1) = -ak*(u(4)-u(1))
|
||||
c Get External Contrib to Residual Force
|
||||
do kdload = 1, ndload
|
||||
if (jdltyp(kdload,1).eq.1001) then
|
||||
rhs(4,1) = rhs(4,1)+adlmag(kdload,1)
|
||||
end if
|
||||
end do
|
||||
else if (lflags(3).eq.2) then
|
||||
c Stiffness
|
||||
amatrx(1,1) = ak
|
||||
amatrx(4,4) = ak
|
||||
amatrx(1,4) = -ak
|
||||
amatrx(4,1) = -ak
|
||||
else if (lflags(3).eq.4) then
|
||||
c Mass
|
||||
do k1 = 1, ndofel
|
||||
amatrx(k1,k1) = am
|
||||
end do
|
||||
else if (lflags(3).eq.5) then
|
||||
print *,'oops'
|
||||
else if (lflags(3).eq.6) then
|
||||
C Mass and Force
|
||||
do k1 = 1, ndofel
|
||||
amatrx(k1,k1) = am
|
||||
end do
|
||||
rhs(1,1) = -ak*(u(1)-u(4))
|
||||
rhs(4,1) = -ak*(u(4)-u(1))
|
||||
END IF
|
||||
c
|
||||
return
|
||||
end
|
||||
202
Unpublished/XFEM/AbaqusUEL/UEL2_TRANHTX.f
Normal file
202
Unpublished/XFEM/AbaqusUEL/UEL2_TRANHTX.f
Normal file
|
|
@ -0,0 +1,202 @@
|
|||
c 1-D Moving Interface User Element - JGrogan 2012.
|
||||
c Subroutine UEXTERNALDB
|
||||
c Calculates interface velocity and position at the start of each increment
|
||||
c and passes it to UEL via common block. It requires a list of current nodal
|
||||
c coordinates, and 'T' and 'a' degrees of freedom.
|
||||
|
||||
subroutine uexternaldb(lop,lrestart,time,dtime,kstep,kinc)
|
||||
c
|
||||
include 'aba_param.inc'
|
||||
c
|
||||
real dpos, npos(6), ndof(6)
|
||||
common dpos,npos,ndof
|
||||
dimension time(2)
|
||||
c
|
||||
if (lop==0)then
|
||||
c initialise common blocks
|
||||
dpos=0.
|
||||
npos=0.
|
||||
tn=0.
|
||||
an=0.
|
||||
print *,'npos',npos,'extrn1',time
|
||||
print *,'ndof',ndof,'extrn1',time
|
||||
else
|
||||
print *,'npos',npos,'extrn',time
|
||||
print *,'ndof',ndof,'extrn',time
|
||||
endif
|
||||
return
|
||||
end
|
||||
c
|
||||
c Subroutine UEL
|
||||
c Calculates element mass and stiffness matrices and residual flux
|
||||
c vector for Abaqus NR Solver.
|
||||
|
||||
subroutine uel(rhs,amatrx,svars,energy,ndofel,nrhs,nsvars,props
|
||||
1 ,nprops,coords,mcrd,nnode,u,du,v,a,jtype,time,dtime,kstep,
|
||||
2 kinc,jelem,params,ndload,jdltyp,adlmag,predef,npredf,lflags
|
||||
3 ,mlvarx,ddlmag,mdload,pnewdt,jprops,njprop,period)
|
||||
c
|
||||
include 'aba_param.inc'
|
||||
c
|
||||
dimension rhs(mlvarx,*),amatrx(ndofel,ndofel),svars(nsvars),
|
||||
1 energy(8),props(*),coords(mcrd,nnode),
|
||||
2 u(ndofel),du(mlvarx,*),v(ndofel),a(ndofel),time(2),
|
||||
3 params(3),jdltyp(mdload,*),adlmag(mdload,*),
|
||||
4 ddlmag(mdload,*),predef(2,npredf,nnode),lflags(*),jprops(*)
|
||||
c
|
||||
dimension gpx(4),gwei(4),phi(4),phix(4),phic(4),gm(4),gm2(4,4)
|
||||
dimension theta(2)
|
||||
real dpos, npos(6), ndof(6)
|
||||
common dpos,npos,ndof
|
||||
c
|
||||
c level set calculation
|
||||
c store nodal positions and temperatures
|
||||
npos(jelem)=coords(1,1)
|
||||
npos(jelem+1)=coords(1,2)
|
||||
ndof(2*jelem-1)=u(1)
|
||||
ndof(2*jelem)=u(2)
|
||||
dpos1=0.2+0.4*time(1)
|
||||
c print *,'npos',npos,'uel',time
|
||||
c print *,'ndof',ndof,'uel',time
|
||||
c material property definition
|
||||
rho = 1.
|
||||
spec = 1.
|
||||
c penalty term
|
||||
beta=40.
|
||||
c initialization (nrhs=1)
|
||||
do k1=1,ndofel
|
||||
rhs(k1,nrhs)=0.
|
||||
do k2=1,ndofel
|
||||
amatrx(k2,k1)=0.
|
||||
enddo
|
||||
enddo
|
||||
if (lflags(3).eq.4) return
|
||||
c transient analysis
|
||||
if (lflags(1).eq.33) then
|
||||
c determine node level set params
|
||||
crdn1=coords(1,1)
|
||||
crdn2=coords(1,2)
|
||||
theta(1)=abs(crdn1-dpos1)*sign(1.,crdn1-dpos1)
|
||||
theta(2)=abs(crdn2-dpos1)*sign(1.,crdn2-dpos1)
|
||||
enr=2
|
||||
elen=abs(crdn2-crdn1)
|
||||
ajacob=elen/2.
|
||||
if (sign(1.,theta(1))/=sign(1.,theta(2)))then
|
||||
c enriched element
|
||||
enr=4
|
||||
point=(dpos1-crdn1)/ajacob-1.
|
||||
rlen1=abs(-point-1.)
|
||||
rlen2=abs(1.-point)
|
||||
rmid1=-1.+rlen1/2.
|
||||
rmid2=1.-rlen2/2.
|
||||
c Get int point locations and weights
|
||||
gpx(1)=-(rlen1/2.)/sqrt(3.)+rmid1
|
||||
gpx(2)=(rlen1/2.)/sqrt(3.)+rmid1
|
||||
gpx(3)=-(rlen2/2.)/sqrt(3.)+rmid2
|
||||
gpx(4)=(rlen2/2.)/sqrt(3.)+rmid2
|
||||
gwei(1)=(rlen1/2.)
|
||||
gwei(2)=(rlen1/2.)
|
||||
gwei(3)=(rlen2/2.)
|
||||
gwei(4)=(rlen2/2.)
|
||||
else
|
||||
c regular element
|
||||
gpx(1)=-1./sqrt(3.)
|
||||
gpx(2)=1./sqrt(3.)
|
||||
gwei(1)=1.
|
||||
gwei(2)=1.
|
||||
endif
|
||||
c assemble amatrx and rhs
|
||||
do k=1,enr
|
||||
c loop through gauss pts: i
|
||||
c=gpx(k)
|
||||
c get ip level set value: Oi
|
||||
c get shape functions and derivatives
|
||||
c Ni
|
||||
phi(1)=(1.-c)/2.
|
||||
phi(3)=(1.+c)/2.
|
||||
term=theta(1)*phi(1)+theta(2)*phi(3)
|
||||
if (term<0.)then
|
||||
cond=0.
|
||||
spec=0.1
|
||||
else
|
||||
cond=1.
|
||||
spec=1.
|
||||
endif
|
||||
if(enr==4)then
|
||||
phi(2)=phi(1)*(abs(term)-abs(theta(1)))
|
||||
phi(4)=phi(3)*(abs(term)-abs(theta(2)))
|
||||
else
|
||||
phi(2)=0.
|
||||
phi(4)=0.
|
||||
endif
|
||||
c dNdci
|
||||
phic(1)=-0.5
|
||||
phic(3)=0.5
|
||||
dterm=sign(1.,term)*(phic(1)*theta(1)+phic(3)*theta(2))
|
||||
if(enr==4)then
|
||||
phic(2)=phic(1)*(abs(term)-abs(theta(1)))
|
||||
1 +phi(1)*dterm
|
||||
phic(4)=phic(3)*(abs(term)-abs(theta(2)))
|
||||
1 +phi(3)*dterm
|
||||
else
|
||||
phic(2)=0.
|
||||
phic(4)=0.
|
||||
endif
|
||||
c dNdxi
|
||||
phix(1)=phic(1)*(1./ajacob)
|
||||
phix(2)=phic(2)*(1./ajacob)
|
||||
phix(3)=phic(3)*(1./ajacob)
|
||||
phix(4)=phic(4)*(1./ajacob)
|
||||
c interpolate temperatures Tbar to int point: i
|
||||
dtdx=u(1)*phix(1)+u(2)*phix(2)
|
||||
1 +u(3)*phix(3)+u(4)*phix(4)
|
||||
t=u(1)*phi(1)+u(2)*phi(2)
|
||||
1 +u(3)*phi(3)+u(4)*phi(4)
|
||||
told=(u(1)-du(1,nrhs))*phi(1)+(u(2)-du(2,nrhs))*phi(2)+
|
||||
1 (u(3)-du(3,nrhs))*phi(3)+(u(4)-du(4,nrhs))*phi(4)
|
||||
c other housekeeping
|
||||
dtdt=(t-told)/dtime
|
||||
we=gwei(k)*ajacob
|
||||
c Assemble Element Stiffness Matrix and Add to Global
|
||||
do ki=1,4
|
||||
c loop over nodes
|
||||
rhs(ki,nrhs)=rhs(ki,nrhs)-we*(phi(ki)*rho*spec*dtdt
|
||||
1 + cond*(phix(ki)*dtdx))
|
||||
do kj=1,4
|
||||
amatrx(ki,kj)=amatrx(ki,kj)+we*(phi(ki)*phi(kj)
|
||||
1 *rho*spec/dtime+cond*(phix(ki)*phix(kj)))
|
||||
end do
|
||||
end do
|
||||
enddo
|
||||
end if
|
||||
c if interface is in the element an penalty term is needed
|
||||
if(enr==4)then
|
||||
xi=point
|
||||
gm(1)=(1.-xi)/2.
|
||||
gm(3)=(1.+xi)/2.
|
||||
term=theta(1)*gm(1)+theta(2)*gm(3)
|
||||
gm(2)=gm(1)*(abs(term)-abs(theta(1)))
|
||||
gm(4)=gm(3)*(abs(term)-abs(theta(2)))
|
||||
term2=gm(1)*u(1)+gm(2)*u(2)+gm(3)*u(3)+gm(4)*u(4)
|
||||
diff=abs(term2-1.)
|
||||
c add penalty flux/force: BGtc
|
||||
targetT=1.
|
||||
do i=1,4
|
||||
rhs(i,nrhs)=rhs(i,nrhs)+beta*gm(i)*diff
|
||||
enddo
|
||||
c find GtG
|
||||
gm2=0.
|
||||
do i=1,4
|
||||
do j=1,4
|
||||
gm2(i,j)=gm(i)*gm(j)
|
||||
enddo
|
||||
enddo
|
||||
c add penalty stiffness
|
||||
do i=1,4
|
||||
do j=1,4
|
||||
amatrx(i,j)=amatrx(i,j)+beta*gm2(i,j)
|
||||
enddo
|
||||
enddo
|
||||
endif
|
||||
return
|
||||
end
|
||||
165
Unpublished/XFEM/AbaqusUEL/UEL2_TRANHTX.for
Normal file
165
Unpublished/XFEM/AbaqusUEL/UEL2_TRANHTX.for
Normal file
|
|
@ -0,0 +1,165 @@
|
|||
c Subroutine UEL
|
||||
c Calculates element mass and stiffness matrices and residual flux
|
||||
c vector for Abaqus NR Solver.
|
||||
subroutine uel(rhs,amatrx,svars,energy,ndofel,nrhs,nsvars,props
|
||||
1 ,nprops,coords,mcrd,nnode,u,du,v,a,jtype,time,dtime,kstep,
|
||||
2 kinc,jelem,params,ndload,jdltyp,adlmag,predef,npredf,lflags
|
||||
3 ,mlvarx,ddlmag,mdload,pnewdt,jprops,njprop,period)
|
||||
c
|
||||
include 'aba_param.inc'
|
||||
c
|
||||
dimension rhs(mlvarx,*),amatrx(ndofel,ndofel),svars(nsvars),
|
||||
1 energy(8),props(*),coords(mcrd,nnode),
|
||||
2 u(ndofel),du(mlvarx,*),v(ndofel),a(ndofel),time(2),
|
||||
3 params(3),jdltyp(mdload,*),adlmag(mdload,*),
|
||||
4 ddlmag(mdload,*),predef(2,npredf,nnode),lflags(*),jprops(*)
|
||||
c
|
||||
dimension gpx(4),gwei(4),phi(4),phix(4),phic(4),gm(4),gm2(4,4)
|
||||
dimension theta(2)
|
||||
real dpos, npos(6), ndof(6)
|
||||
common dpos,npos,ndof
|
||||
c
|
||||
c level set calculation
|
||||
c store nodal positions and temperatures
|
||||
dpos1=0.6
|
||||
c material property definition
|
||||
rho = 1.
|
||||
spec = 1.
|
||||
c penalty term
|
||||
beta=100.
|
||||
c initialization (nrhs=1)
|
||||
do k1=1,ndofel
|
||||
rhs(k1,nrhs)=0.
|
||||
do k2=1,ndofel
|
||||
amatrx(k2,k1)=0.
|
||||
enddo
|
||||
enddo
|
||||
if (lflags(3).eq.4) return
|
||||
c transient analysis
|
||||
if (lflags(1).eq.33) then
|
||||
c determine node level set params
|
||||
crdn1=coords(1,1)
|
||||
crdn2=coords(1,2)
|
||||
theta(1)=abs(crdn1-dpos1)*sign(1.,crdn1-dpos1)
|
||||
theta(2)=abs(crdn2-dpos1)*sign(1.,crdn2-dpos1)
|
||||
enr=2
|
||||
elen=abs(crdn2-crdn1)
|
||||
ajacob=elen/2.
|
||||
if (sign(1.,theta(1))/=sign(1.,theta(2)))then
|
||||
c enriched element
|
||||
enr=4
|
||||
point=(dpos1-crdn1)/ajacob-1.
|
||||
rlen1=abs(-point-1.)
|
||||
rlen2=abs(1.-point)
|
||||
rmid1=-1.+rlen1/2.
|
||||
rmid2=1.-rlen2/2.
|
||||
c Get int point locations and weights
|
||||
gpx(1)=-(rlen1/2.)/sqrt(3.)+rmid1
|
||||
gpx(2)=(rlen1/2.)/sqrt(3.)+rmid1
|
||||
gpx(3)=-(rlen2/2.)/sqrt(3.)+rmid2
|
||||
gpx(4)=(rlen2/2.)/sqrt(3.)+rmid2
|
||||
gwei(1)=(rlen1/2.)
|
||||
gwei(2)=(rlen1/2.)
|
||||
gwei(3)=(rlen2/2.)
|
||||
gwei(4)=(rlen2/2.)
|
||||
else
|
||||
c regular element
|
||||
gpx(1)=-1./sqrt(3.)
|
||||
gpx(2)=1./sqrt(3.)
|
||||
gwei(1)=1.
|
||||
gwei(2)=1.
|
||||
endif
|
||||
c assemble amatrx and rhs
|
||||
do k=1,enr
|
||||
c loop through gauss pts: i
|
||||
c=gpx(k)
|
||||
c get ip level set value: Oi
|
||||
c get shape functions and derivatives
|
||||
c Ni
|
||||
phi(1)=(1.-c)/2.
|
||||
phi(3)=(1.+c)/2.
|
||||
term=theta(1)*phi(1)+theta(2)*phi(3)
|
||||
c if (term<0.)then
|
||||
c cond=0.
|
||||
c spec=0.1
|
||||
c else
|
||||
cond=1.
|
||||
spec=1.
|
||||
c endif
|
||||
c if(enr==4)then
|
||||
phi(2)=phi(1)*(abs(term)-abs(theta(1)))
|
||||
phi(4)=phi(3)*(abs(term)-abs(theta(2)))
|
||||
c else
|
||||
c phi(2)=0.
|
||||
c phi(4)=0.
|
||||
c endif
|
||||
c dNdci
|
||||
phic(1)=-0.5
|
||||
phic(3)=0.5
|
||||
dterm=sign(1.,term)*(phic(1)*theta(1)+phic(3)*theta(2))
|
||||
c if(enr==4)then
|
||||
phic(2)=phic(1)*(abs(term)-abs(theta(1)))
|
||||
1 +phi(1)*dterm
|
||||
phic(4)=phic(3)*(abs(term)-abs(theta(2)))
|
||||
1 +phi(3)*dterm
|
||||
c else
|
||||
c phic(2)=0.
|
||||
c phic(4)=0.
|
||||
c endif
|
||||
c dNdxi
|
||||
phix(1)=phic(1)*(1./ajacob)
|
||||
phix(2)=phic(2)*(1./ajacob)
|
||||
phix(3)=phic(3)*(1./ajacob)
|
||||
phix(4)=phic(4)*(1./ajacob)
|
||||
c interpolate temperatures Tbar to int point: i
|
||||
dtdx=u(1)*phix(1)+u(2)*phix(2)
|
||||
1 +u(3)*phix(3)+u(4)*phix(4)
|
||||
t=u(1)*phi(1)+u(2)*phi(2)
|
||||
1 +u(3)*phi(3)+u(4)*phi(4)
|
||||
told=(u(1)-du(1,nrhs))*phi(1)+(u(2)-du(2,nrhs))*phi(2)+
|
||||
1 (u(3)-du(3,nrhs))*phi(3)+(u(4)-du(4,nrhs))*phi(4)
|
||||
c other housekeeping
|
||||
dtdt=(t-told)/dtime
|
||||
we=gwei(k)*ajacob
|
||||
c Assemble Element Stiffness Matrix and Add to Global
|
||||
do ki=1,4
|
||||
c loop over nodes
|
||||
rhs(ki,nrhs)=rhs(ki,nrhs)-we*(phi(ki)*rho*spec*dtdt
|
||||
1 + cond*(phix(ki)*dtdx))
|
||||
do kj=1,4
|
||||
amatrx(ki,kj)=amatrx(ki,kj)+we*(phi(ki)*phi(kj)
|
||||
1 *rho*spec/dtime+cond*(phix(ki)*phix(kj)))
|
||||
end do
|
||||
end do
|
||||
enddo
|
||||
end if
|
||||
c if interface is in the element a penalty term is needed
|
||||
if(enr==4)then
|
||||
xi=point
|
||||
gm(1)=(1.-xi)/2.
|
||||
gm(3)=(1.+xi)/2.
|
||||
term=theta(1)*gm(1)+theta(2)*gm(3)
|
||||
gm(2)=gm(1)*(abs(term)-abs(theta(1)))
|
||||
gm(4)=gm(3)*(abs(term)-abs(theta(2)))
|
||||
term2=gm(1)*u(1)+gm(2)*u(2)+gm(3)*u(3)+gm(4)*u(4)
|
||||
diff=abs(term2-1.)
|
||||
c add penalty flux/force: BGtc
|
||||
do i=1,4
|
||||
rhs(i,nrhs)=rhs(i,nrhs)+beta*gm(i)*diff
|
||||
enddo
|
||||
c find GtG
|
||||
gm2=0.
|
||||
do i=1,4
|
||||
do j=1,4
|
||||
gm2(i,j)=gm(i)*gm(j)
|
||||
enddo
|
||||
enddo
|
||||
c add penalty stiffness
|
||||
do i=1,4
|
||||
do j=1,4
|
||||
amatrx(i,j)=amatrx(i,j)+beta*gm2(i,j)
|
||||
enddo
|
||||
enddo
|
||||
endif
|
||||
return
|
||||
end
|
||||
80
Unpublished/XFEM/AbaqusUEL/UEL_TRANHT.for
Normal file
80
Unpublished/XFEM/AbaqusUEL/UEL_TRANHT.for
Normal file
|
|
@ -0,0 +1,80 @@
|
|||
subroutine uel(rhs,amatrx,svars,energy,ndofel,nrhs,nsvars,props
|
||||
1 ,nprops,coords,mcrd,nnode,u,du,v,a,jtype,time,dtime,kstep,
|
||||
2 kinc,jelem,params,ndload,jdltyp,adlmag,predef,npredf,lflags
|
||||
3 ,mlvarx,ddlmag,mdload,pnewdt,jprops,njprop,period)
|
||||
c
|
||||
include 'aba_param.inc'
|
||||
c
|
||||
dimension rhs(mlvarx,*),amatrx(ndofel,ndofel),svars(nsvars),
|
||||
1 energy(8),props(*),coords(mcrd,nnode),
|
||||
2 u(ndofel),du(mlvarx,*),v(ndofel),a(ndofel),time(2),
|
||||
3 params(3),jdltyp(mdload,*),adlmag(mdload,*),
|
||||
4 ddlmag(mdload,*),predef(2,npredf,nnode),lflags(*),jprops(*)
|
||||
c
|
||||
dimension gpx(9),gwei(9),phi(8),phix(8),phic(8),stiffk(2,2)
|
||||
dimension stiffm(2,2)
|
||||
c
|
||||
c print *,u(1),u(2),du(1,nhrs),du(2,nhrs),time(1),lflags(3)
|
||||
c material property definition
|
||||
rho = 1.
|
||||
spec = 1.
|
||||
conduc = 1.
|
||||
c initialization (nrhs=1)
|
||||
do k1=1,ndofel
|
||||
rhs(k1,nrhs)=0.
|
||||
do k2=1,ndofel
|
||||
amatrx(k2,k1)=0.
|
||||
stiffk(k2,k1)=0.
|
||||
stiffm(k2,k1)=0.
|
||||
enddo
|
||||
enddo
|
||||
if (lflags(3).eq.4) return
|
||||
c transient analysis
|
||||
if (lflags(1).eq.33) then
|
||||
c determine gauss point locations
|
||||
gpx(1)=-1./sqrt(3.)
|
||||
gpx(2)=1./sqrt(3.)
|
||||
gwei(1)=1.
|
||||
gwei(2)=1.
|
||||
c assemble amatrx and rhs
|
||||
do k=1,2
|
||||
c loop through gauss pts
|
||||
c=gpx(k)
|
||||
c get shape functions and derivatives
|
||||
phi(1)=(1.-c)/2.
|
||||
phi(2)=(1.+c)/2.
|
||||
phic(1)=-0.5
|
||||
phic(2)=0.5
|
||||
dxdc=abs(coords(1,2)-coords(1,1))/2.
|
||||
ajacob=dxdc
|
||||
phix(1)=phic(1)*(1./ajacob)
|
||||
phix(2)=phic(2)*(1./ajacob)
|
||||
c interpolate temperatures to int points
|
||||
dtdx=u(1)*phix(1)+u(2)*phix(2)
|
||||
t=u(1)*phi(1)+u(2)*phi(2)
|
||||
told=(u(1)-du(1,nrhs))*phi(1)+(u(2)-du(2,nrhs))*phi(2)
|
||||
c other housekeeping
|
||||
cond=conduc
|
||||
dtdt=(t-told)/dtime
|
||||
we=gwei(k)*ajacob
|
||||
c Assemble Element Stiffness Matrix and Add to Global
|
||||
do ki=1,2
|
||||
c loop over nodes
|
||||
rhs(ki,nrhs)=rhs(ki,nrhs)-we*(phi(ki)*rho*spec*dtdt
|
||||
1 + cond*(phix(ki)*dtdx))
|
||||
do kj=1,2
|
||||
stiffk(ki,kj)=stiffk(ki,kj)+
|
||||
1 we*cond*(phix(ki)*phix(kj))
|
||||
stiffm(ki,kj)=stiffm(ki,kj)+
|
||||
1 we*(phi(ki)*phi(kj)*rho*spec)/dtime
|
||||
end do
|
||||
end do
|
||||
do i=1,2
|
||||
do j=1,2
|
||||
amatrx(i,j)=stiffk(i,j)+stiffm(i,j)
|
||||
enddo
|
||||
enddo
|
||||
enddo
|
||||
end if
|
||||
return
|
||||
end
|
||||
81
Unpublished/XFEM/AbaqusUEL/UEL_TRANHTX.f
Normal file
81
Unpublished/XFEM/AbaqusUEL/UEL_TRANHTX.f
Normal file
|
|
@ -0,0 +1,81 @@
|
|||
subroutine uel(rhs,amatrx,svars,energy,ndofel,nrhs,nsvars,props
|
||||
1 ,nprops,coords,mcrd,nnode,u,du,v,a,jtype,time,dtime,kstep,
|
||||
2 kinc,jelem,params,ndload,jdltyp,adlmag,predef,npredf,lflags
|
||||
3 ,mlvarx,ddlmag,mdload,pnewdt,jprops,njprop,period)
|
||||
c
|
||||
include 'aba_param.inc'
|
||||
c
|
||||
dimension rhs(mlvarx,*),amatrx(ndofel,ndofel),svars(nsvars),
|
||||
1 energy(8),props(*),coords(mcrd,nnode),
|
||||
2 u(ndofel),du(mlvarx,*),v(ndofel),a(ndofel),time(2),
|
||||
3 params(3),jdltyp(mdload,*),adlmag(mdload,*),
|
||||
4 ddlmag(mdload,*),predef(2,npredf,nnode),lflags(*),jprops(*)
|
||||
c
|
||||
dimension gpx(9),gwei(9),phi(8),phix(8),phic(8)
|
||||
c
|
||||
c print *,u(1),u(2),du(1,nhrs),du(2,nhrs),time(1),lflags(3)
|
||||
c level set calculation
|
||||
dpos=0.01*time
|
||||
c
|
||||
c material property definition
|
||||
rho = 1.
|
||||
spec = 1.
|
||||
conduc = 1.
|
||||
c initialization (nrhs=1)
|
||||
do k1=1,ndofel
|
||||
rhs(k1,nrhs)=0.
|
||||
do k2=1,ndofel
|
||||
amatrx(k2,k1)=0.
|
||||
enddo
|
||||
enddo
|
||||
if (lflags(3).eq.4) return
|
||||
c transient analysis
|
||||
if (lflags(1).eq.33) then
|
||||
c determine gauss point locations
|
||||
gpx(1)=-1./sqrt(3.)
|
||||
gpx(2)=1./sqrt(3.)
|
||||
gwei(1)=1.
|
||||
gwei(2)=1.
|
||||
c determine node level sets
|
||||
rnl1=abs(coords(1,1)-dpos)
|
||||
rnl2=abs(coords(1,2)-dpos)
|
||||
c get jacobian
|
||||
dxdc=abs(coords(1,2)-coords(1,1))/2.
|
||||
ajacob=dxdc
|
||||
c assemble amatrx and rhs
|
||||
do k=1,4
|
||||
c loop through gauss pts
|
||||
c=gpx(k)
|
||||
c get shape functions and derivatives
|
||||
phi(1)=(1.-c)/2.
|
||||
phi(2)=(1.+c)/2.
|
||||
c get ip position
|
||||
pos=coord(1,1)+ajacob(1.+c)
|
||||
phi(3)=abs(c)
|
||||
phic(1)=-0.5
|
||||
phic(2)=0.5
|
||||
|
||||
phix(1)=phic(1)*(1./ajacob)
|
||||
phix(2)=phic(2)*(1./ajacob)
|
||||
c interpolate temperatures to int points
|
||||
dtdx=u(1)*phix(1)+u(2)*phix(2)
|
||||
t=u(1)*phi(1)+u(2)*phi(2)
|
||||
told=(u(1)-du(1,nrhs))*phi(1)+(u(2)-du(2,nrhs))*phi(2)
|
||||
c other housekeeping
|
||||
cond=conduc
|
||||
dtdt=(t-told)/dtime
|
||||
we=gwei(k)*ajacob
|
||||
c Assemble Element Stiffness Matrix and Add to Global
|
||||
do ki=1,2
|
||||
c loop over nodes
|
||||
rhs(ki,nrhs)=rhs(ki,nrhs)-we*(phi(ki)*rho*spec*dtdt
|
||||
1 + cond*(phix(ki)*dtdx))
|
||||
do kj=1,2
|
||||
amatrx(ki,kj)=amatrx(ki,kj)+we*(phi(ki)*phi(kj)
|
||||
1 *rho*spec/dtime+cond*(phix(ki)*phix(kj)))
|
||||
end do
|
||||
end do
|
||||
enddo
|
||||
end if
|
||||
return
|
||||
end
|
||||
202
Unpublished/XFEM/AbaqusUEL/UEL_TRANHTX.for
Normal file
202
Unpublished/XFEM/AbaqusUEL/UEL_TRANHTX.for
Normal file
|
|
@ -0,0 +1,202 @@
|
|||
c 1-D Moving Interface User Element - JGrogan 2012.
|
||||
c Subroutine UEXTERNALDB
|
||||
c Calculates interface velocity and position at the start of each increment
|
||||
c and passes it to UEL via common block. It requires a list of current nodal
|
||||
c coordinates, and 'T' and 'a' degrees of freedom.
|
||||
|
||||
subroutine uexternaldb(lop,lrestart,time,dtime,kstep,kinc)
|
||||
c
|
||||
include 'aba_param.inc'
|
||||
c
|
||||
real dpos, npos(6), ndof(6)
|
||||
common dpos,npos,ndof
|
||||
dimension time(2)
|
||||
c
|
||||
if (lop==0)then
|
||||
c initialise common blocks
|
||||
dpos=0.
|
||||
npos=0.
|
||||
tn=0.
|
||||
an=0.
|
||||
print *,'npos',npos,'extrn1',time
|
||||
print *,'ndof',ndof,'extrn1',time
|
||||
else
|
||||
print *,'npos',npos,'extrn',time
|
||||
print *,'ndof',ndof,'extrn',time
|
||||
endif
|
||||
return
|
||||
end
|
||||
c
|
||||
c Subroutine UEL
|
||||
c Calculates element mass and stiffness matrices and residual flux
|
||||
c vector for Abaqus NR Solver.
|
||||
|
||||
subroutine uel(rhs,amatrx,svars,energy,ndofel,nrhs,nsvars,props
|
||||
1 ,nprops,coords,mcrd,nnode,u,du,v,a,jtype,time,dtime,kstep,
|
||||
2 kinc,jelem,params,ndload,jdltyp,adlmag,predef,npredf,lflags
|
||||
3 ,mlvarx,ddlmag,mdload,pnewdt,jprops,njprop,period)
|
||||
c
|
||||
include 'aba_param.inc'
|
||||
c
|
||||
dimension rhs(mlvarx,*),amatrx(ndofel,ndofel),svars(nsvars),
|
||||
1 energy(8),props(*),coords(mcrd,nnode),
|
||||
2 u(ndofel),du(mlvarx,*),v(ndofel),a(ndofel),time(2),
|
||||
3 params(3),jdltyp(mdload,*),adlmag(mdload,*),
|
||||
4 ddlmag(mdload,*),predef(2,npredf,nnode),lflags(*),jprops(*)
|
||||
c
|
||||
dimension gpx(4),gwei(4),phi(4),phix(4),phic(4),gm(4),gm2(4,4)
|
||||
dimension theta(2)
|
||||
real dpos, npos(6), ndof(6)
|
||||
common dpos,npos,ndof
|
||||
c
|
||||
c level set calculation
|
||||
c store nodal positions and temperatures
|
||||
npos(jelem)=coords(1,1)
|
||||
npos(jelem+1)=coords(1,2)
|
||||
ndof(2*jelem-1)=u(1)
|
||||
ndof(2*jelem)=u(2)
|
||||
dpos1=0.2+0.4*time(1)
|
||||
c print *,'npos',npos,'uel',time
|
||||
c print *,'ndof',ndof,'uel',time
|
||||
c material property definition
|
||||
rho = 1.
|
||||
spec = 1.
|
||||
c penalty term
|
||||
beta=40.
|
||||
c initialization (nrhs=1)
|
||||
do k1=1,ndofel
|
||||
rhs(k1,nrhs)=0.
|
||||
do k2=1,ndofel
|
||||
amatrx(k2,k1)=0.
|
||||
enddo
|
||||
enddo
|
||||
if (lflags(3).eq.4) return
|
||||
c transient analysis
|
||||
if (lflags(1).eq.33) then
|
||||
c determine node level set params
|
||||
crdn1=coords(1,1)
|
||||
crdn2=coords(1,2)
|
||||
theta(1)=abs(crdn1-dpos1)*sign(1.,crdn1-dpos1)
|
||||
theta(2)=abs(crdn2-dpos1)*sign(1.,crdn2-dpos1)
|
||||
enr=2
|
||||
elen=abs(crdn2-crdn1)
|
||||
ajacob=elen/2.
|
||||
if (sign(1.,theta(1))/=sign(1.,theta(2)))then
|
||||
c enriched element
|
||||
enr=4
|
||||
point=(dpos1-crdn1)/ajacob-1.
|
||||
rlen1=abs(-point-1.)
|
||||
rlen2=abs(1.-point)
|
||||
rmid1=-1.+rlen1/2.
|
||||
rmid2=1.-rlen2/2.
|
||||
c Get int point locations and weights
|
||||
gpx(1)=-(rlen1/2.)/sqrt(3.)+rmid1
|
||||
gpx(2)=(rlen1/2.)/sqrt(3.)+rmid1
|
||||
gpx(3)=-(rlen2/2.)/sqrt(3.)+rmid2
|
||||
gpx(4)=(rlen2/2.)/sqrt(3.)+rmid2
|
||||
gwei(1)=(rlen1/2.)
|
||||
gwei(2)=(rlen1/2.)
|
||||
gwei(3)=(rlen2/2.)
|
||||
gwei(4)=(rlen2/2.)
|
||||
else
|
||||
c regular element
|
||||
gpx(1)=-1./sqrt(3.)
|
||||
gpx(2)=1./sqrt(3.)
|
||||
gwei(1)=1.
|
||||
gwei(2)=1.
|
||||
endif
|
||||
c assemble amatrx and rhs
|
||||
do k=1,enr
|
||||
c loop through gauss pts: i
|
||||
c=gpx(k)
|
||||
c get ip level set value: Oi
|
||||
c get shape functions and derivatives
|
||||
c Ni
|
||||
phi(1)=(1.-c)/2.
|
||||
phi(3)=(1.+c)/2.
|
||||
term=theta(1)*phi(1)+theta(2)*phi(3)
|
||||
if (term<0.)then
|
||||
cond=0.
|
||||
spec=0.1
|
||||
else
|
||||
cond=1.
|
||||
spec=1.
|
||||
endif
|
||||
if(enr==4)then
|
||||
phi(2)=phi(1)*(abs(term)-abs(theta(1)))
|
||||
phi(4)=phi(3)*(abs(term)-abs(theta(2)))
|
||||
else
|
||||
phi(2)=0.
|
||||
phi(4)=0.
|
||||
endif
|
||||
c dNdci
|
||||
phic(1)=-0.5
|
||||
phic(3)=0.5
|
||||
dterm=sign(1.,term)*(phic(1)*theta(1)+phic(3)*theta(2))
|
||||
if(enr==4)then
|
||||
phic(2)=phic(1)*(abs(term)-abs(theta(1)))
|
||||
1 +phi(1)*dterm
|
||||
phic(4)=phic(3)*(abs(term)-abs(theta(2)))
|
||||
1 +phi(3)*dterm
|
||||
else
|
||||
phic(2)=0.
|
||||
phic(4)=0.
|
||||
endif
|
||||
c dNdxi
|
||||
phix(1)=phic(1)*(1./ajacob)
|
||||
phix(2)=phic(2)*(1./ajacob)
|
||||
phix(3)=phic(3)*(1./ajacob)
|
||||
phix(4)=phic(4)*(1./ajacob)
|
||||
c interpolate temperatures Tbar to int point: i
|
||||
dtdx=u(1)*phix(1)+u(2)*phix(2)
|
||||
1 +u(3)*phix(3)+u(4)*phix(4)
|
||||
t=u(1)*phi(1)+u(2)*phi(2)
|
||||
1 +u(3)*phi(3)+u(4)*phi(4)
|
||||
told=(u(1)-du(1,nrhs))*phi(1)+(u(2)-du(2,nrhs))*phi(2)+
|
||||
1 (u(3)-du(3,nrhs))*phi(3)+(u(4)-du(4,nrhs))*phi(4)
|
||||
c other housekeeping
|
||||
dtdt=(t-told)/dtime
|
||||
we=gwei(k)*ajacob
|
||||
c Assemble Element Stiffness Matrix and Add to Global
|
||||
do ki=1,4
|
||||
c loop over nodes
|
||||
rhs(ki,nrhs)=rhs(ki,nrhs)-we*(phi(ki)*rho*spec*dtdt
|
||||
1 + cond*(phix(ki)*dtdx))
|
||||
do kj=1,4
|
||||
amatrx(ki,kj)=amatrx(ki,kj)+we*(phi(ki)*phi(kj)
|
||||
1 *rho*spec/dtime+cond*(phix(ki)*phix(kj)))
|
||||
end do
|
||||
end do
|
||||
enddo
|
||||
end if
|
||||
c if interface is in the element an penalty term is needed
|
||||
if(enr==4)then
|
||||
xi=point
|
||||
gm(1)=(1.-xi)/2.
|
||||
gm(3)=(1.+xi)/2.
|
||||
term=theta(1)*gm(1)+theta(2)*gm(3)
|
||||
gm(2)=gm(1)*(abs(term)-abs(theta(1)))
|
||||
gm(4)=gm(3)*(abs(term)-abs(theta(2)))
|
||||
term2=gm(1)*u(1)+gm(2)*u(2)+gm(3)*u(3)+gm(4)*u(4)
|
||||
diff=abs(term2-1.)
|
||||
c add penalty flux/force: BGtc
|
||||
targetT=1.
|
||||
do i=1,4
|
||||
rhs(i,nrhs)=rhs(i,nrhs)+beta*gm(i)*diff
|
||||
enddo
|
||||
c find GtG
|
||||
gm2=0.
|
||||
do i=1,4
|
||||
do j=1,4
|
||||
gm2(i,j)=gm(i)*gm(j)
|
||||
enddo
|
||||
enddo
|
||||
c add penalty stiffness
|
||||
do i=1,4
|
||||
do j=1,4
|
||||
amatrx(i,j)=amatrx(i,j)+beta*gm2(i,j)
|
||||
enddo
|
||||
enddo
|
||||
endif
|
||||
return
|
||||
end
|
||||
114
Unpublished/XFEM/AbaqusUEL/UEL_TRANHT_2d.for
Normal file
114
Unpublished/XFEM/AbaqusUEL/UEL_TRANHT_2d.for
Normal file
|
|
@ -0,0 +1,114 @@
|
|||
subroutine uel(rhs,amatrx,svars,energy,ndofel,nrhs,nsvars,props
|
||||
1 ,nprops,coords,mcrd,nnode,u,du,v,a,jtype,time,dtime,kstep,
|
||||
2 kinc,jelem,params,ndload,jdltyp,adlmag,predef,npredf,lflags
|
||||
3 ,mlvarx,ddlmag,mdload,pnewdt,jprops,njprop,period)
|
||||
c
|
||||
include 'aba_param.inc'
|
||||
c
|
||||
dimension rhs(mlvarx,*),amatrx(ndofel,ndofel),svars(nsvars),
|
||||
1 energy(8),props(*),coords(mcrd,nnode),
|
||||
2 u(ndofel),du(mlvarx,*),v(ndofel),a(ndofel),time(2),
|
||||
3 params(3),jdltyp(mdload,*),adlmag(mdload,*),
|
||||
4 ddlmag(mdload,*),predef(2,npredf,nnode),lflags(*),jprops(*)
|
||||
c
|
||||
dimension gx(4),hx(4),phi(4),phix(4),phiy(4),phig(4),phih(4)
|
||||
dimension rjac(2,2),rjaci(2,2)
|
||||
c
|
||||
c material property definition
|
||||
rho = 1.
|
||||
spec = 1.
|
||||
cond = 1.
|
||||
c initialization (nrhs=1)
|
||||
do k1=1,ndofel
|
||||
rhs(k1,nrhs)=0.
|
||||
do k2=1,ndofel
|
||||
amatrx(k2,k1)=0.
|
||||
enddo
|
||||
enddo
|
||||
if (lflags(3).eq.4) return
|
||||
c transient analysis
|
||||
if (lflags(1).eq.33) then
|
||||
c determine gauss point locations
|
||||
gpos=1./sqrt(3.)
|
||||
gx(1)=-gpos
|
||||
gx(2)=gpos
|
||||
gx(3)=gpos
|
||||
gx(4)=-gpos
|
||||
hx(1)=-gpos
|
||||
hx(2)=-gpos
|
||||
hx(3)=gpos
|
||||
hx(4)=gpos
|
||||
c assemble amatrx and rhs
|
||||
do k=1,4
|
||||
c loop through gauss pts
|
||||
g=gx(k)
|
||||
h=hx(k)
|
||||
c get shape functions and derivatives
|
||||
phi(1)=0.25*(1.-g)*(1.-h)
|
||||
phi(2)=0.25*(1.+g)*(1.-h)
|
||||
phi(3)=0.25*(1.+g)*(1.+h)
|
||||
phi(4)=0.25*(1.-g)*(1.+h)
|
||||
phig(1)=0.25*-(1.-h)
|
||||
phig(2)=0.25*(1.-h)
|
||||
phig(3)=0.25*(1.+h)
|
||||
phig(4)=0.25*-(1.+h)
|
||||
phih(1)=0.25*-(1.-g)
|
||||
phih(2)=0.25*-(1.+g)
|
||||
phih(3)=0.25*(1.+g)
|
||||
phih(4)=0.25*(1.-g)
|
||||
c get ip coords
|
||||
crdx=0.
|
||||
crdy=0.
|
||||
do k1=1,4
|
||||
crdx=crdx+phi(k1)*coords(1,k1)
|
||||
crdy=crdy+phi(k1)*coords(2,k1)
|
||||
end do
|
||||
c get jacobian
|
||||
rjac=0.
|
||||
do i=1,4
|
||||
rjac(1,1)=rjac(1,1)+phig(i)*coords(1,i)
|
||||
rjac(1,2)=rjac(1,2)+phig(i)*coords(2,i)
|
||||
rjac(2,1)=rjac(2,1)+phih(i)*coords(1,i)
|
||||
rjac(2,2)=rjac(2,2)+phih(i)*coords(2,i)
|
||||
enddo
|
||||
djac=rjac(1,1)*rjac(2,2)-rjac(1,2)*rjac(2,1)
|
||||
print *,djac
|
||||
rjaci(1,1) = rjac(2,2)/djac
|
||||
rjaci(2,2) = rjac(1,1)/djac
|
||||
rjaci(1,2) = -rjac(1,2)/djac
|
||||
rjaci(2,1) = -rjac(2,1)/djac
|
||||
c get b matrix
|
||||
phix(1)=rjaci(1,1)*phig(1)+rjaci(1,2)*phih(1)
|
||||
phiy(1)=rjaci(2,1)*phig(1)+rjaci(2,2)*phih(1)
|
||||
phix(2)=rjaci(1,1)*phig(2)+rjaci(1,2)*phih(2)
|
||||
phiy(2)=rjaci(2,1)*phig(2)+rjaci(2,2)*phih(2)
|
||||
phix(3)=rjaci(1,1)*phig(3)+rjaci(1,2)*phih(3)
|
||||
phiy(3)=rjaci(2,1)*phig(3)+rjaci(2,2)*phih(3)
|
||||
phix(4)=rjaci(1,1)*phig(4)+rjaci(1,2)*phih(4)
|
||||
phiy(4)=rjaci(2,1)*phig(4)+rjaci(2,2)*phih(4)
|
||||
c interpolate temperatures to int points
|
||||
dtdx=u(1)*phix(1)+u(2)*phix(2)
|
||||
1 +u(3)*phix(3)+u(4)*phix(4)
|
||||
dtdy=u(1)*phiy(1)+u(2)*phiy(2)
|
||||
1 +u(3)*phiy(3)+u(4)*phiy(4)
|
||||
t=u(1)*phi(1)+u(2)*phi(2)+u(3)*phi(3)+u(4)*phi(4)
|
||||
told=(u(1)-du(1,nrhs))*phi(1)+(u(2)-du(2,nrhs))*phi(2)+
|
||||
1 (u(3)-du(3,nrhs))*phi(3)+(u(4)-du(4,nrhs))*phi(4)
|
||||
c other housekeeping
|
||||
dtdt=(t-told)/dtime
|
||||
we=djac
|
||||
c Assemble Element Stiffness Matrix and Add to Global
|
||||
do ki=1,4
|
||||
c loop over nodes
|
||||
rhs(ki,nrhs)=rhs(ki,nrhs)-we*(phi(ki)*rho*spec*dtdt
|
||||
1 + cond*(phix(ki)*dtdx+phiy(ki)*dtdy))
|
||||
do kj=1,4
|
||||
amatrx(ki,kj)=amatrx(ki,kj)+we*(phi(ki)*phi(kj)
|
||||
1 *rho*spec/dtime+cond*(phix(ki)*phix(kj)+
|
||||
1 phiy(ki)*phiy(kj)))
|
||||
end do
|
||||
end do
|
||||
enddo
|
||||
end if
|
||||
return
|
||||
end
|
||||
198
Unpublished/XFEM/AbaqusUEL/htelem.for
Normal file
198
Unpublished/XFEM/AbaqusUEL/htelem.for
Normal file
|
|
@ -0,0 +1,198 @@
|
|||
SUBROUTINE UEL(RHS,AMATRX,SVARS,ENERGY,NDOFEL,NRHS,NSVARS,PROPS,
|
||||
1 NPROPS,COORDS,MCRD,NNODE,U,DU,V,A,JTYPE,TIME,DTIME,KSTEP,KINC,
|
||||
2 JELEM,PARAMS,NDLOAD,JDLTYP,ADLMAG,PREDEF,NPREDF,LFLAGS,
|
||||
3 MLVARX,DDLMAG,MDLOAD,PNEWDT,JPROPS,NJPROP,PERIOD)
|
||||
C
|
||||
INCLUDE 'aba_param.inc'
|
||||
C
|
||||
DIMENSION RHS(MLVARX,*),AMATRX(NDOFEL,NDOFEL),SVARS(NSVARS),
|
||||
1 ENERGY(8),PROPS(*),COORDS(MCRD,NNODE),
|
||||
2 U(NDOFEL),DU(MLVARX,*),V(NDOFEL),A(NDOFEL),TIME(2),
|
||||
3 PARAMS(3),JDLTYP(MDLOAD,*),ADLMAG(MDLOAD,*),
|
||||
4 DDLMAG(MDLOAD,*),PREDEF(2,NPREDF,NNODE),LFLAGS(*),JPROPS(*)
|
||||
C
|
||||
DIMENSION GPX(9),GPY(9),GWEI(9),PHI(8),PHIX(8),PHIY(8),PHIC(8),
|
||||
1 PHIE(8),IFACE(9),GWE(3),AR(3)
|
||||
C
|
||||
PARAMETER(ZERO=0.D0,TWOHUN=200.D0,FIVHUN=500.D0,CONDUC=204.D0)
|
||||
DATA IFACE/1,5,2,6,3,7,4,8,1/
|
||||
C
|
||||
C
|
||||
C MATERIAL PROPERTY DEFINITION
|
||||
C
|
||||
THICK = PROPS(1)
|
||||
RHO = PROPS(2)
|
||||
SPEC = PROPS(3)
|
||||
C
|
||||
C INITIALIZATION (NRHS=1)
|
||||
C
|
||||
DO 6 K1=1,NDOFEL
|
||||
RHS(K1,NRHS)=ZERO
|
||||
DO 4 K2=1,NDOFEL
|
||||
AMATRX(K2,K1)=ZERO
|
||||
4 CONTINUE
|
||||
6 CONTINUE
|
||||
C
|
||||
IF (LFLAGS(3).EQ.4) RETURN
|
||||
C
|
||||
C TRANSIENT ANALYSIS
|
||||
C
|
||||
IF (LFLAGS(1).EQ.33) THEN
|
||||
C
|
||||
C DETERMINE GAUSS POINT LOCATIONS
|
||||
C
|
||||
SUBROUTINE GSPT(GPX,GPY)
|
||||
INCLUDE 'aba_param.inc'
|
||||
DIMENSION AR(3),GPX(9),GPY(9)
|
||||
C
|
||||
PARAMETER(ZERO=0.D0,ONENEG=-1.D0,ONE=1.D0,SIX=6.D0,TEN=10.D0)
|
||||
C
|
||||
C GPX: X COORDINATE OF GAUSS PT
|
||||
C GPY: Y COORDINATE OF GAUSS PT
|
||||
C
|
||||
R=SQRT(SIX/TEN)
|
||||
AR(1)=-1.
|
||||
AR(2)=0.
|
||||
AR(3)=1.
|
||||
DO 10 I=1,3
|
||||
DO 10 J=1,3
|
||||
NUMGP=(I-1)*3+J
|
||||
GPX(NUMGP)=AR(I)*R
|
||||
GPY(NUMGP)=AR(J)*R
|
||||
10 CONTINUE
|
||||
RETURN
|
||||
END
|
||||
CALL GSPT(GPX,GPY)
|
||||
C
|
||||
C DETERMINE GAUSS WEIGHTS
|
||||
C
|
||||
CALL GSWT(GWEI,GWE)
|
||||
C
|
||||
C ASSEMBLE AMATRX AND RHS
|
||||
C
|
||||
DO 300 K=1,9
|
||||
C LOOP THROUGH GAUSS PTS
|
||||
C=GPX(K)
|
||||
E=GPY(K)
|
||||
CALL DER(C,E,GPX,GPY,GWEI,PHI,PHIX,PHIY,PHIC,PHIE
|
||||
1 ,DXDC,DXDE,DYDC,DYDE,AJACOB,COORDS,MCRD,NNODE)
|
||||
DTDX=ZERO
|
||||
DTDY=ZERO
|
||||
T =ZERO
|
||||
TOLD=ZERO
|
||||
DO I=1,8
|
||||
DTDX=U(I)*PHIX(I)+DTDX
|
||||
DTDY=U(I)*PHIY(I)+DTDY
|
||||
T =U(I)*PHI(I)+T
|
||||
TOLD=(U(I)-DU(I,NRHS))*PHI(I)+TOLD
|
||||
END DO
|
||||
C CHECK ON TEMPERATURE DEPENDENCE OF THERMAL CONDUCTIVITY
|
||||
COND=CONDUC
|
||||
DCDT=ZERO
|
||||
DTDT=(T-TOLD)/DTIME
|
||||
WE=GWEI(K)*AJACOB
|
||||
DO KI=1,8
|
||||
C LOOP OVER NODES
|
||||
RHS(KI,NRHS) = RHS(KI,NRHS) -
|
||||
1 WE*(PHI(KI)*RHO*SPEC*DTDT +
|
||||
2 COND*(PHIX(KI)*DTDX + PHIY(KI)*DTDY))
|
||||
|
||||
DO KJ=1,8
|
||||
AMATRX(KI,KJ)= AMATRX(KI,KJ) + WE*(PHI(KI)*PHI(KJ)*RHO*
|
||||
1 SPEC/DTIME + COND*(PHIX(KI)*PHIX(KJ) + PHIY(KI)*
|
||||
2 PHIY(KJ)) + DCDT*PHI(KJ)*(PHIX(KI)*DTDX +
|
||||
3 PHIY(KI)*DTDY))
|
||||
|
||||
END DO
|
||||
END DO
|
||||
300 CONTINUE
|
||||
C
|
||||
RETURN
|
||||
END
|
||||
C
|
||||
|
||||
C
|
||||
SUBROUTINE GSWT(GWEI,GWE)
|
||||
INCLUDE 'aba_param.inc'
|
||||
DIMENSION GWEI(9),GWE(3)
|
||||
C
|
||||
PARAMETER(FIVE=5.D0,EIGHT=8.D0,NINE=9.D0)
|
||||
C
|
||||
C GWEI : GAUSS WEIGHT
|
||||
C
|
||||
GWE(1)=FIVE/NINE
|
||||
GWE(2)=EIGHT/NINE
|
||||
GWE(3)=FIVE/NINE
|
||||
DO 10 I=1,3
|
||||
DO 10 J=1,3
|
||||
NUMGP=(I-1)*3+J
|
||||
GWEI(NUMGP)=GWE(I)*GWE(J)
|
||||
10 CONTINUE
|
||||
RETURN
|
||||
END
|
||||
C
|
||||
SUBROUTINE DER(C,E,GPX,GPY,GWEI,PHI,PHIX,PHIY,PHIC,PHIE,
|
||||
1 DXDC,DXDE,DYDC,DYDE,AJACOB,COORDS,MCRD,NNODE)
|
||||
INCLUDE 'aba_param.inc'
|
||||
DIMENSION PHI(8),PHIX(8),PHIY(8),PHIC(8),PHIE(8),
|
||||
1 COORDS(MCRD,NNODE)
|
||||
C
|
||||
PARAMETER(ZERO=0.D0,FOURTH=0.25D0,HALF=0.5D0,ONE=1.D0,TWO=2.D0)
|
||||
C
|
||||
C INTERPOLATION FUNCTIONS
|
||||
C
|
||||
PHI(1) = FOURTH*(ONE-C)*(ONE-E)*(-C-E-ONE)
|
||||
PHI(2) = FOURTH*(ONE+C)*(ONE-E)*(C-E-ONE)
|
||||
PHI(3) = FOURTH*(ONE+C)*(ONE+E)*(C+E-ONE)
|
||||
PHI(4) = FOURTH*(ONE-C)*(ONE+E)*(-C+E-ONE)
|
||||
PHI(5) = HALF*(ONE-C*C)*(ONE-E)
|
||||
PHI(6) = HALF*(ONE+C)*(ONE-E*E)
|
||||
PHI(7) = HALF*(ONE-C*C)*(ONE+E)
|
||||
PHI(8) = HALF*(ONE-C)*(ONE-E*E)
|
||||
C
|
||||
C DERIVATIVES WRT TO C
|
||||
C
|
||||
PHIC(1) = FOURTH*(ONE-E)*(TWO*C+E)
|
||||
PHIC(2) = FOURTH*(ONE-E)*(TWO*C-E)
|
||||
PHIC(3) = FOURTH*(ONE+E)*(TWO*C+E)
|
||||
PHIC(4) = FOURTH*(ONE+E)*(TWO*C-E)
|
||||
PHIC(5) = -C*(ONE-E)
|
||||
PHIC(6) = HALF*(ONE-E*E)
|
||||
PHIC(7) = -C*(ONE+E)
|
||||
PHIC(8) = -HALF*(ONE-E*E)
|
||||
C
|
||||
C DERIVATIVES WRT TO E
|
||||
C
|
||||
PHIE(1) = FOURTH*(ONE-C)*(TWO*E+C)
|
||||
PHIE(2) = FOURTH*(ONE+C)*(TWO*E-C)
|
||||
PHIE(3) = FOURTH*(ONE+C)*(TWO*E+C)
|
||||
PHIE(4) = FOURTH*(ONE-C)*(TWO*E-C)
|
||||
PHIE(5) = -HALF*(ONE-C*C)
|
||||
PHIE(6) = -E*(ONE+C)
|
||||
PHIE(7) = HALF*(ONE-C*C)
|
||||
PHIE(8) = -E*(ONE-C)
|
||||
|
||||
DXDC=ZERO
|
||||
DXDE=ZERO
|
||||
DYDC=ZERO
|
||||
DYDE=ZERO
|
||||
|
||||
DO 3 I=1,8
|
||||
DXDC=DXDC+COORDS(1,I)*PHIC(I)
|
||||
DXDE=DXDE+COORDS(1,I)*PHIE(I)
|
||||
DYDC=DYDC+COORDS(2,I)*PHIC(I)
|
||||
DYDE=DYDE+COORDS(2,I)*PHIE(I)
|
||||
3 CONTINUE
|
||||
C
|
||||
C CALCULATION OF JACOBIAN
|
||||
C
|
||||
AJACOB=(DXDC*DYDE-DXDE*DYDC)
|
||||
C
|
||||
C DERIVATIVES WRT TO X AND Y
|
||||
C
|
||||
DO 5 I=1,8
|
||||
PHIX(I)=(PHIC(I)*DYDE-PHIE(I)*DYDC)/AJACOB
|
||||
PHIY(I)=(PHIE(I)*DXDC-PHIC(I)*DXDE)/AJACOB
|
||||
5 CONTINUE
|
||||
RETURN
|
||||
END
|
||||
192
Unpublished/XFEM/AbaqusUEL/uel.for
Normal file
192
Unpublished/XFEM/AbaqusUEL/uel.for
Normal file
|
|
@ -0,0 +1,192 @@
|
|||
SUBROUTINE UEL(RHS,AMATRX,SVARS,ENERGY,NDOFEL,NRHS,NSVARS,
|
||||
1 PROPS,NPROPS,COORDS,MCRD,NNODE,U,DU,V,A,JTYPE,TIME,
|
||||
2 DTIME,KSTEP,KINC,JELEM,PARAMS,NDLOAD,JDLTYP,ADLMAG,
|
||||
3 PREDEF,NPREDF,LFLAGS,MLVARX,DDLMAG,MDLOAD,PNEWDT,
|
||||
4 JPROPS,NJPROP,PERIOD)
|
||||
C
|
||||
INCLUDE 'ABA_PARAM.INC'
|
||||
PARAMETER ( ZERO = 0.D0, HALF = 0.5D0, ONE = 1.D0 )
|
||||
C
|
||||
DIMENSION RHS(MLVARX,*),AMATRX(NDOFEL,NDOFEL),
|
||||
1 SVARS(NSVARS),ENERGY(8),PROPS(*),COORDS(MCRD,NNODE),
|
||||
2 U(NDOFEL),DU(MLVARX,*),V(NDOFEL),A(NDOFEL),TIME(2),
|
||||
3 PARAMS(3),JDLTYP(MDLOAD,*),ADLMAG(MDLOAD,*),
|
||||
4 DDLMAG(MDLOAD,*),PREDEF(2,NPREDF,NNODE),LFLAGS(*),
|
||||
5 JPROPS(*)
|
||||
DIMENSION SRESID(6)
|
||||
C
|
||||
C UEL SUBROUTINE FOR A HORIZONTAL TRUSS ELEMENT
|
||||
C
|
||||
C SRESID - stores the static residual at time t+dt
|
||||
C SVARS - In 1-6, contains the static residual at time t
|
||||
C upon entering the routine. SRESID is copied to
|
||||
C SVARS(1-6) after the dynamic residual has been
|
||||
C calculated.
|
||||
C - For half-increment residual calculations: In 7-12,
|
||||
C contains the static residual at the beginning
|
||||
C of the previous increment. SVARS(1-6) are copied
|
||||
C into SVARS(7-12) after the dynamic residual has
|
||||
C been calculated.
|
||||
C
|
||||
AREA = PROPS(1)
|
||||
E = PROPS(2)
|
||||
ANU = PROPS(3)
|
||||
RHO = PROPS(4)
|
||||
C
|
||||
ALEN = ABS(COORDS(1,2)-COORDS(1,1))
|
||||
AK = AREA*E/ALEN
|
||||
AM = HALF*AREA*RHO*ALEN
|
||||
C
|
||||
DO K1 = 1, NDOFEL
|
||||
SRESID(K1) = ZERO
|
||||
DO KRHS = 1, NRHS
|
||||
RHS(K1,KRHS) = ZERO
|
||||
END DO
|
||||
DO K2 = 1, NDOFEL
|
||||
AMATRX(K2,K1) = ZERO
|
||||
END DO
|
||||
END DO
|
||||
C
|
||||
IF (LFLAGS(3).EQ.1) THEN
|
||||
C Normal incrementation
|
||||
IF (LFLAGS(1).EQ.1 .OR. LFLAGS(1).EQ.2) THEN
|
||||
C *STATIC
|
||||
AMATRX(1,1) = AK
|
||||
AMATRX(4,4) = AK
|
||||
AMATRX(1,4) = -AK
|
||||
AMATRX(4,1) = -AK
|
||||
IF (LFLAGS(4).NE.0) THEN
|
||||
FORCE = AK*(U(4)-U(1))
|
||||
DFORCE = AK*(DU(4,1)-DU(1,1))
|
||||
SRESID(1) = -DFORCE
|
||||
SRESID(4) = DFORCE
|
||||
RHS(1,1) = RHS(1,1)-SRESID(1)
|
||||
RHS(4,1) = RHS(4,1)-SRESID(4)
|
||||
ENERGY(2) = HALF*FORCE*(DU(4,1)-DU(1,1))
|
||||
* + HALF*DFORCE*(U(4)-U(1))
|
||||
* + HALF*DFORCE*(DU(4,1)-DU(1,1))
|
||||
ELSE
|
||||
FORCE = AK*(U(4)-U(1))
|
||||
SRESID(1) = -FORCE
|
||||
SRESID(4) = FORCE
|
||||
RHS(1,1) = RHS(1,1)-SRESID(1)
|
||||
RHS(4,1) = RHS(4,1)-SRESID(4)
|
||||
DO KDLOAD = 1, NDLOAD
|
||||
IF (JDLTYP(KDLOAD,1).EQ.1001) THEN
|
||||
RHS(4,1) = RHS(4,1)+ADLMAG(KDLOAD,1)
|
||||
ENERGY(8) = ENERGY(8)+(ADLMAG(KDLOAD,1)
|
||||
* - HALF*DDLMAG(KDLOAD,1))*DU(4,1)
|
||||
IF (NRHS.EQ.2) THEN
|
||||
C Riks
|
||||
RHS(4,2) = RHS(4,2)+DDLMAG(KDLOAD,1)
|
||||
END IF
|
||||
END IF
|
||||
END DO
|
||||
ENERGY(2) = HALF*FORCE*(U(4)-U(1))
|
||||
END IF
|
||||
ELSE IF (LFLAGS(1).EQ.11 .OR. LFLAGS(1).EQ.12) THEN
|
||||
C *DYNAMIC
|
||||
ALPHA = PARAMS(1)
|
||||
BETA = PARAMS(2)
|
||||
GAMMA = PARAMS(3)
|
||||
C
|
||||
DADU = ONE/(BETA*DTIME**2)
|
||||
DVDU = GAMMA/(BETA*DTIME)
|
||||
C
|
||||
DO K1 = 1, NDOFEL
|
||||
AMATRX(K1,K1) = AM*DADU
|
||||
RHS(K1,1) = RHS(K1,1)-AM*A(K1)
|
||||
END DO
|
||||
AMATRX(1,1) = AMATRX(1,1)+(ONE+ALPHA)*AK
|
||||
AMATRX(4,4) = AMATRX(4,4)+(ONE+ALPHA)*AK
|
||||
AMATRX(1,4) = AMATRX(1,4)-(ONE+ALPHA)*AK
|
||||
AMATRX(4,1) = AMATRX(4,1)-(ONE+ALPHA)*AK
|
||||
FORCE = AK*(U(4)-U(1))
|
||||
SRESID(1) = -FORCE
|
||||
SRESID(4) = FORCE
|
||||
RHS(1,1) = RHS(1,1) -
|
||||
* ((ONE+ALPHA)*SRESID(1)-ALPHA*SVARS(1))
|
||||
RHS(4,1) = RHS(4,1) -
|
||||
* ((ONE+ALPHA)*SRESID(4)-ALPHA*SVARS(4))
|
||||
ENERGY(1) = ZERO
|
||||
DO K1 = 1, NDOFEL
|
||||
SVARS(K1+6) = SVARS(k1)
|
||||
SVARS(K1) = SRESID(K1)
|
||||
ENERGY(1) = ENERGY(1)+HALF*V(K1)*AM*V(K1)
|
||||
END DO
|
||||
ENERGY(2) = HALF*FORCE*(U(4)-U(1))
|
||||
END IF
|
||||
ELSE IF (LFLAGS(3).EQ.2) THEN
|
||||
C Stiffness matrix
|
||||
AMATRX(1,1) = AK
|
||||
AMATRX(4,4) = AK
|
||||
AMATRX(1,4) = -AK
|
||||
AMATRX(4,1) = -AK
|
||||
ELSE IF (LFLAGS(3).EQ.4) THEN
|
||||
C Mass matrix
|
||||
DO K1 = 1, NDOFEL
|
||||
AMATRX(K1,K1) = AM
|
||||
END DO
|
||||
ELSE IF (LFLAGS(3).EQ.5) THEN
|
||||
C Half-increment residual calculation
|
||||
ALPHA = PARAMS(1)
|
||||
FORCE = AK*(U(4)-U(1))
|
||||
SRESID(1) = -FORCE
|
||||
SRESID(4) = FORCE
|
||||
RHS(1,1) = RHS(1,1)-AM*A(1)-(ONE+ALPHA)*SRESID(1)
|
||||
* + HALF*ALPHA*( SVARS(1)+SVARS(7) )
|
||||
RHS(4,1) = RHS(4,1)-AM*A(4)-(ONE+ALPHA)*SRESID(4)
|
||||
* + HALF*ALPHA*( SVARS(4)+SVARS(10) )
|
||||
ELSE IF (LFLAGS(3).EQ.6) THEN
|
||||
C Initial acceleration calculation
|
||||
DO K1 = 1, NDOFEL
|
||||
AMATRX(K1,K1) = AM
|
||||
END DO
|
||||
FORCE = AK*(U(4)-U(1))
|
||||
SRESID(1) = -FORCE
|
||||
SRESID(4) = FORCE
|
||||
RHS(1,1) = RHS(1,1)-SRESID(1)
|
||||
RHS(4,1) = RHS(4,1)-SRESID(4)
|
||||
ENERGY(1) = ZERO
|
||||
DO K1 = 1, NDOFEL
|
||||
SVARS(K1) = SRESID(K1)
|
||||
ENERGY(1) = ENERGY(1)+HALF*V(K1)*AM*V(K1)
|
||||
END DO
|
||||
ENERGY(2) = HALF*FORCE*(U(4)-U(1))
|
||||
ELSE IF (LFLAGS(3).EQ.100) THEN
|
||||
C Output for perturbations
|
||||
IF (LFLAGS(1).EQ.1 .OR. LFLAGS(1).EQ.2) THEN
|
||||
C *STATIC
|
||||
FORCE = AK*(U(4)-U(1))
|
||||
DFORCE = AK*(DU(4,1)-DU(1,1))
|
||||
SRESID(1) = -DFORCE
|
||||
SRESID(4) = DFORCE
|
||||
RHS(1,1) = RHS(1,1)-SRESID(1)
|
||||
RHS(4,1) = RHS(4,1)-SRESID(4)
|
||||
ENERGY(2) = HALF*FORCE*(DU(4,1)-DU(1,1))
|
||||
* + HALF*DFORCE*(U(4)-U(1))
|
||||
* + HALF*DFORCE*(DU(4,1)-DU(1,1))
|
||||
DO KVAR = 1, NSVARS
|
||||
SVARS(KVAR) = ZERO
|
||||
END DO
|
||||
SVARS(1) = RHS(1,1)
|
||||
SVARS(4) = RHS(4,1)
|
||||
ELSE IF (LFLAGS(1).EQ.41) THEN
|
||||
C *FREQUENCY
|
||||
DO KRHS = 1, NRHS
|
||||
DFORCE = AK*(DU(4,KRHS)-DU(1,KRHS))
|
||||
SRESID(1) = -DFORCE
|
||||
SRESID(4) = DFORCE
|
||||
RHS(1,KRHS) = RHS(1,KRHS)-SRESID(1)
|
||||
RHS(4,KRHS) = RHS(4,KRHS)-SRESID(4)
|
||||
END DO
|
||||
DO KVAR = 1, NSVARS
|
||||
SVARS(KVAR) = ZERO
|
||||
END DO
|
||||
SVARS(1) = RHS(1,1)
|
||||
SVARS(4) = RHS(4,1)
|
||||
END IF
|
||||
END IF
|
||||
C
|
||||
RETURN
|
||||
END
|
||||
367
Unpublished/XFEM/AbaqusUEL/uelmat.for
Normal file
367
Unpublished/XFEM/AbaqusUEL/uelmat.for
Normal file
|
|
@ -0,0 +1,367 @@
|
|||
c***********************************************************
|
||||
subroutine uelmat(rhs,amatrx,svars,energy,ndofel,nrhs,
|
||||
1 nsvars,props,nprops,coords,mcrd,nnode,u,du,
|
||||
2 v,a,jtype,time,dtime,kstep,kinc,jelem,params,
|
||||
3 ndload,jdltyp,adlmag,predef,npredf,lflags,mlvarx,
|
||||
4 ddlmag,mdload,pnewdt,jprops,njpro,period,
|
||||
5 materiallib)
|
||||
c
|
||||
include 'aba_param.inc'
|
||||
C
|
||||
dimension rhs(mlvarx,*), amatrx(ndofel, ndofel), props(*),
|
||||
1 svars(*), energy(*), coords(mcrd, nnode), u(ndofel),
|
||||
2 du(mlvarx,*), v(ndofel), a(ndofel), time(2), params(*),
|
||||
3 jdltyp(mdload,*), adlmag(mdload,*), ddlmag(mdload,*),
|
||||
4 predef(2, npredf, nnode), lflags(*), jprops(*)
|
||||
parameter (zero=0.d0, dmone=-1.0d0, one=1.d0, four=4.0d0,
|
||||
1 fourth=0.25d0,gaussCoord=0.577350269d0)
|
||||
parameter (ndim=2, ndof=2, nshr=1,nnodemax=4,
|
||||
1 ntens=4, ninpt=4, nsvint=4)
|
||||
c
|
||||
c ndim ... number of spatial dimensions
|
||||
c ndof ... number of degrees of freedom per node
|
||||
c nshr ... number of shear stress component
|
||||
c ntens ... total number of stress tensor components
|
||||
c (=ndi+nshr)
|
||||
c ninpt ... number of integration points
|
||||
c nsvint... number of state variables per integration pt
|
||||
c (strain)
|
||||
c
|
||||
dimension stiff(ndof*nnodemax,ndof*nnodemax),
|
||||
1 force(ndof*nnodemax), shape(nnodemax), dshape(ndim,nnodemax),
|
||||
2 xjac(ndim,ndim),xjaci(ndim,ndim), bmat(nnodemax*ndim),
|
||||
3 statevLocal(nsvint),stress(ntens), ddsdde(ntens, ntens),
|
||||
4 stran(ntens), dstran(ntens), wght(ninpt)
|
||||
c
|
||||
dimension predef_loc(npredf),dpredef_loc(npredf),
|
||||
1 defGrad(3,3),utmp(3),xdu(3),stiff_p(3,3),force_p(3)
|
||||
dimension coord24(2,4),coords_ip(3)
|
||||
data coord24 /dmone, dmone,
|
||||
2 one, dmone,
|
||||
3 one, one,
|
||||
4 dmone, one/
|
||||
c
|
||||
data wght /one, one, one, one/
|
||||
c
|
||||
c*************************************************************
|
||||
c
|
||||
c U1 = first-order, plane strain, full integration
|
||||
c
|
||||
c State variables: each integration point has nsvint SDVs
|
||||
c
|
||||
c isvinc=(npt-1)*nsvint ... integration point counter
|
||||
c statev(1+isvinc ) ... strain
|
||||
c
|
||||
c*************************************************************
|
||||
if (lflags(3).eq.4) then
|
||||
do i=1, ndofel
|
||||
do j=1, ndofel
|
||||
amatrx(i,j) = zero
|
||||
end do
|
||||
amatrx(i,i) = one
|
||||
end do
|
||||
goto 999
|
||||
end if
|
||||
c
|
||||
c PRELIMINARIES
|
||||
c
|
||||
pnewdtLocal = pnewdt
|
||||
if(jtype .ne. 1) then
|
||||
write(7,*)'Incorrect element type'
|
||||
call xit
|
||||
endif
|
||||
if(nsvars .lt. ninpt*nsvint) then
|
||||
write(7,*)'Increase the number of SDVs to', ninpt*nsvint
|
||||
call xit
|
||||
endif
|
||||
thickness = 0.1d0
|
||||
c
|
||||
c INITIALIZE RHS AND LHS
|
||||
c
|
||||
do k1=1, ndof*nnode
|
||||
rhs(k1, 1)= zero
|
||||
do k2=1, ndof*nnode
|
||||
amatrx(k1, k2)= zero
|
||||
end do
|
||||
end do
|
||||
c
|
||||
c LOOP OVER INTEGRATION POINTS
|
||||
c
|
||||
do kintk = 1, ninpt
|
||||
c
|
||||
c EVALUATE SHAPE FUNCTIONS AND THEIR DERIVATIVES
|
||||
c
|
||||
c determine (g,h)
|
||||
c
|
||||
g = coord24(1,kintk)*gaussCoord
|
||||
h = coord24(2,kintk)*gaussCoord
|
||||
c
|
||||
c shape functions
|
||||
shape(1) = (one - g)*(one - h)/four;
|
||||
shape(2) = (one + g)*(one - h)/four;
|
||||
shape(3) = (one + g)*(one + h)/four;
|
||||
shape(4) = (one - g)*(one + h)/four;
|
||||
c
|
||||
c derivative d(Ni)/d(g)
|
||||
dshape(1,1) = -(one - h)/four;
|
||||
dshape(1,2) = (one - h)/four;
|
||||
dshape(1,3) = (one + h)/four;
|
||||
dshape(1,4) = -(one + h)/four;
|
||||
c
|
||||
c derivative d(Ni)/d(h)
|
||||
dshape(2,1) = -(one - g)/four;
|
||||
dshape(2,2) = -(one + g)/four;
|
||||
dshape(2,3) = (one + g)/four;
|
||||
dshape(2,4) = (one - g)/four;
|
||||
c
|
||||
c compute coordinates at the integration point
|
||||
c
|
||||
do k1=1, 3
|
||||
coords_ip(k1) = zero
|
||||
end do
|
||||
do k1=1,nnode
|
||||
do k2=1,mcrd
|
||||
coords_ip(k2)=coords_ip(k2)+shape(k1)*coords(k2,k1)
|
||||
end do
|
||||
end do
|
||||
c
|
||||
c INTERPOLATE FIELD VARIABLES
|
||||
c
|
||||
if(npredf.gt.0) then
|
||||
|
||||
do k1=1,npredf
|
||||
predef_loc(k1) = zero
|
||||
dpredef_loc(k1) = zero
|
||||
do k2=1,nnode
|
||||
predef_loc(k1) =
|
||||
& predef_loc(k1)+
|
||||
& (predef(1,k1,k2)-predef(2,k1,k2))*shape(k2)
|
||||
dpredef_loc(k1) =
|
||||
& dpredef_loc(k1)+predef(2,k1,k2)*shape(k2)
|
||||
end do
|
||||
end do
|
||||
end if
|
||||
c
|
||||
c FORM B-MATRIX
|
||||
c
|
||||
djac = one
|
||||
c
|
||||
do i = 1, ndim
|
||||
do j = 1, ndim
|
||||
xjac(i,j) = zero
|
||||
xjaci(i,j) = zero
|
||||
end do
|
||||
end do
|
||||
c
|
||||
do inod= 1, nnode
|
||||
do idim = 1, ndim
|
||||
do jdim = 1, ndim
|
||||
xjac(jdim,idim) = xjac(jdim,idim) +
|
||||
1 dshape(jdim,inod)*coords(idim,inod)
|
||||
end do
|
||||
end do
|
||||
end do
|
||||
djac = xjac(1,1)*xjac(2,2) - xjac(1,2)*xjac(2,1)
|
||||
if (djac .gt. zero) then
|
||||
! jacobian is positive - o.k.
|
||||
xjaci(1,1) = xjac(2,2)/djac
|
||||
xjaci(2,2) = xjac(1,1)/djac
|
||||
xjaci(1,2) = -xjac(1,2)/djac
|
||||
xjaci(2,1) = -xjac(2,1)/djac
|
||||
else
|
||||
! negative or zero jacobian
|
||||
write(7,*)'WARNING: element',jelem,'has neg.
|
||||
1 Jacobian'
|
||||
pnewdt = fourth
|
||||
endif
|
||||
|
||||
|
||||
if (pnewdt .lt. pnewdtLocal) pnewdtLocal = pnewdt
|
||||
c
|
||||
do i = 1, nnode*ndim
|
||||
bmat(i) = zero
|
||||
end do
|
||||
|
||||
do inod = 1, nnode
|
||||
do ider = 1, ndim
|
||||
do idim = 1, ndim
|
||||
irow = idim + (inod - 1)*ndim
|
||||
bmat(irow) = bmat(irow) +
|
||||
1 xjaci(idim,ider)*dshape(ider,inod)
|
||||
end do
|
||||
end do
|
||||
end do
|
||||
|
||||
c
|
||||
c CALCULATE INCREMENTAL STRAINS
|
||||
c
|
||||
do i = 1, ntens
|
||||
dstran(i) = zero
|
||||
end do
|
||||
!
|
||||
! set deformation gradient to Identity matrix
|
||||
do k1=1,3
|
||||
do k2=1,3
|
||||
defGrad(k1,k2) = zero
|
||||
end do
|
||||
defGrad(k1,k1) = one
|
||||
end do
|
||||
c
|
||||
c COMPUTE INCREMENTAL STRAINS
|
||||
c
|
||||
do nodi = 1, nnode
|
||||
|
||||
incr_row = (nodi - 1)*ndof
|
||||
|
||||
do i = 1, ndof
|
||||
xdu(i)= du(i + incr_row,1)
|
||||
utmp(i) = u(i + incr_row)
|
||||
end do
|
||||
|
||||
dNidx = bmat(1 + (nodi-1)*ndim)
|
||||
dNidy = bmat(2 + (nodi-1)*ndim)
|
||||
|
||||
dstran(1) = dstran(1) + dNidx*xdu(1)
|
||||
dstran(2) = dstran(2) + dNidy*xdu(2)
|
||||
dstran(4) = dstran(4) +
|
||||
1 dNidy*xdu(1) +
|
||||
2 dNidx*xdu(2)
|
||||
|
||||
c deformation gradient
|
||||
|
||||
defGrad(1,1) = defGrad(1,1) + dNidx*utmp(1)
|
||||
defGrad(1,2) = defGrad(1,2) + dNidy*utmp(1)
|
||||
defGrad(2,1) = defGrad(2,1) + dNidx*utmp(2)
|
||||
defGrad(2,2) = defGrad(2,2) + dNidy*utmp(2)
|
||||
end do
|
||||
|
||||
c
|
||||
c CALL CONSTITUTIVE ROUTINE
|
||||
c
|
||||
|
||||
isvinc= (kintk-1)*nsvint ! integration point increment
|
||||
c
|
||||
c prepare arrays for entry into material routines
|
||||
c
|
||||
do i = 1, nsvint
|
||||
statevLocal(i)=svars(i+isvinc)
|
||||
end do
|
||||
c
|
||||
c state variables
|
||||
c
|
||||
do k1=1,ntens
|
||||
stran(k1) = statevLocal(k1)
|
||||
stress(k1) = zero
|
||||
end do
|
||||
c
|
||||
do i=1, ntens
|
||||
do j=1, ntens
|
||||
ddsdde(i,j) = zero
|
||||
end do
|
||||
ddsdde(i,j) = one
|
||||
enddo
|
||||
c
|
||||
c compute characteristic element length
|
||||
c
|
||||
celent = sqrt(djac*dble(ninpt))
|
||||
dvmat = djac*thickness
|
||||
c
|
||||
dvdv0 = one
|
||||
call material_lib_mech(materiallib,stress,ddsdde,
|
||||
1 stran,dstran,kintk,dvdv0,dvmat,defGrad,
|
||||
2 predef_loc,dpredef_loc,npredf,celent,coords_ip)
|
||||
c
|
||||
do k1=1,ntens
|
||||
statevLocal(k1) = stran(k1) + dstran(k1)
|
||||
end do
|
||||
c
|
||||
isvinc= (kintk-1)*nsvint ! integration point increment
|
||||
c
|
||||
c update element state variables
|
||||
c
|
||||
do i = 1, nsvint
|
||||
svars(i+isvinc)=statevLocal(i)
|
||||
end do
|
||||
c
|
||||
c form stiffness matrix and internal force vector
|
||||
c
|
||||
dNjdx = zero
|
||||
dNjdy = zero
|
||||
do i = 1, ndof*nnode
|
||||
force(i) = zero
|
||||
do j = 1, ndof*nnode
|
||||
stiff(j,i) = zero
|
||||
end do
|
||||
end do
|
||||
|
||||
dvol= wght(kintk)*djac
|
||||
do nodj = 1, nnode
|
||||
|
||||
incr_col = (nodj - 1)*ndof
|
||||
|
||||
dNjdx = bmat(1+(nodj-1)*ndim)
|
||||
dNjdy = bmat(2+(nodj-1)*ndim)
|
||||
force_p(1) = dNjdx*stress(1) + dNjdy*stress(4)
|
||||
force_p(2) = dNjdy*stress(2) + dNjdx*stress(4)
|
||||
do jdof = 1, ndof
|
||||
|
||||
jcol = jdof + incr_col
|
||||
|
||||
force(jcol) = force(jcol) +
|
||||
& force_p(jdof)*dvol
|
||||
|
||||
end do
|
||||
|
||||
do nodi = 1, nnode
|
||||
|
||||
incr_row = (nodi -1)*ndof
|
||||
|
||||
dNidx = bmat(1+(nodi-1)*ndim)
|
||||
dNidy = bmat(2+(nodi-1)*ndim)
|
||||
stiff_p(1,1) = dNidx*ddsdde(1,1)*dNjdx
|
||||
& + dNidy*ddsdde(4,4)*dNjdy
|
||||
& + dNidx*ddsdde(1,4)*dNjdy
|
||||
& + dNidy*ddsdde(4,1)*dNjdx
|
||||
|
||||
stiff_p(1,2) = dNidx*ddsdde(1,2)*dNjdy
|
||||
& + dNidy*ddsdde(4,4)*dNjdx
|
||||
& + dNidx*ddsdde(1,4)*dNjdx
|
||||
& + dNidy*ddsdde(4,2)*dNjdy
|
||||
|
||||
stiff_p(2,1) = dNidy*ddsdde(2,1)*dNjdx
|
||||
& + dNidx*ddsdde(4,4)*dNjdy
|
||||
& + dNidy*ddsdde(2,4)*dNjdy
|
||||
& + dNidx*ddsdde(4,1)*dNjdx
|
||||
|
||||
stiff_p(2,2) = dNidy*ddsdde(2,2)*dNjdy
|
||||
& + dNidx*ddsdde(4,4)*dNjdx
|
||||
& + dNidy*ddsdde(2,4)*dNjdx
|
||||
& + dNidx*ddsdde(4,2)*dNjdy
|
||||
|
||||
do jdof = 1, ndof
|
||||
icol = jdof + incr_col
|
||||
do idof = 1, ndof
|
||||
irow = idof + incr_row
|
||||
stiff(irow,icol) = stiff(irow,icol) +
|
||||
& stiff_p(idof,jdof)*dvol
|
||||
end do
|
||||
end do
|
||||
end do
|
||||
end do
|
||||
|
||||
c
|
||||
c assemble rhs and lhs
|
||||
c
|
||||
do k1=1, ndof*nnode
|
||||
rhs(k1, 1) = rhs(k1, 1) - force(k1)
|
||||
do k2=1, ndof*nnode
|
||||
amatrx(k1, k2) = amatrx(k1, k2) + stiff(k1,k2)
|
||||
end do
|
||||
end do
|
||||
end do ! end loop on material integration points
|
||||
pnewdt = pnewdtLocal
|
||||
c
|
||||
999 continue
|
||||
c
|
||||
return
|
||||
end
|
||||
367
Unpublished/XFEM/AbaqusUEL/uelmat2.for
Normal file
367
Unpublished/XFEM/AbaqusUEL/uelmat2.for
Normal file
|
|
@ -0,0 +1,367 @@
|
|||
c***********************************************************
|
||||
subroutine uelmat(rhs,amatrx,svars,energy,ndofel,nrhs,
|
||||
1 nsvars,props,nprops,coords,mcrd,nnode,u,du,
|
||||
2 v,a,jtype,time,dtime,kstep,kinc,jelem,params,
|
||||
3 ndload,jdltyp,adlmag,predef,npredf,lflags,mlvarx,
|
||||
4 ddlmag,mdload,pnewdt,jprops,njpro,period,
|
||||
5 materiallib)
|
||||
c
|
||||
include 'aba_param.inc'
|
||||
C
|
||||
dimension rhs(mlvarx,*), amatrx(ndofel, ndofel), props(*),
|
||||
1 svars(*), energy(*), coords(mcrd, nnode), u(ndofel),
|
||||
2 du(mlvarx,*), v(ndofel), a(ndofel), time(2), params(*),
|
||||
3 jdltyp(mdload,*), adlmag(mdload,*), ddlmag(mdload,*),
|
||||
4 predef(2, npredf, nnode), lflags(*), jprops(*)
|
||||
parameter (zero=0.d0, dmone=-1.0d0, one=1.d0, four=4.0d0,
|
||||
1 fourth=0.25d0,gaussCoord=0.577350269d0)
|
||||
parameter (ndim=2, ndof=2, nshr=1,nnodemax=4,
|
||||
1 ntens=4, ninpt=4, nsvint=4)
|
||||
c
|
||||
c ndim ... number of spatial dimensions
|
||||
c ndof ... number of degrees of freedom per node
|
||||
c nshr ... number of shear stress component
|
||||
c ntens ... total number of stress tensor components
|
||||
c (=ndi+nshr)
|
||||
c ninpt ... number of integration points
|
||||
c nsvint... number of state variables per integration pt
|
||||
c (strain)
|
||||
c
|
||||
dimension stiff(ndof*nnodemax,ndof*nnodemax),
|
||||
1 force(ndof*nnodemax), shape(nnodemax), dshape(ndim,nnodemax),
|
||||
2 xjac(ndim,ndim),xjaci(ndim,ndim), bmat(nnodemax*ndim),
|
||||
3 statevLocal(nsvint),stress(ntens), ddsdde(ntens, ntens),
|
||||
4 stran(ntens), dstran(ntens), wght(ninpt)
|
||||
c
|
||||
dimension predef_loc(npredf),dpredef_loc(npredf),
|
||||
1 defGrad(3,3),utmp(3),xdu(3),stiff_p(3,3),force_p(3)
|
||||
dimension coord24(2,4),coords_ip(3)
|
||||
data coord24 /dmone, dmone,
|
||||
2 one, dmone,
|
||||
3 one, one,
|
||||
4 dmone, one/
|
||||
c
|
||||
data wght /one, one, one, one/
|
||||
c
|
||||
c*************************************************************
|
||||
c
|
||||
c U1 = first-order, plane strain, full integration
|
||||
c
|
||||
c State variables: each integration point has nsvint SDVs
|
||||
c
|
||||
c isvinc=(npt-1)*nsvint ... integration point counter
|
||||
c statev(1+isvinc ) ... strain
|
||||
c
|
||||
c*************************************************************
|
||||
if (lflags(3).eq.4) then
|
||||
do i=1, ndofel
|
||||
do j=1, ndofel
|
||||
amatrx(i,j) = zero
|
||||
end do
|
||||
amatrx(i,i) = one
|
||||
end do
|
||||
goto 999
|
||||
end if
|
||||
c
|
||||
c PRELIMINARIES
|
||||
c
|
||||
pnewdtLocal = pnewdt
|
||||
if(jtype .ne. 1) then
|
||||
write(7,*)'Incorrect element type'
|
||||
call xit
|
||||
endif
|
||||
if(nsvars .lt. ninpt*nsvint) then
|
||||
write(7,*)'Increase the number of SDVs to', ninpt*nsvint
|
||||
call xit
|
||||
endif
|
||||
thickness = 0.1d0
|
||||
c
|
||||
c INITIALIZE RHS AND LHS
|
||||
c
|
||||
do k1=1, ndof*nnode
|
||||
rhs(k1, 1)= zero
|
||||
do k2=1, ndof*nnode
|
||||
amatrx(k1, k2)= zero
|
||||
end do
|
||||
end do
|
||||
c
|
||||
c LOOP OVER INTEGRATION POINTS
|
||||
c
|
||||
do kintk = 1, ninpt
|
||||
c
|
||||
c EVALUATE SHAPE FUNCTIONS AND THEIR DERIVATIVES
|
||||
c
|
||||
c determine (g,h)
|
||||
c
|
||||
g = coord24(1,kintk)*gaussCoord
|
||||
h = coord24(2,kintk)*gaussCoord
|
||||
c
|
||||
c shape functions
|
||||
shape(1) = (one - g)*(one - h)/four;
|
||||
shape(2) = (one + g)*(one - h)/four;
|
||||
shape(3) = (one + g)*(one + h)/four;
|
||||
shape(4) = (one - g)*(one + h)/four;
|
||||
c
|
||||
c derivative d(Ni)/d(g)
|
||||
dshape(1,1) = -(one - h)/four;
|
||||
dshape(1,2) = (one - h)/four;
|
||||
dshape(1,3) = (one + h)/four;
|
||||
dshape(1,4) = -(one + h)/four;
|
||||
c
|
||||
c derivative d(Ni)/d(h)
|
||||
dshape(2,1) = -(one - g)/four;
|
||||
dshape(2,2) = -(one + g)/four;
|
||||
dshape(2,3) = (one + g)/four;
|
||||
dshape(2,4) = (one - g)/four;
|
||||
c
|
||||
c compute coordinates at the integration point
|
||||
c
|
||||
do k1=1, 3
|
||||
coords_ip(k1) = zero
|
||||
end do
|
||||
do k1=1,nnode
|
||||
do k2=1,mcrd
|
||||
coords_ip(k2)=coords_ip(k2)+shape(k1)*coords(k2,k1)
|
||||
end do
|
||||
end do
|
||||
c
|
||||
c INTERPOLATE FIELD VARIABLES
|
||||
c
|
||||
if(npredf.gt.0) then
|
||||
|
||||
do k1=1,npredf
|
||||
predef_loc(k1) = zero
|
||||
dpredef_loc(k1) = zero
|
||||
do k2=1,nnode
|
||||
predef_loc(k1) =
|
||||
& predef_loc(k1)+
|
||||
& (predef(1,k1,k2)-predef(2,k1,k2))*shape(k2)
|
||||
dpredef_loc(k1) =
|
||||
& dpredef_loc(k1)+predef(2,k1,k2)*shape(k2)
|
||||
end do
|
||||
end do
|
||||
end if
|
||||
c
|
||||
c FORM B-MATRIX
|
||||
c
|
||||
djac = one
|
||||
c
|
||||
do i = 1, ndim
|
||||
do j = 1, ndim
|
||||
xjac(i,j) = zero
|
||||
xjaci(i,j) = zero
|
||||
end do
|
||||
end do
|
||||
c
|
||||
do inod= 1, nnode
|
||||
do idim = 1, ndim
|
||||
do jdim = 1, ndim
|
||||
xjac(jdim,idim) = xjac(jdim,idim) +
|
||||
1 dshape(jdim,inod)*coords(idim,inod)
|
||||
end do
|
||||
end do
|
||||
end do
|
||||
djac = xjac(1,1)*xjac(2,2) - xjac(1,2)*xjac(2,1)
|
||||
if (djac .gt. zero) then
|
||||
! jacobian is positive - o.k.
|
||||
xjaci(1,1) = xjac(2,2)/djac
|
||||
xjaci(2,2) = xjac(1,1)/djac
|
||||
xjaci(1,2) = -xjac(1,2)/djac
|
||||
xjaci(2,1) = -xjac(2,1)/djac
|
||||
else
|
||||
! negative or zero jacobian
|
||||
write(7,*)'WARNING: element',jelem,'has neg.
|
||||
1 Jacobian'
|
||||
pnewdt = fourth
|
||||
endif
|
||||
|
||||
|
||||
if (pnewdt .lt. pnewdtLocal) pnewdtLocal = pnewdt
|
||||
c
|
||||
do i = 1, nnode*ndim
|
||||
bmat(i) = zero
|
||||
end do
|
||||
|
||||
do inod = 1, nnode
|
||||
do ider = 1, ndim
|
||||
do idim = 1, ndim
|
||||
irow = idim + (inod - 1)*ndim
|
||||
bmat(irow) = bmat(irow) +
|
||||
1 xjaci(idim,ider)*dshape(ider,inod)
|
||||
end do
|
||||
end do
|
||||
end do
|
||||
|
||||
c
|
||||
c CALCULATE INCREMENTAL STRAINS
|
||||
c
|
||||
do i = 1, ntens
|
||||
dstran(i) = zero
|
||||
end do
|
||||
!
|
||||
! set deformation gradient to Identity matrix
|
||||
do k1=1,3
|
||||
do k2=1,3
|
||||
defGrad(k1,k2) = zero
|
||||
end do
|
||||
defGrad(k1,k1) = one
|
||||
end do
|
||||
c
|
||||
c COMPUTE INCREMENTAL STRAINS
|
||||
c
|
||||
do nodi = 1, nnode
|
||||
|
||||
incr_row = (nodi - 1)*ndof
|
||||
|
||||
do i = 1, ndof
|
||||
xdu(i)= du(i + incr_row,1)
|
||||
utmp(i) = u(i + incr_row)
|
||||
end do
|
||||
|
||||
dNidx = bmat(1 + (nodi-1)*ndim)
|
||||
dNidy = bmat(2 + (nodi-1)*ndim)
|
||||
|
||||
dstran(1) = dstran(1) + dNidx*xdu(1)
|
||||
dstran(2) = dstran(2) + dNidy*xdu(2)
|
||||
dstran(4) = dstran(4) +
|
||||
1 dNidy*xdu(1) +
|
||||
2 dNidx*xdu(2)
|
||||
|
||||
c deformation gradient
|
||||
|
||||
defGrad(1,1) = defGrad(1,1) + dNidx*utmp(1)
|
||||
defGrad(1,2) = defGrad(1,2) + dNidy*utmp(1)
|
||||
defGrad(2,1) = defGrad(2,1) + dNidx*utmp(2)
|
||||
defGrad(2,2) = defGrad(2,2) + dNidy*utmp(2)
|
||||
end do
|
||||
|
||||
c
|
||||
c CALL CONSTITUTIVE ROUTINE
|
||||
c
|
||||
|
||||
isvinc= (kintk-1)*nsvint ! integration point increment
|
||||
c
|
||||
c prepare arrays for entry into material routines
|
||||
c
|
||||
do i = 1, nsvint
|
||||
statevLocal(i)=svars(i+isvinc)
|
||||
end do
|
||||
c
|
||||
c state variables
|
||||
c
|
||||
do k1=1,ntens
|
||||
stran(k1) = statevLocal(k1)
|
||||
stress(k1) = zero
|
||||
end do
|
||||
c
|
||||
do i=1, ntens
|
||||
do j=1, ntens
|
||||
ddsdde(i,j) = zero
|
||||
end do
|
||||
ddsdde(i,j) = one
|
||||
enddo
|
||||
c
|
||||
c compute characteristic element length
|
||||
c
|
||||
celent = sqrt(djac*dble(ninpt))
|
||||
dvmat = djac*thickness
|
||||
c
|
||||
dvdv0 = one
|
||||
call material_lib_mech(materiallib,stress,ddsdde,
|
||||
1 stran,dstran,kintk,dvdv0,dvmat,defGrad,
|
||||
2 predef_loc,dpredef_loc,npredf,celent,coords_ip)
|
||||
c
|
||||
do k1=1,ntens
|
||||
statevLocal(k1) = stran(k1) + dstran(k1)
|
||||
end do
|
||||
c
|
||||
isvinc= (kintk-1)*nsvint ! integration point increment
|
||||
c
|
||||
c update element state variables
|
||||
c
|
||||
do i = 1, nsvint
|
||||
svars(i+isvinc)=statevLocal(i)
|
||||
end do
|
||||
c
|
||||
c form stiffness matrix and internal force vector
|
||||
c
|
||||
dNjdx = zero
|
||||
dNjdy = zero
|
||||
do i = 1, ndof*nnode
|
||||
force(i) = zero
|
||||
do j = 1, ndof*nnode
|
||||
stiff(j,i) = zero
|
||||
end do
|
||||
end do
|
||||
|
||||
dvol= wght(kintk)*djac
|
||||
do nodj = 1, nnode
|
||||
|
||||
incr_col = (nodj - 1)*ndof
|
||||
|
||||
dNjdx = bmat(1+(nodj-1)*ndim)
|
||||
dNjdy = bmat(2+(nodj-1)*ndim)
|
||||
force_p(1) = dNjdx*stress(1) + dNjdy*stress(4)
|
||||
force_p(2) = dNjdy*stress(2) + dNjdx*stress(4)
|
||||
do jdof = 1, ndof
|
||||
|
||||
jcol = jdof + incr_col
|
||||
|
||||
force(jcol) = force(jcol) +
|
||||
& force_p(jdof)*dvol
|
||||
|
||||
end do
|
||||
|
||||
do nodi = 1, nnode
|
||||
|
||||
incr_row = (nodi -1)*ndof
|
||||
|
||||
dNidx = bmat(1+(nodi-1)*ndim)
|
||||
dNidy = bmat(2+(nodi-1)*ndim)
|
||||
stiff_p(1,1) = dNidx*ddsdde(1,1)*dNjdx
|
||||
& + dNidy*ddsdde(4,4)*dNjdy
|
||||
& + dNidx*ddsdde(1,4)*dNjdy
|
||||
& + dNidy*ddsdde(4,1)*dNjdx
|
||||
|
||||
stiff_p(1,2) = dNidx*ddsdde(1,2)*dNjdy
|
||||
& + dNidy*ddsdde(4,4)*dNjdx
|
||||
& + dNidx*ddsdde(1,4)*dNjdx
|
||||
& + dNidy*ddsdde(4,2)*dNjdy
|
||||
|
||||
stiff_p(2,1) = dNidy*ddsdde(2,1)*dNjdx
|
||||
& + dNidx*ddsdde(4,4)*dNjdy
|
||||
& + dNidy*ddsdde(2,4)*dNjdy
|
||||
& + dNidx*ddsdde(4,1)*dNjdx
|
||||
|
||||
stiff_p(2,2) = dNidy*ddsdde(2,2)*dNjdy
|
||||
& + dNidx*ddsdde(4,4)*dNjdx
|
||||
& + dNidy*ddsdde(2,4)*dNjdx
|
||||
& + dNidx*ddsdde(4,2)*dNjdy
|
||||
|
||||
do jdof = 1, ndof
|
||||
icol = jdof + incr_col
|
||||
do idof = 1, ndof
|
||||
irow = idof + incr_row
|
||||
stiff(irow,icol) = stiff(irow,icol) +
|
||||
& stiff_p(idof,jdof)*dvol
|
||||
end do
|
||||
end do
|
||||
end do
|
||||
end do
|
||||
|
||||
c
|
||||
c assemble rhs and lhs
|
||||
c
|
||||
do k1=1, ndof*nnode
|
||||
rhs(k1, 1) = rhs(k1, 1) - force(k1)
|
||||
do k2=1, ndof*nnode
|
||||
amatrx(k1, k2) = amatrx(k1, k2) + stiff(k1,k2)
|
||||
end do
|
||||
end do
|
||||
end do ! end loop on material integration points
|
||||
pnewdt = pnewdtLocal
|
||||
c
|
||||
999 continue
|
||||
c
|
||||
return
|
||||
end
|
||||
367
Unpublished/XFEM/AbaqusUEL/uelmatinp.for
Normal file
367
Unpublished/XFEM/AbaqusUEL/uelmatinp.for
Normal file
|
|
@ -0,0 +1,367 @@
|
|||
c***********************************************************
|
||||
subroutine uelmat(rhs,amatrx,svars,energy,ndofel,nrhs,
|
||||
1 nsvars,props,nprops,coords,mcrd,nnode,u,du,
|
||||
2 v,a,jtype,time,dtime,kstep,kinc,jelem,params,
|
||||
3 ndload,jdltyp,adlmag,predef,npredf,lflags,mlvarx,
|
||||
4 ddlmag,mdload,pnewdt,jprops,njpro,period,
|
||||
5 materiallib)
|
||||
c
|
||||
include 'aba_param.inc'
|
||||
C
|
||||
dimension rhs(mlvarx,*), amatrx(ndofel, ndofel), props(*),
|
||||
1 svars(*), energy(*), coords(mcrd, nnode), u(ndofel),
|
||||
2 du(mlvarx,*), v(ndofel), a(ndofel), time(2), params(*),
|
||||
3 jdltyp(mdload,*), adlmag(mdload,*), ddlmag(mdload,*),
|
||||
4 predef(2, npredf, nnode), lflags(*), jprops(*)
|
||||
parameter (zero=0.d0, dmone=-1.0d0, one=1.d0, four=4.0d0,
|
||||
1 fourth=0.25d0,gaussCoord=0.577350269d0)
|
||||
parameter (ndim=2, ndof=2, nshr=1,nnodemax=4,
|
||||
1 ntens=4, ninpt=4, nsvint=4)
|
||||
c
|
||||
c ndim ... number of spatial dimensions
|
||||
c ndof ... number of degrees of freedom per node
|
||||
c nshr ... number of shear stress component
|
||||
c ntens ... total number of stress tensor components
|
||||
c (=ndi+nshr)
|
||||
c ninpt ... number of integration points
|
||||
c nsvint... number of state variables per integration pt
|
||||
c (strain)
|
||||
c
|
||||
dimension stiff(ndof*nnodemax,ndof*nnodemax),
|
||||
1 force(ndof*nnodemax), shape(nnodemax), dshape(ndim,nnodemax),
|
||||
2 xjac(ndim,ndim),xjaci(ndim,ndim), bmat(nnodemax*ndim),
|
||||
3 statevLocal(nsvint),stress(ntens), ddsdde(ntens, ntens),
|
||||
4 stran(ntens), dstran(ntens), wght(ninpt)
|
||||
c
|
||||
dimension predef_loc(npredf),dpredef_loc(npredf),
|
||||
1 defGrad(3,3),utmp(3),xdu(3),stiff_p(3,3),force_p(3)
|
||||
dimension coord24(2,4),coords_ip(3)
|
||||
data coord24 /dmone, dmone,
|
||||
2 one, dmone,
|
||||
3 one, one,
|
||||
4 dmone, one/
|
||||
c
|
||||
data wght /one, one, one, one/
|
||||
c
|
||||
c*************************************************************
|
||||
c
|
||||
c U1 = first-order, plane strain, full integration
|
||||
c
|
||||
c State variables: each integration point has nsvint SDVs
|
||||
c
|
||||
c isvinc=(npt-1)*nsvint ... integration point counter
|
||||
c statev(1+isvinc ) ... strain
|
||||
c
|
||||
c*************************************************************
|
||||
if (lflags(3).eq.4) then
|
||||
do i=1, ndofel
|
||||
do j=1, ndofel
|
||||
amatrx(i,j) = zero
|
||||
end do
|
||||
amatrx(i,i) = one
|
||||
end do
|
||||
goto 999
|
||||
end if
|
||||
c
|
||||
c PRELIMINARIES
|
||||
c
|
||||
pnewdtLocal = pnewdt
|
||||
if(jtype .ne. 1) then
|
||||
write(7,*)'Incorrect element type'
|
||||
call xit
|
||||
endif
|
||||
if(nsvars .lt. ninpt*nsvint) then
|
||||
write(7,*)'Increase the number of SDVs to', ninpt*nsvint
|
||||
call xit
|
||||
endif
|
||||
thickness = 0.1d0
|
||||
c
|
||||
c INITIALIZE RHS AND LHS
|
||||
c
|
||||
do k1=1, ndof*nnode
|
||||
rhs(k1, 1)= zero
|
||||
do k2=1, ndof*nnode
|
||||
amatrx(k1, k2)= zero
|
||||
end do
|
||||
end do
|
||||
c
|
||||
c LOOP OVER INTEGRATION POINTS
|
||||
c
|
||||
do kintk = 1, ninpt
|
||||
c
|
||||
c EVALUATE SHAPE FUNCTIONS AND THEIR DERIVATIVES
|
||||
c
|
||||
c determine (g,h)
|
||||
c
|
||||
g = coord24(1,kintk)*gaussCoord
|
||||
h = coord24(2,kintk)*gaussCoord
|
||||
c
|
||||
c shape functions
|
||||
shape(1) = (one - g)*(one - h)/four;
|
||||
shape(2) = (one + g)*(one - h)/four;
|
||||
shape(3) = (one + g)*(one + h)/four;
|
||||
shape(4) = (one - g)*(one + h)/four;
|
||||
c
|
||||
c derivative d(Ni)/d(g)
|
||||
dshape(1,1) = -(one - h)/four;
|
||||
dshape(1,2) = (one - h)/four;
|
||||
dshape(1,3) = (one + h)/four;
|
||||
dshape(1,4) = -(one + h)/four;
|
||||
c
|
||||
c derivative d(Ni)/d(h)
|
||||
dshape(2,1) = -(one - g)/four;
|
||||
dshape(2,2) = -(one + g)/four;
|
||||
dshape(2,3) = (one + g)/four;
|
||||
dshape(2,4) = (one - g)/four;
|
||||
c
|
||||
c compute coordinates at the integration point
|
||||
c
|
||||
do k1=1, 3
|
||||
coords_ip(k1) = zero
|
||||
end do
|
||||
do k1=1,nnode
|
||||
do k2=1,mcrd
|
||||
coords_ip(k2)=coords_ip(k2)+shape(k1)*coords(k2,k1)
|
||||
end do
|
||||
end do
|
||||
c
|
||||
c INTERPOLATE FIELD VARIABLES
|
||||
c
|
||||
if(npredf.gt.0) then
|
||||
|
||||
do k1=1,npredf
|
||||
predef_loc(k1) = zero
|
||||
dpredef_loc(k1) = zero
|
||||
do k2=1,nnode
|
||||
predef_loc(k1) =
|
||||
& predef_loc(k1)+
|
||||
& (predef(1,k1,k2)-predef(2,k1,k2))*shape(k2)
|
||||
dpredef_loc(k1) =
|
||||
& dpredef_loc(k1)+predef(2,k1,k2)*shape(k2)
|
||||
end do
|
||||
end do
|
||||
end if
|
||||
c
|
||||
c FORM B-MATRIX
|
||||
c
|
||||
djac = one
|
||||
c
|
||||
do i = 1, ndim
|
||||
do j = 1, ndim
|
||||
xjac(i,j) = zero
|
||||
xjaci(i,j) = zero
|
||||
end do
|
||||
end do
|
||||
c
|
||||
do inod= 1, nnode
|
||||
do idim = 1, ndim
|
||||
do jdim = 1, ndim
|
||||
xjac(jdim,idim) = xjac(jdim,idim) +
|
||||
1 dshape(jdim,inod)*coords(idim,inod)
|
||||
end do
|
||||
end do
|
||||
end do
|
||||
djac = xjac(1,1)*xjac(2,2) - xjac(1,2)*xjac(2,1)
|
||||
if (djac .gt. zero) then
|
||||
! jacobian is positive - o.k.
|
||||
xjaci(1,1) = xjac(2,2)/djac
|
||||
xjaci(2,2) = xjac(1,1)/djac
|
||||
xjaci(1,2) = -xjac(1,2)/djac
|
||||
xjaci(2,1) = -xjac(2,1)/djac
|
||||
else
|
||||
! negative or zero jacobian
|
||||
write(7,*)'WARNING: element',jelem,'has neg.
|
||||
1 Jacobian'
|
||||
pnewdt = fourth
|
||||
endif
|
||||
|
||||
|
||||
if (pnewdt .lt. pnewdtLocal) pnewdtLocal = pnewdt
|
||||
c
|
||||
do i = 1, nnode*ndim
|
||||
bmat(i) = zero
|
||||
end do
|
||||
|
||||
do inod = 1, nnode
|
||||
do ider = 1, ndim
|
||||
do idim = 1, ndim
|
||||
irow = idim + (inod - 1)*ndim
|
||||
bmat(irow) = bmat(irow) +
|
||||
1 xjaci(idim,ider)*dshape(ider,inod)
|
||||
end do
|
||||
end do
|
||||
end do
|
||||
|
||||
c
|
||||
c CALCULATE INCREMENTAL STRAINS
|
||||
c
|
||||
do i = 1, ntens
|
||||
dstran(i) = zero
|
||||
end do
|
||||
!
|
||||
! set deformation gradient to Identity matrix
|
||||
do k1=1,3
|
||||
do k2=1,3
|
||||
defGrad(k1,k2) = zero
|
||||
end do
|
||||
defGrad(k1,k1) = one
|
||||
end do
|
||||
c
|
||||
c COMPUTE INCREMENTAL STRAINS
|
||||
c
|
||||
do nodi = 1, nnode
|
||||
|
||||
incr_row = (nodi - 1)*ndof
|
||||
|
||||
do i = 1, ndof
|
||||
xdu(i)= du(i + incr_row,1)
|
||||
utmp(i) = u(i + incr_row)
|
||||
end do
|
||||
|
||||
dNidx = bmat(1 + (nodi-1)*ndim)
|
||||
dNidy = bmat(2 + (nodi-1)*ndim)
|
||||
|
||||
dstran(1) = dstran(1) + dNidx*xdu(1)
|
||||
dstran(2) = dstran(2) + dNidy*xdu(2)
|
||||
dstran(4) = dstran(4) +
|
||||
1 dNidy*xdu(1) +
|
||||
2 dNidx*xdu(2)
|
||||
|
||||
c deformation gradient
|
||||
|
||||
defGrad(1,1) = defGrad(1,1) + dNidx*utmp(1)
|
||||
defGrad(1,2) = defGrad(1,2) + dNidy*utmp(1)
|
||||
defGrad(2,1) = defGrad(2,1) + dNidx*utmp(2)
|
||||
defGrad(2,2) = defGrad(2,2) + dNidy*utmp(2)
|
||||
end do
|
||||
|
||||
c
|
||||
c CALL CONSTITUTIVE ROUTINE
|
||||
c
|
||||
|
||||
isvinc= (kintk-1)*nsvint ! integration point increment
|
||||
c
|
||||
c prepare arrays for entry into material routines
|
||||
c
|
||||
do i = 1, nsvint
|
||||
statevLocal(i)=svars(i+isvinc)
|
||||
end do
|
||||
c
|
||||
c state variables
|
||||
c
|
||||
do k1=1,ntens
|
||||
stran(k1) = statevLocal(k1)
|
||||
stress(k1) = zero
|
||||
end do
|
||||
c
|
||||
do i=1, ntens
|
||||
do j=1, ntens
|
||||
ddsdde(i,j) = zero
|
||||
end do
|
||||
ddsdde(i,j) = one
|
||||
enddo
|
||||
c
|
||||
c compute characteristic element length
|
||||
c
|
||||
celent = sqrt(djac*dble(ninpt))
|
||||
dvmat = djac*thickness
|
||||
c
|
||||
dvdv0 = one
|
||||
call material_lib_mech(materiallib,stress,ddsdde,
|
||||
1 stran,dstran,kintk,dvdv0,dvmat,defGrad,
|
||||
2 predef_loc,dpredef_loc,npredf,celent,coords_ip)
|
||||
c
|
||||
do k1=1,ntens
|
||||
statevLocal(k1) = stran(k1) + dstran(k1)
|
||||
end do
|
||||
c
|
||||
isvinc= (kintk-1)*nsvint ! integration point increment
|
||||
c
|
||||
c update element state variables
|
||||
c
|
||||
do i = 1, nsvint
|
||||
svars(i+isvinc)=statevLocal(i)
|
||||
end do
|
||||
c
|
||||
c form stiffness matrix and internal force vector
|
||||
c
|
||||
dNjdx = zero
|
||||
dNjdy = zero
|
||||
do i = 1, ndof*nnode
|
||||
force(i) = zero
|
||||
do j = 1, ndof*nnode
|
||||
stiff(j,i) = zero
|
||||
end do
|
||||
end do
|
||||
|
||||
dvol= wght(kintk)*djac
|
||||
do nodj = 1, nnode
|
||||
|
||||
incr_col = (nodj - 1)*ndof
|
||||
|
||||
dNjdx = bmat(1+(nodj-1)*ndim)
|
||||
dNjdy = bmat(2+(nodj-1)*ndim)
|
||||
force_p(1) = dNjdx*stress(1) + dNjdy*stress(4)
|
||||
force_p(2) = dNjdy*stress(2) + dNjdx*stress(4)
|
||||
do jdof = 1, ndof
|
||||
|
||||
jcol = jdof + incr_col
|
||||
|
||||
force(jcol) = force(jcol) +
|
||||
& force_p(jdof)*dvol
|
||||
|
||||
end do
|
||||
|
||||
do nodi = 1, nnode
|
||||
|
||||
incr_row = (nodi -1)*ndof
|
||||
|
||||
dNidx = bmat(1+(nodi-1)*ndim)
|
||||
dNidy = bmat(2+(nodi-1)*ndim)
|
||||
stiff_p(1,1) = dNidx*ddsdde(1,1)*dNjdx
|
||||
& + dNidy*ddsdde(4,4)*dNjdy
|
||||
& + dNidx*ddsdde(1,4)*dNjdy
|
||||
& + dNidy*ddsdde(4,1)*dNjdx
|
||||
|
||||
stiff_p(1,2) = dNidx*ddsdde(1,2)*dNjdy
|
||||
& + dNidy*ddsdde(4,4)*dNjdx
|
||||
& + dNidx*ddsdde(1,4)*dNjdx
|
||||
& + dNidy*ddsdde(4,2)*dNjdy
|
||||
|
||||
stiff_p(2,1) = dNidy*ddsdde(2,1)*dNjdx
|
||||
& + dNidx*ddsdde(4,4)*dNjdy
|
||||
& + dNidy*ddsdde(2,4)*dNjdy
|
||||
& + dNidx*ddsdde(4,1)*dNjdx
|
||||
|
||||
stiff_p(2,2) = dNidy*ddsdde(2,2)*dNjdy
|
||||
& + dNidx*ddsdde(4,4)*dNjdx
|
||||
& + dNidy*ddsdde(2,4)*dNjdx
|
||||
& + dNidx*ddsdde(4,2)*dNjdy
|
||||
|
||||
do jdof = 1, ndof
|
||||
icol = jdof + incr_col
|
||||
do idof = 1, ndof
|
||||
irow = idof + incr_row
|
||||
stiff(irow,icol) = stiff(irow,icol) +
|
||||
& stiff_p(idof,jdof)*dvol
|
||||
end do
|
||||
end do
|
||||
end do
|
||||
end do
|
||||
|
||||
c
|
||||
c assemble rhs and lhs
|
||||
c
|
||||
do k1=1, ndof*nnode
|
||||
rhs(k1, 1) = rhs(k1, 1) - force(k1)
|
||||
do k2=1, ndof*nnode
|
||||
amatrx(k1, k2) = amatrx(k1, k2) + stiff(k1,k2)
|
||||
end do
|
||||
end do
|
||||
end do ! end loop on material integration points
|
||||
pnewdt = pnewdtLocal
|
||||
c
|
||||
999 continue
|
||||
c
|
||||
return
|
||||
end
|
||||
62
Unpublished/XFEM/AbaqusUEL/uelmatinp.inp
Normal file
62
Unpublished/XFEM/AbaqusUEL/uelmatinp.inp
Normal file
|
|
@ -0,0 +1,62 @@
|
|||
*HEADING
|
||||
Test for passing abaqus material to UELMAT: transient heat transfer
|
||||
*RESTART,WRITE,NUMBER INTERVAL=10
|
||||
*PREPRINT,MODEL=YES
|
||||
*PART,NAME=part1
|
||||
*NODE,NSET=NALL
|
||||
1,0,0,0
|
||||
2,1,0,0
|
||||
3,0,1,0
|
||||
4,1,1,0
|
||||
5,0,2,0
|
||||
6,1,2,0
|
||||
*NSET,NSET=Left
|
||||
1,3,5
|
||||
*NSET,NSET=Right
|
||||
2,4,6
|
||||
*USER ELEMENT, TYPE=U1, NODES=4, COORDINATES=2,
|
||||
INTEGRATION=4,TENSOR=TWOD
|
||||
11,
|
||||
*ELEMENT,TYPE=U1,ELSET=SOLID
|
||||
1, 1,2,4,3
|
||||
2, 3,4,6,5
|
||||
*END PART
|
||||
*ASSEMBLY,NAME=A1
|
||||
*INSTANCE,NAME=I1,PART=PART1
|
||||
*END INSTANCE
|
||||
*Nset, nset=Set-6, instance=I1
|
||||
1,3,5
|
||||
*Nset, nset=Set-7, instance=I1
|
||||
2,4,6
|
||||
*END ASSEMBLY
|
||||
*UEL PROPERTY, ELSET=I1.SOLID, MATERIAL=MAT_THERM
|
||||
**************************************
|
||||
***************************************
|
||||
*MATERIAL,NAME=MAT_THERM
|
||||
*CONDUCTIVITY
|
||||
1.0,
|
||||
*SPECIFIC HEAT
|
||||
1.,
|
||||
*DENSITY
|
||||
1.,
|
||||
*Initial Conditions, type=TEMPERATURE
|
||||
Set-6, 1.,0.
|
||||
*Initial Conditions, type=TEMPERATURE
|
||||
Set-7, 0.,0.
|
||||
*STEP
|
||||
*HEAT TRANSFER, DELTMX=1.
|
||||
0.1,1.0,,0.1
|
||||
**
|
||||
*BOUNDARY
|
||||
Set-6,11,11,1.
|
||||
*OUTPUT,FIELD,freq=1
|
||||
*ELEMENT OUTPUT,ELSET=I1.SOLID
|
||||
HFL,
|
||||
*NODE OUTPUT,NSET=I1.NALL
|
||||
NT,
|
||||
*OUTPUT,HISTORY
|
||||
*ELEMENT OUTPUT,ELSET=I1.SOLID
|
||||
HFL,
|
||||
*NODE OUTPUT,NSET=I1.NALL
|
||||
NT11,
|
||||
*END STEP
|
||||
53
Unpublished/XFEM/AbaqusUEL/umeshbak.for
Normal file
53
Unpublished/XFEM/AbaqusUEL/umeshbak.for
Normal file
|
|
@ -0,0 +1,53 @@
|
|||
C USER INPUT FOR ADAPTIVE MESH CONSTRAINT
|
||||
C
|
||||
SUBROUTINE UMESHMOTION(UREF,ULOCAL,NODE,NNDOF,
|
||||
$ LNODETYPE,ALOCAL,NDIM,TIME,DTIME,PNEWDT,
|
||||
$ KSTEP,KINC,KMESHSWEEP,JMATYP,JGVBLOCK,LSMOOTH)
|
||||
C
|
||||
include 'ABA_PARAM.INC'
|
||||
C
|
||||
C USER DEFINED DIMENSION STATEMENTS
|
||||
C
|
||||
CHARACTER*80 PARTNAME
|
||||
DIMENSION ARRAY(1000),JPOS(15),HFARRAY(1000)
|
||||
DIMENSION ULOCAL(*),UGLOBAL(NDIM),TLOCAL(NDIM)
|
||||
DIMENSION JGVBLOCK(*),JMATYP(*)
|
||||
DIMENSION NODELIST(100),JELEMLIST(10),JELEMTYPE(10)
|
||||
DIMENSION ALOCAL(NDIM,*)
|
||||
DIMENSION UTEMP(2)
|
||||
C
|
||||
C The dimensions of the variables ARRAY and JARRAY
|
||||
C must be set equal to or greater than 15
|
||||
C
|
||||
CALL GETPARTINFO(NODE,0,PARTNAME,LOCNUM,JRCD)
|
||||
CALL GETVRN(LOCNUM,'COORD',ARRAY,JRCD,JGVBLOCK,LTRN)
|
||||
NELEMS=10
|
||||
CALL GETNODETOELEMCONN(NODE, NELEMS, JELEMLIST, JELEMTYPE,
|
||||
$ JRCD, JGVBLOCK)
|
||||
CALL GETVRMAVGATNODE(NODE,1,'HFL',HFARRAY,JRCD,JELEMLIST,
|
||||
$ NELEMS,JMATYP,JGVBLOCK)
|
||||
C PRINT *,'****'
|
||||
C PRINT *, HFARRAY(1),HFARRAY(2),HFARRAY(3),HFARRAY(4)
|
||||
C PRINT *,NODE,TIME
|
||||
FluxX=HFARRAY(2)
|
||||
FluxY=HFARRAY(3)
|
||||
FluxZ=HFARRAY(4)
|
||||
if(abs(FluxX)<0.001)FluxX=0.
|
||||
if(abs(FluxY)<0.001)FluxY=0.
|
||||
if(abs(FluxZ)<0.001)FluxZ=0.
|
||||
UGLOBAL(1) = -2.*FluxX
|
||||
UGLOBAL(2) = -2.*FluxY
|
||||
UGLOBAL(3) = 0.
|
||||
DO I=1,NDIM
|
||||
TLOCAL(I)=0.
|
||||
DO J=1,NDIM
|
||||
TLOCAL(I)=TLOCAL(I)+UGLOBAL(J)*ALOCAL(J,I)
|
||||
ENDDO
|
||||
ENDDO
|
||||
DO I=1,NDIM
|
||||
ULOCAL(I)=TLOCAL(I)
|
||||
ENDDO
|
||||
lsmooth=1
|
||||
C
|
||||
RETURN
|
||||
END
|
||||
27
Unpublished/XFEM/AbaqusUEL/usfdld.f
Normal file
27
Unpublished/XFEM/AbaqusUEL/usfdld.f
Normal file
|
|
@ -0,0 +1,27 @@
|
|||
c J. Grogan, 2012
|
||||
c -------------------------------------------------------------------
|
||||
SUBROUTINE USDFLD(FIELD,STATEV,PNEWDT,DIRECT,T,CELENT,
|
||||
1 TIME,DTIME,CMNAME,ORNAME,NFIELD,NSTATV,NOEL,NPT,LAYER,
|
||||
2 KSPT,KSTEP,KINC,NDI,NSHR,COORD,JMAC,JMATYP,MATLAYO,
|
||||
3 LACCFLA)
|
||||
C
|
||||
INCLUDE 'ABA_PARAM.INC'
|
||||
C
|
||||
CHARACTER*80 CMNAME,ORNAME
|
||||
CHARACTER*3 FLGRAY(15)
|
||||
DIMENSION FIELD(NFIELD),STATEV(NSTATV),DIRECT(3,3),
|
||||
1 T(3,3),TIME(2)
|
||||
DIMENSION ARRAY(15),JARRAY(15),JMAC(*),JMATYP(*),
|
||||
1 COORD(*)
|
||||
c -------------------------------------------------------------------
|
||||
field(1)=0.
|
||||
return
|
||||
end subroutine
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
220
Unpublished/XFEM/AbaqusUEL/usfdld.for
Normal file
220
Unpublished/XFEM/AbaqusUEL/usfdld.for
Normal file
|
|
@ -0,0 +1,220 @@
|
|||
c J. Grogan, 2012
|
||||
c -------------------------------------------------------------------
|
||||
SUBROUTINE USDFLD(FIELD,STATEV,PNEWDT,DIRECT,T,CELENT,
|
||||
1 TIME,DTIME,CMNAME,ORNAME,NFIELD,NSTATV,NOEL,NPT,LAYER,
|
||||
2 KSPT,KSTEP,KINC,NDI,NSHR,COORD,JMAC,JMATYP,MATLAYO,
|
||||
3 LACCFLA)
|
||||
C
|
||||
INCLUDE 'ABA_PARAM.INC'
|
||||
C
|
||||
CHARACTER*80 CMNAME,ORNAME
|
||||
CHARACTER*3 FLGRAY(15)
|
||||
DIMENSION FIELD(NFIELD),STATEV(NSTATV),DIRECT(3,3),
|
||||
1 T(3,3),TIME(2)
|
||||
DIMENSION ARRAY(15),JARRAY(15),JMAC(*),JMATYP(*),
|
||||
1 COORD(*)
|
||||
c -------------------------------------------------------------------
|
||||
field(1)=0.
|
||||
print *, coord(1),time(1),dtime,T,'****'
|
||||
return
|
||||
end subroutine
|
||||
SUBROUTINE UEL(RHS,AMATRX,SVARS,ENERGY,NDOFEL,NRHS,NSVARS,
|
||||
1 PROPS,NPROPS,COORDS,MCRD,NNODE,U,DU,V,A,JTYPE,TIME,
|
||||
2 DTIME,KSTEP,KINC,JELEM,PARAMS,NDLOAD,JDLTYP,ADLMAG,
|
||||
3 PREDEF,NPREDF,LFLAGS,MLVARX,DDLMAG,MDLOAD,PNEWDT,
|
||||
4 JPROPS,NJPROP,PERIOD)
|
||||
C
|
||||
INCLUDE 'ABA_PARAM.INC'
|
||||
PARAMETER ( ZERO = 0.D0, HALF = 0.5D0, ONE = 1.D0 )
|
||||
C
|
||||
DIMENSION RHS(MLVARX,*),AMATRX(NDOFEL,NDOFEL),
|
||||
1 SVARS(NSVARS),ENERGY(8),PROPS(*),COORDS(MCRD,NNODE),
|
||||
2 U(NDOFEL),DU(MLVARX,*),V(NDOFEL),A(NDOFEL),TIME(2),
|
||||
3 PARAMS(3),JDLTYP(MDLOAD,*),ADLMAG(MDLOAD,*),
|
||||
4 DDLMAG(MDLOAD,*),PREDEF(2,NPREDF,NNODE),LFLAGS(*),
|
||||
5 JPROPS(*)
|
||||
DIMENSION SRESID(6)
|
||||
C
|
||||
C UEL SUBROUTINE FOR A HORIZONTAL TRUSS ELEMENT
|
||||
C
|
||||
C SRESID - stores the static residual at time t+dt
|
||||
C SVARS - In 1-6, contains the static residual at time t
|
||||
C upon entering the routine. SRESID is copied to
|
||||
C SVARS(1-6) after the dynamic residual has been
|
||||
C calculated.
|
||||
C - For half-increment residual calculations: In 7-12,
|
||||
C contains the static residual at the beginning
|
||||
C of the previous increment. SVARS(1-6) are copied
|
||||
C into SVARS(7-12) after the dynamic residual has
|
||||
C been calculated.
|
||||
C
|
||||
AREA = PROPS(1)
|
||||
E = PROPS(2)
|
||||
ANU = PROPS(3)
|
||||
RHO = PROPS(4)
|
||||
C
|
||||
ALEN = ABS(COORDS(1,2)-COORDS(1,1))
|
||||
AK = AREA*E/ALEN
|
||||
AM = HALF*AREA*RHO*ALEN
|
||||
C
|
||||
DO K1 = 1, NDOFEL
|
||||
SRESID(K1) = ZERO
|
||||
DO KRHS = 1, NRHS
|
||||
RHS(K1,KRHS) = ZERO
|
||||
END DO
|
||||
DO K2 = 1, NDOFEL
|
||||
AMATRX(K2,K1) = ZERO
|
||||
END DO
|
||||
END DO
|
||||
C
|
||||
IF (LFLAGS(3).EQ.1) THEN
|
||||
C Normal incrementation
|
||||
IF (LFLAGS(1).EQ.1 .OR. LFLAGS(1).EQ.2) THEN
|
||||
C *STATIC
|
||||
AMATRX(1,1) = AK
|
||||
AMATRX(4,4) = AK
|
||||
AMATRX(1,4) = -AK
|
||||
AMATRX(4,1) = -AK
|
||||
IF (LFLAGS(4).NE.0) THEN
|
||||
FORCE = AK*(U(4)-U(1))
|
||||
DFORCE = AK*(DU(4,1)-DU(1,1))
|
||||
SRESID(1) = -DFORCE
|
||||
SRESID(4) = DFORCE
|
||||
RHS(1,1) = RHS(1,1)-SRESID(1)
|
||||
RHS(4,1) = RHS(4,1)-SRESID(4)
|
||||
ENERGY(2) = HALF*FORCE*(DU(4,1)-DU(1,1))
|
||||
* + HALF*DFORCE*(U(4)-U(1))
|
||||
* + HALF*DFORCE*(DU(4,1)-DU(1,1))
|
||||
ELSE
|
||||
FORCE = AK*(U(4)-U(1))
|
||||
SRESID(1) = -FORCE
|
||||
SRESID(4) = FORCE
|
||||
RHS(1,1) = RHS(1,1)-SRESID(1)
|
||||
RHS(4,1) = RHS(4,1)-SRESID(4)
|
||||
DO KDLOAD = 1, NDLOAD
|
||||
IF (JDLTYP(KDLOAD,1).EQ.1001) THEN
|
||||
RHS(4,1) = RHS(4,1)+ADLMAG(KDLOAD,1)
|
||||
ENERGY(8) = ENERGY(8)+(ADLMAG(KDLOAD,1)
|
||||
* - HALF*DDLMAG(KDLOAD,1))*DU(4,1)
|
||||
IF (NRHS.EQ.2) THEN
|
||||
C Riks
|
||||
RHS(4,2) = RHS(4,2)+DDLMAG(KDLOAD,1)
|
||||
END IF
|
||||
END IF
|
||||
END DO
|
||||
ENERGY(2) = HALF*FORCE*(U(4)-U(1))
|
||||
END IF
|
||||
ELSE IF (LFLAGS(1).EQ.11 .OR. LFLAGS(1).EQ.12) THEN
|
||||
C *DYNAMIC
|
||||
ALPHA = PARAMS(1)
|
||||
BETA = PARAMS(2)
|
||||
GAMMA = PARAMS(3)
|
||||
C
|
||||
DADU = ONE/(BETA*DTIME**2)
|
||||
DVDU = GAMMA/(BETA*DTIME)
|
||||
C
|
||||
DO K1 = 1, NDOFEL
|
||||
AMATRX(K1,K1) = AM*DADU
|
||||
RHS(K1,1) = RHS(K1,1)-AM*A(K1)
|
||||
END DO
|
||||
AMATRX(1,1) = AMATRX(1,1)+(ONE+ALPHA)*AK
|
||||
AMATRX(4,4) = AMATRX(4,4)+(ONE+ALPHA)*AK
|
||||
AMATRX(1,4) = AMATRX(1,4)-(ONE+ALPHA)*AK
|
||||
AMATRX(4,1) = AMATRX(4,1)-(ONE+ALPHA)*AK
|
||||
FORCE = AK*(U(4)-U(1))
|
||||
SRESID(1) = -FORCE
|
||||
SRESID(4) = FORCE
|
||||
RHS(1,1) = RHS(1,1) -
|
||||
* ((ONE+ALPHA)*SRESID(1)-ALPHA*SVARS(1))
|
||||
RHS(4,1) = RHS(4,1) -
|
||||
* ((ONE+ALPHA)*SRESID(4)-ALPHA*SVARS(4))
|
||||
ENERGY(1) = ZERO
|
||||
DO K1 = 1, NDOFEL
|
||||
SVARS(K1+6) = SVARS(k1)
|
||||
SVARS(K1) = SRESID(K1)
|
||||
ENERGY(1) = ENERGY(1)+HALF*V(K1)*AM*V(K1)
|
||||
END DO
|
||||
ENERGY(2) = HALF*FORCE*(U(4)-U(1))
|
||||
END IF
|
||||
ELSE IF (LFLAGS(3).EQ.2) THEN
|
||||
C Stiffness matrix
|
||||
AMATRX(1,1) = AK
|
||||
AMATRX(4,4) = AK
|
||||
AMATRX(1,4) = -AK
|
||||
AMATRX(4,1) = -AK
|
||||
ELSE IF (LFLAGS(3).EQ.4) THEN
|
||||
C Mass matrix
|
||||
DO K1 = 1, NDOFEL
|
||||
AMATRX(K1,K1) = AM
|
||||
END DO
|
||||
ELSE IF (LFLAGS(3).EQ.5) THEN
|
||||
C Half-increment residual calculation
|
||||
ALPHA = PARAMS(1)
|
||||
FORCE = AK*(U(4)-U(1))
|
||||
SRESID(1) = -FORCE
|
||||
SRESID(4) = FORCE
|
||||
RHS(1,1) = RHS(1,1)-AM*A(1)-(ONE+ALPHA)*SRESID(1)
|
||||
* + HALF*ALPHA*( SVARS(1)+SVARS(7) )
|
||||
RHS(4,1) = RHS(4,1)-AM*A(4)-(ONE+ALPHA)*SRESID(4)
|
||||
* + HALF*ALPHA*( SVARS(4)+SVARS(10) )
|
||||
ELSE IF (LFLAGS(3).EQ.6) THEN
|
||||
C Initial acceleration calculation
|
||||
DO K1 = 1, NDOFEL
|
||||
AMATRX(K1,K1) = AM
|
||||
END DO
|
||||
FORCE = AK*(U(4)-U(1))
|
||||
SRESID(1) = -FORCE
|
||||
SRESID(4) = FORCE
|
||||
RHS(1,1) = RHS(1,1)-SRESID(1)
|
||||
RHS(4,1) = RHS(4,1)-SRESID(4)
|
||||
ENERGY(1) = ZERO
|
||||
DO K1 = 1, NDOFEL
|
||||
SVARS(K1) = SRESID(K1)
|
||||
ENERGY(1) = ENERGY(1)+HALF*V(K1)*AM*V(K1)
|
||||
END DO
|
||||
ENERGY(2) = HALF*FORCE*(U(4)-U(1))
|
||||
ELSE IF (LFLAGS(3).EQ.100) THEN
|
||||
C Output for perturbations
|
||||
IF (LFLAGS(1).EQ.1 .OR. LFLAGS(1).EQ.2) THEN
|
||||
C *STATIC
|
||||
FORCE = AK*(U(4)-U(1))
|
||||
DFORCE = AK*(DU(4,1)-DU(1,1))
|
||||
SRESID(1) = -DFORCE
|
||||
SRESID(4) = DFORCE
|
||||
RHS(1,1) = RHS(1,1)-SRESID(1)
|
||||
RHS(4,1) = RHS(4,1)-SRESID(4)
|
||||
ENERGY(2) = HALF*FORCE*(DU(4,1)-DU(1,1))
|
||||
* + HALF*DFORCE*(U(4)-U(1))
|
||||
* + HALF*DFORCE*(DU(4,1)-DU(1,1))
|
||||
DO KVAR = 1, NSVARS
|
||||
SVARS(KVAR) = ZERO
|
||||
END DO
|
||||
SVARS(1) = RHS(1,1)
|
||||
SVARS(4) = RHS(4,1)
|
||||
ELSE IF (LFLAGS(1).EQ.41) THEN
|
||||
C *FREQUENCY
|
||||
DO KRHS = 1, NRHS
|
||||
DFORCE = AK*(DU(4,KRHS)-DU(1,KRHS))
|
||||
SRESID(1) = -DFORCE
|
||||
SRESID(4) = DFORCE
|
||||
RHS(1,KRHS) = RHS(1,KRHS)-SRESID(1)
|
||||
RHS(4,KRHS) = RHS(4,KRHS)-SRESID(4)
|
||||
END DO
|
||||
DO KVAR = 1, NSVARS
|
||||
SVARS(KVAR) = ZERO
|
||||
END DO
|
||||
SVARS(1) = RHS(1,1)
|
||||
SVARS(4) = RHS(4,1)
|
||||
END IF
|
||||
END IF
|
||||
C
|
||||
RETURN
|
||||
END
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
154
Unpublished/XFEM/Other/2DSimp.m
Normal file
154
Unpublished/XFEM/Other/2DSimp.m
Normal file
|
|
@ -0,0 +1,154 @@
|
|||
function [] = 2DSimp()
|
||||
% MATLAB based 2-D XFEM Solver
|
||||
% J. Grogan (2012)
|
||||
clear all
|
||||
% Define Mesh
|
||||
NumX=3;
|
||||
NumY=3;
|
||||
delX=1.;
|
||||
delY=1.;
|
||||
for j=1:NumY+1
|
||||
for i=1:NumX+1
|
||||
index=i+(NumX+1)*(j-1);
|
||||
Node(index,1)=single((i-1.))*delX;
|
||||
Node(index,2)=single((j-1.))*delY;
|
||||
end
|
||||
end
|
||||
numNodes=(NumX+1)*(NumY+1);
|
||||
for j=1:NumY
|
||||
for i=1:NumX
|
||||
index=i+NumX*(j-1);
|
||||
Element(index,1)=i+(NumX+1)*(j-1);
|
||||
Element(index,2)=i+(NumX+1)*(j-1)+1;
|
||||
Element(index,3)=i+(NumX+1)*(j);
|
||||
Element(index,4)=i+(NumX+1)*(j)+1;
|
||||
end
|
||||
end
|
||||
numElem=(NumX)*(NumY);
|
||||
% dofs per node
|
||||
ndof=1;
|
||||
% Define Section Properties
|
||||
rho=1.;
|
||||
% initial interface position
|
||||
dpos=0.25;
|
||||
% Initial temperatures
|
||||
Tnew=zeros(numNodes,1);
|
||||
Bound=zeros(numNodes,1);
|
||||
stored(1)=dpos;
|
||||
for e=1:numElem
|
||||
for n=1:4
|
||||
crdn=Node(Element(e,n),1);
|
||||
if crdn<=dpos
|
||||
Tnew(Element(e,n))=1.;
|
||||
Bound(Element(e,n))=1.;
|
||||
end
|
||||
end
|
||||
end
|
||||
% Define Time Step
|
||||
dtime=0.05;
|
||||
tsteps=20;
|
||||
time=0.;
|
||||
% Loop through time steps
|
||||
for ts=1:tsteps
|
||||
K=zeros(numNodes*ndof,numNodes*ndof);
|
||||
M=zeros(numNodes*ndof,numNodes*ndof);
|
||||
% Loop Through Elements
|
||||
for e=1:numElem
|
||||
Ke=zeros(4*ndof);
|
||||
Me=zeros(4*ndof);
|
||||
for icrd=1:4;
|
||||
crdnx(icrd)=Node(Element(e,icrd),1);
|
||||
crdny(icrd)=Node(Element(e,icrd),2);
|
||||
end
|
||||
% regular element - fix extra dofs
|
||||
gpos=1/sqrt(3.);
|
||||
gx(1)=-gpos;
|
||||
gx(2)=gpos;
|
||||
gx(3)=gpos;
|
||||
gx(4)=-gpos;
|
||||
hx(1)=-gpos;
|
||||
hx(2)=-gpos;
|
||||
hx(3)=-gpos;
|
||||
hx(4)=gpos;
|
||||
% Loop Through Int Points
|
||||
for i=1:4;
|
||||
g=gx(i);
|
||||
h=hx(i);
|
||||
phi(1)=0.25*(1.-g)*(1.-h);
|
||||
phi(2)=0.25*(1.+g)*(1.-h);
|
||||
phi(3)=0.25*(1.+g)*(1.+h);
|
||||
phi(4)=0.25*(1.-g)*(1.+h);
|
||||
cond=1.;
|
||||
spec=1.;
|
||||
phig(1)=0.25*-(1.-h);
|
||||
phig(2)=0.25*(1.-h);
|
||||
phig(3)=0.25*(1.+h);
|
||||
phig(4)=0.25*-(1.+h);
|
||||
phih(1)=0.25*-(1.-g);
|
||||
phih(2)=0.25*-(1.+g);
|
||||
phih(3)=0.25*(1.+g);
|
||||
phih(4)=0.25*(1.-g);
|
||||
rjac=zeros(2,2);
|
||||
for iter=1:4
|
||||
rjac(1,1)=rjac(1,1)+phig(iter)*crdnx(iter);
|
||||
rjac(1,2)=rjac(1,2)+phig(iter)*crdny(iter);
|
||||
rjac(2,1)=rjac(2,1)+phih(iter)*crdnx(iter);
|
||||
rjac(2,2)=rjac(2,2)+phih(iter)*crdny(iter);
|
||||
end
|
||||
djac=rjac(1,1)*rjac(2,2)-rjac(1,2)*rjac(2,1);
|
||||
rjaci(1,1)= rjac(2,2)/djac;
|
||||
rjaci(2,2)= rjac(1,1)/djac;
|
||||
rjaci(1,2)=-rjac(1,2)/djac;
|
||||
rjaci(2,1)=-rjac(2,1)/djac ;
|
||||
for iter=1:4
|
||||
phix(iter)=rjaci(1,1)*phig(iter)+rjaci(1,2)*phih(iter);
|
||||
phiy(iter)=rjaci(2,1)*phig(iter)+rjaci(2,2)*phih(iter);
|
||||
end
|
||||
we=djac;
|
||||
Ke=Ke+we*cond*(phix'*phix+phiy'*phiy);
|
||||
Me=Me+(we*rho*spec*phi'*phi)/dtime;
|
||||
end
|
||||
% Add penalty term and get temp gradient on interface
|
||||
% Assemble Global Matrices
|
||||
gnum(1)=Element(e,1);
|
||||
gnum(2)=Element(e,2);
|
||||
gnum(3)=Element(e,3);
|
||||
gnum(4)=Element(e,4);
|
||||
for i=1:4;
|
||||
for j=1:4;
|
||||
K(gnum(j),gnum(i))=K(gnum(j),gnum(i))+Ke(j,i);
|
||||
M(gnum(j),gnum(i))=M(gnum(j),gnum(i))+Me(j,i);
|
||||
end
|
||||
end
|
||||
end
|
||||
%Remove inactive DOFs(Reduce Matrices)
|
||||
RHS=M*Tnew;
|
||||
A=K+M;
|
||||
Sub=A*Bound;
|
||||
iindex=0;
|
||||
for i=1:ndof*numNodes;
|
||||
if Bound(i)==0.;
|
||||
iindex=iindex+1;
|
||||
RHSred(iindex)=RHS(i)-Sub(i);
|
||||
jindex=0;
|
||||
for j=1:ndof*numNodes;
|
||||
if Bound(j)==0.;
|
||||
jindex=jindex+1;
|
||||
Ared(iindex,jindex)=A(i,j);
|
||||
end
|
||||
end
|
||||
end
|
||||
end
|
||||
%Solve
|
||||
StiffI=Ared^-1;
|
||||
Tnewr=(Ared^-1)*RHSred';
|
||||
iindex=0;
|
||||
for i=1:ndof*numNodes;
|
||||
if Bound(i)==0.;
|
||||
iindex=iindex+1;
|
||||
Tnew(i)=Tnewr(iindex);
|
||||
end
|
||||
end
|
||||
Tnew
|
||||
end
|
||||
stored'
|
||||
91
Unpublished/XFEM/Other/AbInp.inp
Normal file
91
Unpublished/XFEM/Other/AbInp.inp
Normal file
|
|
@ -0,0 +1,91 @@
|
|||
*Heading
|
||||
** Job name: Job-1 Model name: Model-1
|
||||
** Generated by: Abaqus/CAE 6.12-1
|
||||
*Preprint, echo=NO, model=NO, history=NO, contact=NO
|
||||
**
|
||||
** PARTS
|
||||
**
|
||||
*Part, name=Part-1
|
||||
*Node
|
||||
1, 0., 0., 0.
|
||||
2, 0.2, 0., 0.
|
||||
3, 0.4, 0., 0.
|
||||
4, 0.6, 0., 0.
|
||||
5, 0.8, 0., 0.
|
||||
6, 1., 0., 0.
|
||||
7, 1.2, 0., 0.
|
||||
8, 1.4, 0., 0.
|
||||
9, 1.6, 0., 0.
|
||||
10, 1.8, 0., 0.
|
||||
11, 2., 0., 0.
|
||||
*USER ELEMENT,NODES=2,TYPE=U8008,PROP=1,COORDINATES=1,VAR=2,unsymm
|
||||
11,12
|
||||
*Element, type=U8008,ELSET=UEL
|
||||
1, 1, 2
|
||||
2, 2, 3
|
||||
3, 3, 4
|
||||
4, 4, 5
|
||||
5, 5, 6
|
||||
6, 6, 7
|
||||
7, 7, 8
|
||||
8, 8, 9
|
||||
9, 9, 10
|
||||
10, 10, 11
|
||||
*UEL Property, Elset=UEL
|
||||
1.
|
||||
*End Part
|
||||
**
|
||||
**
|
||||
** ASSEMBLY
|
||||
**
|
||||
*Assembly, name=Assembly
|
||||
**
|
||||
*Instance, name=Part-1-1, part=Part-1
|
||||
*End Instance
|
||||
**
|
||||
*Nset, nset=_PickedSet16, internal, instance=Part-1-1
|
||||
1,
|
||||
*Nset, nset=_PickedSet17, internal, instance=Part-1-1
|
||||
2,
|
||||
*Nset, nset=Set-6, instance=Part-1-1
|
||||
1,
|
||||
*End Assembly
|
||||
**
|
||||
** MATERIALS
|
||||
**
|
||||
*Material, name=Material-1
|
||||
*Conductivity
|
||||
1.,
|
||||
*Density
|
||||
1.,
|
||||
*Specific Heat
|
||||
1.,
|
||||
** ----------------------------------------------------------------
|
||||
**
|
||||
** Name: Predefined Field-1 Type: Temperature
|
||||
*Initial Conditions, type=TEMPERATURE
|
||||
_PickedSet16, 1.,0.
|
||||
** Name: Predefined Field-2 Type: Temperature
|
||||
*Initial Conditions, type=TEMPERATURE
|
||||
_PickedSet17, 0.,0.
|
||||
** STEP: Step-1
|
||||
**
|
||||
*Step, name=Step-1
|
||||
*Heat Transfer, end=PERIOD, deltmx=100.
|
||||
0.1, 1.6, 1e-09, 0.1,
|
||||
**
|
||||
** BOUNDARY CONDITIONS
|
||||
**
|
||||
** Name: BC-1 Type: Temperature
|
||||
*Boundary
|
||||
Set-6, 11, 11, 1.
|
||||
**
|
||||
** OUTPUT REQUESTS
|
||||
**
|
||||
*Restart, write, frequency=0
|
||||
**
|
||||
** FIELD OUTPUT: F-Output-1
|
||||
**
|
||||
*Output, field, variable=PRESELECT
|
||||
*Output, history, frequency=0
|
||||
*End Step
|
||||
80
Unpublished/XFEM/Other/FESolve.m
Normal file
80
Unpublished/XFEM/Other/FESolve.m
Normal file
|
|
@ -0,0 +1,80 @@
|
|||
function [] = FESolve()
|
||||
% MATLAB based FE Solver
|
||||
% J. Grogan (2012)
|
||||
clear all
|
||||
% Define Geometry
|
||||
len=1.;
|
||||
% Define Section Properties
|
||||
rho=1.;
|
||||
spec=1.;
|
||||
cond=1.;
|
||||
% Generate Mesh
|
||||
numElem=10;
|
||||
ndCoords=linspace(0,len,numElem+1);
|
||||
numNodes=size(ndCoords,2);
|
||||
indx=1:numElem;
|
||||
elemNodes(:,1)=indx;
|
||||
elemNodes(:,2)=indx+1;
|
||||
% Initialize Conditions
|
||||
Tnew=zeros(numNodes,1);
|
||||
Tnew(1)=1.;
|
||||
% Define Time Step
|
||||
dtime=.1;
|
||||
tsteps=10;
|
||||
time=0.;
|
||||
% Loop through time steps
|
||||
for ts=1:tsteps;
|
||||
time=time+dtime;
|
||||
K=zeros(numNodes,numNodes);
|
||||
M=zeros(numNodes,numNodes);
|
||||
% Loop Through Elements
|
||||
for e=1:numElem;
|
||||
Ke=zeros(2);
|
||||
Me=zeros(2);
|
||||
gpx(1)=-1./sqrt(3.);
|
||||
gpx(2)=1./sqrt(3.);
|
||||
ajacob=abs(ndCoords(elemNodes(e,2))-ndCoords(elemNodes(e,1)))/2.;
|
||||
% Loop Through Int Points
|
||||
for i=1:2;
|
||||
c=gpx(i);
|
||||
phi(1)=(1.-c)/2.;
|
||||
phi(2)=(1.+c)/2.;
|
||||
phic(1)=-0.5;
|
||||
phic(2)=0.5;
|
||||
phix(1)=phic(1)/ajacob;
|
||||
phix(2)=phic(2)/ajacob;
|
||||
we=ajacob;
|
||||
Ke=Ke+we*cond*phix'*phix;
|
||||
Me=Me+(we*rho*spec*phi'*phi)/dtime;
|
||||
end
|
||||
% Assemble Global Matrices
|
||||
K(elemNodes(e,1),elemNodes(e,1))=K(elemNodes(e,1),elemNodes(e,1))+Ke(1,1);
|
||||
K(elemNodes(e,1),elemNodes(e,2))=K(elemNodes(e,1),elemNodes(e,2))+Ke(1,2);
|
||||
K(elemNodes(e,2),elemNodes(e,1))=K(elemNodes(e,2),elemNodes(e,1))+Ke(2,1);
|
||||
K(elemNodes(e,2),elemNodes(e,2))=K(elemNodes(e,2),elemNodes(e,2))+Ke(2,2);
|
||||
M(elemNodes(e,1),elemNodes(e,1))=M(elemNodes(e,1),elemNodes(e,1))+Me(1,1);
|
||||
M(elemNodes(e,1),elemNodes(e,2))=M(elemNodes(e,1),elemNodes(e,2))+Me(1,2);
|
||||
M(elemNodes(e,2),elemNodes(e,1))=M(elemNodes(e,2),elemNodes(e,1))+Me(2,1);
|
||||
M(elemNodes(e,2),elemNodes(e,2))=M(elemNodes(e,2),elemNodes(e,2))+Me(2,2);
|
||||
end
|
||||
%Apply Boundary Conditions (Reduce Matrices)
|
||||
T1=1;
|
||||
RHS=M*Tnew;
|
||||
for i=1:numNodes-1;
|
||||
for j=1:numNodes-1;
|
||||
Kred(i,j)=K(i+1,j+1);
|
||||
Mred(i,j)=M(i+1,j+1);
|
||||
end
|
||||
Subr(i)=(K(i+1,1)+M(i+1,1))*T1;
|
||||
RHSr(i)=RHS(i+1);
|
||||
end
|
||||
%Solve
|
||||
StiffI=(Mred+Kred)^-1;
|
||||
Tnewr=StiffI*(RHSr'-Subr');
|
||||
for i=1:numNodes-1;
|
||||
Tnew(i+1)=Tnewr(i);
|
||||
end
|
||||
Tnew(1)=1.;
|
||||
Tnew
|
||||
end
|
||||
|
||||
98
Unpublished/XFEM/Other/FESolveSimp.m
Normal file
98
Unpublished/XFEM/Other/FESolveSimp.m
Normal file
|
|
@ -0,0 +1,98 @@
|
|||
function [] = FESolveSimp()
|
||||
% MATLAB based 1-D XFEM Solver
|
||||
% J. Grogan (2012)
|
||||
clear all
|
||||
% Define Geometry
|
||||
len=10.;
|
||||
% Define Section Properties
|
||||
rho=1.;
|
||||
% Generate Mesh
|
||||
numElem=10;
|
||||
charlen=len/numElem;
|
||||
ndCoords=linspace(0,len,numElem+1);
|
||||
numNodes=size(ndCoords,2);
|
||||
indx=1:numElem;
|
||||
elemNodes(:,1)=indx;
|
||||
elemNodes(:,2)=indx+1;
|
||||
% dofs per node
|
||||
ndof=1;
|
||||
% Initial temperatures
|
||||
Tnew=zeros(numNodes,1);
|
||||
Bound=zeros(numNodes,1);
|
||||
Tnew(1)=1.;
|
||||
Bound(1)=1.;
|
||||
% Define Time Step
|
||||
dtime=0.01;
|
||||
tsteps=10;
|
||||
time=0.;
|
||||
% Loop through time steps
|
||||
for ts=1:tsteps
|
||||
K=zeros(numNodes,numNodes);
|
||||
M=zeros(numNodes,numNodes);
|
||||
% Loop Through Elements
|
||||
for e=1:numElem
|
||||
Ke=zeros(2*ndof);
|
||||
Me=zeros(2*ndof);
|
||||
crdn1=ndCoords(elemNodes(e,1));
|
||||
crdn2=ndCoords(elemNodes(e,2));
|
||||
elen=abs(crdn2-crdn1);
|
||||
ajacob=elen/2.;
|
||||
gpx(1)=-1/sqrt(3.);
|
||||
gpx(2)=1/sqrt(3.);
|
||||
w(1)=1.;
|
||||
w(2)=1.;
|
||||
% Loop Through Int Points
|
||||
for i=1:2;
|
||||
c=gpx(i);
|
||||
phi(1)=(1.-c)/2.;
|
||||
phi(2)=(1.+c)/2.;
|
||||
cond=1.;
|
||||
spec=1.;
|
||||
phic(1)=-0.5;
|
||||
phic(2)=0.5;
|
||||
phix(1)=phic(1)/ajacob;
|
||||
phix(2)=phic(2)/ajacob;
|
||||
we=ajacob*w(i);
|
||||
Ke=Ke+we*cond*phix'*phix;
|
||||
Me=Me+(we*rho*spec*phi'*phi)/dtime;
|
||||
end
|
||||
% Assemble Global Matrices
|
||||
gnum=elemNodes(e,1);
|
||||
for i=1:2;
|
||||
for j=1:2;
|
||||
K(gnum+j-1,gnum+i-1)=K(gnum+j-1,gnum+i-1)+Ke(j,i);
|
||||
M(gnum+j-1,gnum+i-1)=M(gnum+j-1,gnum+i-1)+Me(j,i);
|
||||
end
|
||||
end
|
||||
end
|
||||
%Remove NON-ENHANCED DOFs(Reduce Matrices)
|
||||
iindex=0.;
|
||||
A=K+M;
|
||||
Sub=A*Bound;
|
||||
RHS=M*Tnew-Sub;
|
||||
% Apply Boundary Conditions
|
||||
for i=1:numNodes;
|
||||
if Bound(i)==0.;
|
||||
iindex=iindex+1;
|
||||
RHSR(iindex)=RHS(i);
|
||||
jindex=0;
|
||||
for j=1:numNodes;
|
||||
if Bound(j)==0.;
|
||||
jindex=jindex+1;
|
||||
AR(iindex,jindex)=A(i,j);
|
||||
end
|
||||
end
|
||||
end
|
||||
end
|
||||
%Solve
|
||||
Tnewr=(AR^-1)*RHSR';
|
||||
% Restore Matrices
|
||||
iindex=0;
|
||||
for i=1:numNodes;
|
||||
if Bound(i)==0.;
|
||||
iindex=iindex+1;
|
||||
Tnew(i)=Tnewr(iindex);
|
||||
end
|
||||
end
|
||||
Tnew
|
||||
end
|
||||
221
Unpublished/XFEM/Other/FESolveX.m
Normal file
221
Unpublished/XFEM/Other/FESolveX.m
Normal file
|
|
@ -0,0 +1,221 @@
|
|||
function [] = FESolveX()
|
||||
% MATLAB based 1-D XFEM Solver
|
||||
% J. Grogan (2012)
|
||||
clear all
|
||||
% Define Geometry
|
||||
len=10.;
|
||||
% Define Section Properties
|
||||
rho=1.;
|
||||
% Generate Mesh
|
||||
numElem=40;
|
||||
charlen=len/numElem;
|
||||
ndCoords=linspace(0,len,numElem+1);
|
||||
numNodes=size(ndCoords,2);
|
||||
indx=1:numElem;
|
||||
elemNodes(:,1)=indx;
|
||||
elemNodes(:,2)=indx+1;
|
||||
% dofs per node
|
||||
ndof=2;
|
||||
% initial interface position
|
||||
dpos=4.6;
|
||||
% Initial temperatures
|
||||
Tnew=zeros(numNodes*2,1);
|
||||
%storage
|
||||
stored(1)=dpos;
|
||||
for e=1:numElem
|
||||
crdn1=ndCoords(elemNodes(e,1));
|
||||
if crdn1<=dpos
|
||||
Tnew(2*elemNodes(e,1)-1)=1.;
|
||||
end
|
||||
end
|
||||
% Define Time Step
|
||||
dtime=0.1;
|
||||
tsteps=10;
|
||||
time=0.;
|
||||
% penalty term
|
||||
beta=200.;
|
||||
% Loop through time steps
|
||||
for ts=1:tsteps
|
||||
% Get interface velocity
|
||||
d(1)=dpos+charlen;
|
||||
d(2)=dpos+3*charlen/4;
|
||||
d(3)=dpos+charlen/4;
|
||||
d(4)=dpos;
|
||||
for e=1:numElem
|
||||
crdn1=ndCoords(elemNodes(e,1));
|
||||
crdn2=ndCoords(elemNodes(e,2));
|
||||
for j=1:4
|
||||
if d(j)>=crdn1 & d(j)<crdn2
|
||||
elen=abs(crdn2-crdn1);
|
||||
ajacob=elen/2.;
|
||||
point=(d(j)-crdn1)/ajacob-1.;
|
||||
theta(1)=abs(crdn1-dpos)*sign(crdn1-dpos);
|
||||
theta(2)=abs(crdn2-dpos)*sign(crdn2-dpos);
|
||||
tmp1a=Tnew(elemNodes(e,1)*2-1);
|
||||
tmp1b=Tnew(elemNodes(e,1)*2);
|
||||
tmp2a=Tnew(elemNodes(e,2)*2-1);
|
||||
tmp2b=Tnew(elemNodes(e,2)*2);
|
||||
xi=point;
|
||||
gm(1)=(1.-xi)/2.;
|
||||
gm(3)=(1.+xi)/2.;
|
||||
term=theta(1)*gm(1)+theta(2)*gm(3);
|
||||
gm(2)=gm(1)*(abs(term)-abs(theta(1)));
|
||||
gm(4)=gm(3)*(abs(term)-abs(theta(2)));
|
||||
t(j)=gm(1)*tmp1a+gm(2)*tmp1b+gm(3)*tmp2a+gm(4)*tmp2b;
|
||||
end
|
||||
end
|
||||
end
|
||||
vel=1.*(0.5/charlen)*(2*t(1)+t(2)-t(3)-2*t(4));
|
||||
vel=0.;
|
||||
% Update interface position
|
||||
dpos=dpos+vel*dtime;
|
||||
stored(ts+1)=dpos;
|
||||
K=zeros(numNodes*ndof,numNodes*ndof);
|
||||
M=zeros(numNodes*ndof,numNodes*ndof);
|
||||
pforce=zeros(numNodes*ndof,1);
|
||||
% Loop Through Elements
|
||||
for e=1:numElem
|
||||
Ke=zeros(2*ndof);
|
||||
Me=zeros(2*ndof);
|
||||
crdn1=ndCoords(elemNodes(e,1));
|
||||
crdn2=ndCoords(elemNodes(e,2));
|
||||
theta(1)=abs(crdn1-dpos)*sign(crdn1-dpos);
|
||||
theta(2)=abs(crdn2-dpos)*sign(crdn2-dpos);
|
||||
enr=2;
|
||||
elen=abs(crdn2-crdn1);
|
||||
ajacob=elen/2.;
|
||||
if sign(theta(1))~=sign(theta(2))
|
||||
% enriched element
|
||||
enr=4;
|
||||
% get interface position on element
|
||||
point=(dpos-crdn1)/ajacob-1.;
|
||||
% devide element for sub integration
|
||||
len1=abs(-point-1.);
|
||||
len2=abs(1.-point);
|
||||
mid1=-1+len1/2.;
|
||||
mid2=1-len2/2.;
|
||||
gpx(1)=-(len1/2.)/sqrt(3.)+mid1;
|
||||
gpx(2)=(len1/2.)/sqrt(3.)+mid1;
|
||||
gpx(3)=-(len2/2.)/sqrt(3.)+mid2;
|
||||
gpx(4)=(len2/2.)/sqrt(3.)+mid2;
|
||||
w(1)=(len1/2.);
|
||||
w(2)=(len1/2.);
|
||||
w(3)=(len2/2.);
|
||||
w(4)=(len2/2.);
|
||||
fdofs(1)=2*elemNodes(e,1);
|
||||
fdofs(2)=2*elemNodes(e,2);
|
||||
else
|
||||
% regular element - fix extra dofs
|
||||
gpx(1)=-1/sqrt(3.);
|
||||
gpx(2)=1/sqrt(3.);
|
||||
w(1)=1.;
|
||||
w(2)=1.;
|
||||
end
|
||||
% Loop Through Int Points
|
||||
for i=1:enr;
|
||||
c=gpx(i);
|
||||
phi(1)=(1.-c)/2.;
|
||||
phi(3)=(1.+c)/2.;
|
||||
term=theta(1)*phi(1)+theta(2)*phi(3);
|
||||
if term<0
|
||||
cond=0.;
|
||||
spec=0.01;
|
||||
else
|
||||
cond=1.;
|
||||
spec=1.;
|
||||
end
|
||||
phi(2)=phi(1)*(abs(term)-abs(theta(1)));
|
||||
phi(4)=phi(3)*(abs(term)-abs(theta(2)));
|
||||
phic(1)=-0.5;
|
||||
phic(3)=0.5;
|
||||
dterm=sign(term)*(phic(1)*theta(1)+phic(3)*theta(2));
|
||||
phic(2)=phic(1)*(abs(term)-abs(theta(1)))+phi(1)*dterm;
|
||||
phic(4)=phic(3)*(abs(term)-abs(theta(2)))+phi(3)*dterm;
|
||||
phix(1)=phic(1)/ajacob;
|
||||
phix(2)=phic(2)/ajacob;
|
||||
phix(3)=phic(3)/ajacob;
|
||||
phix(4)=phic(4)/ajacob;
|
||||
we=ajacob*w(i);
|
||||
Ke=Ke+we*cond*phix'*phix;
|
||||
Me=Me+(we*rho*spec*phi'*phi)/dtime;
|
||||
end
|
||||
% Add penalty term and get temp gradient on interface
|
||||
if enr==4;
|
||||
xi=point;
|
||||
gm(1)=(1.-xi)/2.;
|
||||
gm(3)=(1.+xi)/2.;
|
||||
term=theta(1)*gm(1)+theta(2)*gm(3);
|
||||
gm(2)=gm(1)*(abs(term)-abs(theta(1)));
|
||||
gm(4)=gm(3)*(abs(term)-abs(theta(2)));
|
||||
tpos=gm(1)*Tnew(1)+gm(2)*Tnew(2)+gm(3)*Tnew(3)+gm(4)*Tnew(4);
|
||||
pen=beta*(gm'*gm);
|
||||
pfL=beta*1*gm';
|
||||
Ke=Ke+pen;
|
||||
else
|
||||
pen=zeros(4);
|
||||
pfL=zeros(4,1);
|
||||
end
|
||||
% Assemble Global Matrices
|
||||
gnum=2.*elemNodes(e,1)-1.;
|
||||
for i=1:4;
|
||||
for j=1:4;
|
||||
K(gnum+j-1,gnum+i-1)=K(gnum+j-1,gnum+i-1)+Ke(j,i);
|
||||
M(gnum+j-1,gnum+i-1)=M(gnum+j-1,gnum+i-1)+Me(j,i);
|
||||
end
|
||||
pforce(gnum+i-1)=pforce(gnum+i-1)+pfL(i);
|
||||
end
|
||||
end
|
||||
%Remove inactive DOFs(Reduce Matrices)
|
||||
T1=1;
|
||||
RHS=M*Tnew;
|
||||
iindex=0;
|
||||
for i=1:ndof*numNodes;
|
||||
check=1;
|
||||
if i==fdofs(1)|i==fdofs(2)
|
||||
check=0;
|
||||
elseif mod(i,2)~=0 & i~=1
|
||||
check=0;
|
||||
end
|
||||
if check==0
|
||||
jindex=0;
|
||||
iindex=iindex+1;
|
||||
for j=1:ndof*numNodes;
|
||||
check=1;
|
||||
if j==fdofs(1)|j==fdofs(2)
|
||||
check=0;
|
||||
elseif mod(j,2)~=0 & j~=1
|
||||
check=0;
|
||||
end
|
||||
if check==0
|
||||
jindex=jindex+1;
|
||||
Kred(iindex,jindex)=K(i,j);
|
||||
Mred(iindex,jindex)=M(i,j);
|
||||
end
|
||||
end
|
||||
Subr(iindex)=(K(i,1)+M(i,1))*T1;
|
||||
RHSr(iindex)=RHS(i);
|
||||
pforcer(iindex)=pforce(i);
|
||||
end
|
||||
end
|
||||
%Solve
|
||||
StiffI=(Mred+Kred)^-1;
|
||||
Tnewr=StiffI*(RHSr'-Subr'+pforcer');
|
||||
iindex=0.;
|
||||
for i=1:ndof*numNodes;
|
||||
check=1;
|
||||
if i==fdofs(1)|i==fdofs(2)
|
||||
check=0;
|
||||
elseif mod(i,2)~=0 & i~=1
|
||||
check=0;
|
||||
end
|
||||
if check==0
|
||||
iindex=iindex+1;
|
||||
Tnew(i)=Tnewr(iindex);
|
||||
else
|
||||
Tnew(i)=0.;
|
||||
end
|
||||
end
|
||||
Tnew(1)=1.;
|
||||
Tnew
|
||||
end
|
||||
stored'
|
||||
269
Unpublished/XFEM/Other/FESolveX2D.m
Normal file
269
Unpublished/XFEM/Other/FESolveX2D.m
Normal file
|
|
@ -0,0 +1,269 @@
|
|||
function [] = FESolveX2D()
|
||||
% MATLAB based 2-D XFEM Solver
|
||||
% J. Grogan (2012)
|
||||
clear all
|
||||
% Define Mesh
|
||||
NumX=4;
|
||||
NumY=1;
|
||||
delX=1.;
|
||||
delY=1.;
|
||||
for j=1:NumY+1
|
||||
for i=1:NumX+1
|
||||
index=i+(NumX+1)*(j-1);
|
||||
Node(index,1)=single((i-1.))*delX;
|
||||
Node(index,2)=single((j-1.))*delY;
|
||||
end
|
||||
end
|
||||
numNodes=(NumX+1)*(NumY+1);
|
||||
for j=1:NumY
|
||||
for i=1:NumX
|
||||
index=i+NumX*(j-1);
|
||||
Element(index,1)=i+(NumX+1)*(j-1);
|
||||
Element(index,2)=i+(NumX+1)*(j-1)+1;
|
||||
Element(index,3)=i+(NumX+1)*(j)+1;
|
||||
Element(index,4)=i+(NumX+1)*(j);
|
||||
end
|
||||
end
|
||||
numElem=(NumX)*(NumY);
|
||||
% dofs per node
|
||||
ndof=2;
|
||||
% Define Section Properties
|
||||
rho=1.;
|
||||
% initial interface position
|
||||
dpos=0.1;
|
||||
% Initial temperatures
|
||||
Tnew=zeros(numNodes*2,1);
|
||||
Bound=zeros(numNodes*2,1);
|
||||
stored(1)=dpos;
|
||||
for e=1:numElem
|
||||
for n=1:4
|
||||
crdn=Node(Element(e,n),1);
|
||||
if crdn<=dpos
|
||||
Tnew(2*Element(e,n)-1)=1.;
|
||||
Bound(2*Element(e,n)-1)=1.;
|
||||
end
|
||||
end
|
||||
end
|
||||
% Define Time Step
|
||||
dtime=0.1;
|
||||
tsteps=10;
|
||||
time=0.;
|
||||
% penalty term
|
||||
beta=80.;
|
||||
% Loop through time steps
|
||||
for ts=1:tsteps
|
||||
% Get interface velocity
|
||||
d(1)=dpos+delX;
|
||||
d(2)=dpos+3*delX/4;
|
||||
d(3)=dpos+delX/4;
|
||||
d(4)=dpos;
|
||||
for e=1:numElem
|
||||
crdn1=Node(Element(e,1),1);
|
||||
crdn2=Node(Element(e,2),1);
|
||||
for j=1:4
|
||||
if d(j)>=crdn1 & d(j)<crdn2
|
||||
elen=abs(crdn2-crdn1);
|
||||
ajacob=elen/2.;
|
||||
point=(d(j)-crdn1)/ajacob-1.;
|
||||
theta(1)=abs(crdn1-dpos)*sign(crdn1-dpos);
|
||||
theta(2)=abs(crdn2-dpos)*sign(crdn2-dpos);
|
||||
tmp1a=Tnew(Element(e,1)*2-1);
|
||||
tmp1b=Tnew(Element(e,1)*2);
|
||||
tmp2a=Tnew(Element(e,2)*2-1);
|
||||
tmp2b=Tnew(Element(e,2)*2);
|
||||
xi=point;
|
||||
gm(1)=(1.-xi)/2.;
|
||||
gm(3)=(1.+xi)/2.;
|
||||
term=theta(1)*gm(1)+theta(2)*gm(3);
|
||||
gm(2)=gm(1)*(abs(term)-abs(theta(1)));
|
||||
gm(4)=gm(3)*(abs(term)-abs(theta(2)));
|
||||
t(j)=gm(1)*tmp1a+gm(2)*tmp1b+gm(3)*tmp2a+gm(4)*tmp2b;
|
||||
end
|
||||
end
|
||||
end
|
||||
% vel=-0.1*(0.5/delX)*(2*t(1)+t(2)-t(3)-2*t(4))
|
||||
vel=0.0;
|
||||
% Update interface position
|
||||
dpos=dpos+vel*dtime;
|
||||
stored(ts+1)=dpos;
|
||||
K=zeros(numNodes*ndof,numNodes*ndof);
|
||||
M=zeros(numNodes*ndof,numNodes*ndof);
|
||||
pforce=zeros(numNodes*ndof,1);
|
||||
% Loop Through Elements
|
||||
for e=1:numElem
|
||||
Ke=zeros(4*ndof);
|
||||
Me=zeros(4*ndof);
|
||||
for icrd=1:4;
|
||||
crdnx(icrd)=Node(Element(e,icrd),1);
|
||||
crdny(icrd)=Node(Element(e,icrd),2);
|
||||
theta(icrd)=abs(crdnx(icrd)-dpos)*sign(crdnx(icrd)-dpos);
|
||||
end
|
||||
if sign(theta(1))~=sign(theta(2))
|
||||
% enriched element
|
||||
enr=8;
|
||||
% get interface position on element
|
||||
elen=abs(crdnx(2)-crdnx(1));
|
||||
frac=abs(dpos-crdnx(1))/elen;
|
||||
len1=2.*frac;
|
||||
len2=2.*(1.-frac);
|
||||
% devide element for sub integration
|
||||
mid1=-1+len1/2.;
|
||||
mid2=1-len2/2.;
|
||||
gx(1)=mid1-(len1/2.)/sqrt(3.);
|
||||
gx(2)=mid1+(len1/2.)/sqrt(3.);
|
||||
gx(3)=mid1+(len1/2.)/sqrt(3.);
|
||||
gx(4)=mid1-(len1/2.)/sqrt(3.);
|
||||
gx(5)=mid2-(len2/2.)/sqrt(3.);
|
||||
gx(6)=mid2+(len2/2.)/sqrt(3.);
|
||||
gx(7)=mid2+(len2/2.)/sqrt(3.);
|
||||
gx(8)=mid2-(len2/2.)/sqrt(3.);
|
||||
gpos=1/sqrt(3.);
|
||||
hx(1)=-gpos;
|
||||
hx(2)=-gpos;
|
||||
hx(3)=+gpos;
|
||||
hx(4)=+gpos;
|
||||
hx(5)=-gpos;
|
||||
hx(6)=-gpos;
|
||||
hx(7)=+gpos;
|
||||
hx(8)=+gpos;
|
||||
for iw=1:4
|
||||
w(iw)=frac/2.;
|
||||
w(iw+4)=(1.-frac)/2.;
|
||||
end
|
||||
else
|
||||
% regular element - fix extra dofs
|
||||
enr=4;
|
||||
gpos=1/sqrt(3.);
|
||||
gx(1)=-gpos;
|
||||
gx(2)=gpos;
|
||||
gx(3)=gpos;
|
||||
gx(4)=-gpos;
|
||||
hx(1)=-gpos;
|
||||
hx(2)=-gpos;
|
||||
hx(3)=gpos;
|
||||
hx(4)=gpos;
|
||||
for iw=1:4
|
||||
w(iw)=1.;
|
||||
end
|
||||
end
|
||||
% Loop Through Int Points
|
||||
for i=1:enr;
|
||||
g=gx(i);
|
||||
h=hx(i);
|
||||
phi(1)=0.25*(1.-g)*(1.-h);
|
||||
phi(3)=0.25*(1.+g)*(1.-h);
|
||||
phi(5)=0.25*(1.+g)*(1.+h);
|
||||
phi(7)=0.25*(1.-g)*(1.+h);
|
||||
iLS=theta(1)*phi(1)+theta(2)*phi(3)+theta(3)*phi(5)+theta(4)*phi(7);
|
||||
if iLS<0.
|
||||
cond=0.;
|
||||
spec=0.01;
|
||||
else
|
||||
cond=1.;
|
||||
spec=1.;
|
||||
end
|
||||
for iter=1:4
|
||||
phi(2*iter)=phi(2*iter-1)*(abs(iLS)-abs(theta(iter)));
|
||||
end
|
||||
phig(1)=0.25*-(1.-h);
|
||||
phig(3)=0.25*(1.-h);
|
||||
phig(5)=0.25*(1.+h);
|
||||
phig(7)=0.25*-(1.+h);
|
||||
phih(1)=0.25*-(1.-g);
|
||||
phih(3)=0.25*-(1.+g);
|
||||
phih(5)=0.25*(1.+g);
|
||||
phih(7)=0.25*(1.-g);
|
||||
diLSg=sign(iLS)*(phig(1)*theta(1)+phig(3)*theta(2)+phig(5)*theta(3)+phig(7)*theta(4));
|
||||
diLSh=sign(iLS)*(phih(1)*theta(1)+phih(3)*theta(2)+phih(5)*theta(3)+phih(7)*theta(4));
|
||||
for iter=1:4
|
||||
phig(2*iter)=phig(2*iter-1)*(abs(iLS)-abs(theta(iter)))+phi(2*iter-1)*diLSg;
|
||||
phih(2*iter)=phih(2*iter-1)*(abs(iLS)-abs(theta(iter)))+phi(2*iter-1)*diLSh;
|
||||
end
|
||||
rjac=zeros(2,2);
|
||||
for iter=1:4
|
||||
rjac(1,1)=rjac(1,1)+phig(2*iter-1)*crdnx(iter);
|
||||
rjac(1,2)=rjac(1,2)+phig(2*iter-1)*crdny(iter);
|
||||
rjac(2,1)=rjac(2,1)+phih(2*iter-1)*crdnx(iter);
|
||||
rjac(2,2)=rjac(2,2)+phih(2*iter-1)*crdny(iter);
|
||||
end
|
||||
djac=rjac(1,1)*rjac(2,2)-rjac(1,2)*rjac(2,1);
|
||||
rjaci(1,1)= rjac(2,2)/djac;
|
||||
rjaci(2,2)= rjac(1,1)/djac;
|
||||
rjaci(1,2)=-rjac(1,2)/djac;
|
||||
rjaci(2,1)=-rjac(2,1)/djac ;
|
||||
for iter=1:8
|
||||
phix(iter)=rjaci(1,1)*phig(iter)+rjaci(1,2)*phih(iter);
|
||||
phiy(iter)=rjaci(2,1)*phig(iter)+rjaci(2,2)*phih(iter);
|
||||
end
|
||||
we=w(i)*djac;
|
||||
Ke=Ke+we*cond*(phix'*phix+phiy'*phiy);
|
||||
Me=Me+(we*rho*spec*phi'*phi)/dtime;
|
||||
end
|
||||
% Add penalty term and get temp gradient on interface
|
||||
if enr==8;
|
||||
xi=2.*frac-1;
|
||||
yi=0.;
|
||||
gm(1)=0.25*(1.-xi)*(1.-yi);
|
||||
gm(3)=0.25*(1.+xi)*(1.-yi);
|
||||
gm(5)=0.25*(1.+xi)*(1.+yi);
|
||||
gm(7)=0.25*(1.-xi)*(1.+yi);
|
||||
gm(2)=gm(1)*(-abs(theta(1)));
|
||||
gm(4)=gm(3)*(-abs(theta(2)));
|
||||
gm(6)=gm(5)*(-abs(theta(3)));
|
||||
gm(8)=gm(7)*(-abs(theta(4)));
|
||||
pen=beta*(gm'*gm);
|
||||
pfL=beta*1.*gm';
|
||||
Ke=Ke+pen;
|
||||
else
|
||||
pen=zeros(8);
|
||||
pfL=zeros(8,1);
|
||||
end
|
||||
% Assemble Global Matrices
|
||||
gnum(1)=2*Element(e,1)-1;
|
||||
gnum(2)=2*Element(e,2)-1;
|
||||
gnum(3)=2*Element(e,3)-1;
|
||||
gnum(4)=2*Element(e,4)-1;
|
||||
for i=1:4;
|
||||
for j=1:4;
|
||||
K(gnum(j),gnum(i))=K(gnum(j),gnum(i))+Ke(2*j-1,2*i-1);
|
||||
K(gnum(j)+1,gnum(i)+1)=K(gnum(j)+1,gnum(i)+1)+Ke(2*j,2*i);
|
||||
M(gnum(j),gnum(i))=M(gnum(j),gnum(i))+Me(2*j-1,2*i-1);
|
||||
M(gnum(j)+1,gnum(i)+1)=M(gnum(j)+1,gnum(i)+1)+Me(2*j,2*i);
|
||||
end
|
||||
end
|
||||
for i=1:4;
|
||||
pforce(gnum(i))=pforce(gnum(i))+pfL(2*i-1);
|
||||
pforce(gnum(i)+1)=pforce(gnum(i)+1)+pfL(2*i);
|
||||
end
|
||||
end
|
||||
%Remove inactive DOFs(Reduce Matrices)
|
||||
RHS=M*Tnew;
|
||||
A=K+M;
|
||||
Sub=A*Bound;
|
||||
iindex=0;
|
||||
for i=1:ndof*numNodes;
|
||||
if Bound(i)==0.;
|
||||
iindex=iindex+1;
|
||||
RHSred(iindex)=RHS(i)-Sub(i)+pforce(i);
|
||||
jindex=0;
|
||||
for j=1:ndof*numNodes;
|
||||
if Bound(j)==0.;
|
||||
jindex=jindex+1;
|
||||
Ared(iindex,jindex)=A(i,j);
|
||||
end
|
||||
end
|
||||
end
|
||||
end
|
||||
%Solve
|
||||
StiffI=Ared^-1;
|
||||
Tnewr=(Ared^-1)*RHSred';
|
||||
iindex=0;
|
||||
for i=1:ndof*numNodes;
|
||||
if Bound(i)==0.;
|
||||
iindex=iindex+1;
|
||||
Tnew(i)=Tnewr(iindex);
|
||||
end
|
||||
end
|
||||
Tnew
|
||||
end
|
||||
stored';
|
||||
269
Unpublished/XFEM/Other/FESolveX2DLS.m
Normal file
269
Unpublished/XFEM/Other/FESolveX2DLS.m
Normal file
|
|
@ -0,0 +1,269 @@
|
|||
function [] = FESolveX2DLS()
|
||||
% MATLAB based 2-D XFEM Solver
|
||||
% J. Grogan (2012)
|
||||
clear all
|
||||
% Define Mesh
|
||||
NumX=3;
|
||||
NumY=1;
|
||||
delX=1.;
|
||||
delY=1.;
|
||||
for j=1:NumY+1
|
||||
for i=1:NumX+1
|
||||
index=i+(NumX+1)*(j-1);
|
||||
Node(index,1)=single((i-1.))*delX;
|
||||
Node(index,2)=single((j-1.))*delY;
|
||||
end
|
||||
end
|
||||
numNodes=(NumX+1)*(NumY+1);
|
||||
for j=1:NumY
|
||||
for i=1:NumX
|
||||
index=i+NumX*(j-1);
|
||||
Element(index,1)=i+(NumX+1)*(j-1);
|
||||
Element(index,2)=i+(NumX+1)*(j-1)+1;
|
||||
Element(index,3)=i+(NumX+1)*(j)+1;
|
||||
Element(index,4)=i+(NumX+1)*(j);
|
||||
end
|
||||
end
|
||||
numElem=(NumX)*(NumY);
|
||||
% dofs per node
|
||||
ndof=2;
|
||||
% Define Section Properties
|
||||
rho=1.;
|
||||
% initial interface position
|
||||
dpos=0.1;
|
||||
% Initial temperatures
|
||||
Tnew=zeros(numNodes*2,1);
|
||||
Bound=zeros(numNodes*2,1);
|
||||
stored(1)=dpos;
|
||||
for e=1:numElem
|
||||
for n=1:4
|
||||
crdn=Node(Element(e,n),1);
|
||||
if crdn<=dpos
|
||||
Tnew(2*Element(e,n)-1)=1.;
|
||||
Bound(2*Element(e,n)-1)=1.;
|
||||
end
|
||||
end
|
||||
end
|
||||
% Define Time Step
|
||||
dtime=0.1;
|
||||
tsteps=20;
|
||||
time=0.;
|
||||
% penalty term
|
||||
beta=80.;
|
||||
% Loop through time steps
|
||||
for ts=1:tsteps
|
||||
% Get interface velocity
|
||||
d(1)=dpos+delX;
|
||||
d(2)=dpos+3*delX/4;
|
||||
d(3)=dpos+delX/4;
|
||||
d(4)=dpos;
|
||||
for e=1:numElem
|
||||
crdn1=Node(Element(e,1),1);
|
||||
crdn2=Node(Element(e,2),1);
|
||||
for j=1:4
|
||||
if d(j)>=crdn1 & d(j)<crdn2
|
||||
elen=abs(crdn2-crdn1);
|
||||
ajacob=elen/2.;
|
||||
point=(d(j)-crdn1)/ajacob-1.;
|
||||
theta(1)=abs(crdn1-dpos)*sign(crdn1-dpos);
|
||||
theta(2)=abs(crdn2-dpos)*sign(crdn2-dpos);
|
||||
tmp1a=Tnew(Element(e,1)*2-1);
|
||||
tmp1b=Tnew(Element(e,1)*2);
|
||||
tmp2a=Tnew(Element(e,2)*2-1);
|
||||
tmp2b=Tnew(Element(e,2)*2);
|
||||
xi=point;
|
||||
gm(1)=(1.-xi)/2.;
|
||||
gm(3)=(1.+xi)/2.;
|
||||
term=theta(1)*gm(1)+theta(2)*gm(3);
|
||||
gm(2)=gm(1)*(abs(term)-abs(theta(1)));
|
||||
gm(4)=gm(3)*(abs(term)-abs(theta(2)));
|
||||
t(j)=gm(1)*tmp1a+gm(2)*tmp1b+gm(3)*tmp2a+gm(4)*tmp2b;
|
||||
end
|
||||
end
|
||||
end
|
||||
% vel=-0.1*(0.5/delX)*(2*t(1)+t(2)-t(3)-2*t(4))
|
||||
vel=0.0;
|
||||
% Update interface position
|
||||
dpos=dpos+vel*dtime;
|
||||
stored(ts+1)=dpos;
|
||||
K=zeros(numNodes*ndof,numNodes*ndof);
|
||||
M=zeros(numNodes*ndof,numNodes*ndof);
|
||||
pforce=zeros(numNodes*ndof,1);
|
||||
% Loop Through Elements
|
||||
for e=1:numElem
|
||||
Ke=zeros(4*ndof);
|
||||
Me=zeros(4*ndof);
|
||||
for icrd=1:4;
|
||||
crdnx(icrd)=Node(Element(e,icrd),1);
|
||||
crdny(icrd)=Node(Element(e,icrd),2);
|
||||
theta(icrd)=abs(crdnx(icrd)-dpos)*sign(crdnx(icrd)-dpos);
|
||||
end
|
||||
if sign(theta(1))~=sign(theta(2))
|
||||
% enriched element
|
||||
enr=8;
|
||||
% get interface position on element
|
||||
elen=abs(crdnx(2)-crdnx(1));
|
||||
frac=abs(dpos-crdnx(1))/elen;
|
||||
len1=2.*frac;
|
||||
len2=2.*(1.-frac);
|
||||
% devide element for sub integration
|
||||
mid1=-1+len1/2.;
|
||||
mid2=1-len2/2.;
|
||||
gx(1)=mid1-(len1/2.)/sqrt(3.);
|
||||
gx(2)=mid1+(len1/2.)/sqrt(3.);
|
||||
gx(3)=mid1+(len1/2.)/sqrt(3.);
|
||||
gx(4)=mid1-(len1/2.)/sqrt(3.);
|
||||
gx(5)=mid2-(len2/2.)/sqrt(3.);
|
||||
gx(6)=mid2+(len2/2.)/sqrt(3.);
|
||||
gx(7)=mid2+(len2/2.)/sqrt(3.);
|
||||
gx(8)=mid2-(len2/2.)/sqrt(3.);
|
||||
gpos=1/sqrt(3.);
|
||||
hx(1)=-gpos;
|
||||
hx(2)=-gpos;
|
||||
hx(3)=+gpos;
|
||||
hx(4)=+gpos;
|
||||
hx(5)=-gpos;
|
||||
hx(6)=-gpos;
|
||||
hx(7)=+gpos;
|
||||
hx(8)=+gpos;
|
||||
for iw=1:4
|
||||
w(iw)=frac/2.;
|
||||
w(iw+4)=(1.-frac)/2.;
|
||||
end
|
||||
else
|
||||
% regular element - fix extra dofs
|
||||
enr=4;
|
||||
gpos=1/sqrt(3.);
|
||||
gx(1)=-gpos;
|
||||
gx(2)=gpos;
|
||||
gx(3)=gpos;
|
||||
gx(4)=-gpos;
|
||||
hx(1)=-gpos;
|
||||
hx(2)=-gpos;
|
||||
hx(3)=gpos;
|
||||
hx(4)=gpos;
|
||||
for iw=1:4
|
||||
w(iw)=1.;
|
||||
end
|
||||
end
|
||||
% Loop Through Int Points
|
||||
for i=1:enr;
|
||||
g=gx(i);
|
||||
h=hx(i);
|
||||
phi(1)=0.25*(1.-g)*(1.-h);
|
||||
phi(3)=0.25*(1.+g)*(1.-h);
|
||||
phi(5)=0.25*(1.+g)*(1.+h);
|
||||
phi(7)=0.25*(1.-g)*(1.+h);
|
||||
iLS=theta(1)*phi(1)+theta(2)*phi(3)+theta(3)*phi(5)+theta(4)*phi(7);
|
||||
if iLS<0.
|
||||
cond=0.;
|
||||
spec=0.01;
|
||||
else
|
||||
cond=1.;
|
||||
spec=1.;
|
||||
end
|
||||
for iter=1:4
|
||||
phi(2*iter)=phi(2*iter-1)*(abs(iLS)-abs(theta(iter)));
|
||||
end
|
||||
phig(1)=0.25*-(1.-h);
|
||||
phig(3)=0.25*(1.-h);
|
||||
phig(5)=0.25*(1.+h);
|
||||
phig(7)=0.25*-(1.+h);
|
||||
phih(1)=0.25*-(1.-g);
|
||||
phih(3)=0.25*-(1.+g);
|
||||
phih(5)=0.25*(1.+g);
|
||||
phih(7)=0.25*(1.-g);
|
||||
diLSg=sign(iLS)*(phig(1)*theta(1)+phig(3)*theta(2)+phig(5)*theta(3)+phig(7)*theta(4));
|
||||
diLSh=sign(iLS)*(phih(1)*theta(1)+phih(3)*theta(2)+phih(5)*theta(3)+phih(7)*theta(4));
|
||||
for iter=1:4
|
||||
phig(2*iter)=phig(2*iter-1)*(abs(iLS)-abs(theta(iter)))+phi(2*iter-1)*diLSg;
|
||||
phih(2*iter)=phih(2*iter-1)*(abs(iLS)-abs(theta(iter)))+phi(2*iter-1)*diLSh;
|
||||
end
|
||||
rjac=zeros(2,2);
|
||||
for iter=1:4
|
||||
rjac(1,1)=rjac(1,1)+phig(2*iter-1)*crdnx(iter);
|
||||
rjac(1,2)=rjac(1,2)+phig(2*iter-1)*crdny(iter);
|
||||
rjac(2,1)=rjac(2,1)+phih(2*iter-1)*crdnx(iter);
|
||||
rjac(2,2)=rjac(2,2)+phih(2*iter-1)*crdny(iter);
|
||||
end
|
||||
djac=rjac(1,1)*rjac(2,2)-rjac(1,2)*rjac(2,1);
|
||||
rjaci(1,1)= rjac(2,2)/djac;
|
||||
rjaci(2,2)= rjac(1,1)/djac;
|
||||
rjaci(1,2)=-rjac(1,2)/djac;
|
||||
rjaci(2,1)=-rjac(2,1)/djac ;
|
||||
for iter=1:8
|
||||
phix(iter)=rjaci(1,1)*phig(iter)+rjaci(1,2)*phih(iter);
|
||||
phiy(iter)=rjaci(2,1)*phig(iter)+rjaci(2,2)*phih(iter);
|
||||
end
|
||||
we=w(i)*djac;
|
||||
Ke=Ke+we*cond*(phix'*phix+phiy'*phiy);
|
||||
Me=Me+(we*rho*spec*phi'*phi)/dtime;
|
||||
end
|
||||
% Add penalty term and get temp gradient on interface
|
||||
if enr==8;
|
||||
xi=2.*frac-1;
|
||||
yi=0.;
|
||||
gm(1)=0.25*(1.-xi)*(1.-yi);
|
||||
gm(3)=0.25*(1.+xi)*(1.-yi);
|
||||
gm(5)=0.25*(1.+xi)*(1.+yi);
|
||||
gm(7)=0.25*(1.-xi)*(1.+yi);
|
||||
gm(2)=gm(1)*(-abs(theta(1)));
|
||||
gm(4)=gm(3)*(-abs(theta(2)));
|
||||
gm(6)=gm(5)*(-abs(theta(3)));
|
||||
gm(8)=gm(7)*(-abs(theta(4)));
|
||||
pen=beta*(gm'*gm);
|
||||
pfL=beta*1.*gm';
|
||||
Ke=Ke+pen;
|
||||
else
|
||||
pen=zeros(8);
|
||||
pfL=zeros(8,1);
|
||||
end
|
||||
% Assemble Global Matrices
|
||||
gnum(1)=2*Element(e,1)-1;
|
||||
gnum(2)=2*Element(e,2)-1;
|
||||
gnum(3)=2*Element(e,3)-1;
|
||||
gnum(4)=2*Element(e,4)-1;
|
||||
for i=1:4;
|
||||
for j=1:4;
|
||||
K(gnum(j),gnum(i))=K(gnum(j),gnum(i))+Ke(2*j-1,2*i-1);
|
||||
K(gnum(j)+1,gnum(i)+1)=K(gnum(j)+1,gnum(i)+1)+Ke(2*j,2*i);
|
||||
M(gnum(j),gnum(i))=M(gnum(j),gnum(i))+Me(2*j-1,2*i-1);
|
||||
M(gnum(j)+1,gnum(i)+1)=M(gnum(j)+1,gnum(i)+1)+Me(2*j,2*i);
|
||||
end
|
||||
end
|
||||
for i=1:4;
|
||||
pforce(gnum(i))=pforce(gnum(i))+pfL(2*i-1);
|
||||
pforce(gnum(i)+1)=pforce(gnum(i)+1)+pfL(2*i);
|
||||
end
|
||||
end
|
||||
%Remove inactive DOFs(Reduce Matrices)
|
||||
RHS=M*Tnew;
|
||||
A=K+M;
|
||||
Sub=A*Bound;
|
||||
iindex=0;
|
||||
for i=1:ndof*numNodes;
|
||||
if Bound(i)==0.;
|
||||
iindex=iindex+1;
|
||||
RHSred(iindex)=RHS(i)-Sub(i)+pforce(i);
|
||||
jindex=0;
|
||||
for j=1:ndof*numNodes;
|
||||
if Bound(j)==0.;
|
||||
jindex=jindex+1;
|
||||
Ared(iindex,jindex)=A(i,j);
|
||||
end
|
||||
end
|
||||
end
|
||||
end
|
||||
%Solve
|
||||
StiffI=Ared^-1;
|
||||
Tnewr=(Ared^-1)*RHSred';
|
||||
iindex=0;
|
||||
for i=1:ndof*numNodes;
|
||||
if Bound(i)==0.;
|
||||
iindex=iindex+1;
|
||||
Tnew(i)=Tnewr(iindex);
|
||||
end
|
||||
end
|
||||
Tnew
|
||||
end
|
||||
stored'
|
||||
199
Unpublished/XFEM/Other/FESolveXT.m
Normal file
199
Unpublished/XFEM/Other/FESolveXT.m
Normal file
|
|
@ -0,0 +1,199 @@
|
|||
function [] = FESolveXT()
|
||||
% MATLAB based 1-D XFEM Solver
|
||||
% J. Grogan (2012)
|
||||
clear all
|
||||
% Define Geometry
|
||||
len=10.;
|
||||
% Define Section Properties
|
||||
rho=1.;
|
||||
% Generate Mesh
|
||||
numElem=10;
|
||||
charlen=len/numElem;
|
||||
ndCoords=linspace(0,len,numElem+1);
|
||||
numNodes=size(ndCoords,2);
|
||||
indx=1:numElem;
|
||||
elemNodes(:,1)=indx;
|
||||
elemNodes(:,2)=indx+1;
|
||||
% dofs per node
|
||||
ndof=2;
|
||||
% initial interface position
|
||||
dpos=4.6;
|
||||
% Initial temperatures
|
||||
Tnew=zeros(numNodes*2,1);
|
||||
Bound=zeros(numNodes*2,1);
|
||||
%storage
|
||||
stored(1)=dpos;
|
||||
for e=1:numElem
|
||||
for n=1:2
|
||||
crdn1=ndCoords(elemNodes(e,n));
|
||||
if crdn1<=dpos
|
||||
Tnew(2*elemNodes(e,n)-1)=1.;
|
||||
Bound(2*elemNodes(e,n)-1)=1.;
|
||||
end
|
||||
end
|
||||
end
|
||||
% Define Time Step
|
||||
dtime=0.01;
|
||||
tsteps=10;
|
||||
time=0.;
|
||||
% penalty term
|
||||
beta=50.;
|
||||
% Loop through time steps
|
||||
for ts=1:tsteps
|
||||
% Get interface velocity
|
||||
d(1)=dpos+charlen;
|
||||
d(2)=dpos+3*charlen/4;
|
||||
d(3)=dpos+charlen/4;
|
||||
d(4)=dpos;
|
||||
for e=1:numElem
|
||||
crdn1=ndCoords(elemNodes(e,1));
|
||||
crdn2=ndCoords(elemNodes(e,2));
|
||||
for j=1:4
|
||||
if d(j)>=crdn1 & d(j)<crdn2
|
||||
elen=abs(crdn2-crdn1);
|
||||
ajacob=elen/2.;
|
||||
point=(d(j)-crdn1)/ajacob-1.;
|
||||
theta(1)=abs(crdn1-dpos)*sign(crdn1-dpos);
|
||||
theta(2)=abs(crdn2-dpos)*sign(crdn2-dpos);
|
||||
tmp1a=Tnew(elemNodes(e,1)*2-1);
|
||||
tmp1b=Tnew(elemNodes(e,1)*2);
|
||||
tmp2a=Tnew(elemNodes(e,2)*2-1);
|
||||
tmp2b=Tnew(elemNodes(e,2)*2);
|
||||
xi=point;
|
||||
gm(1)=(1.-xi)/2.;
|
||||
gm(3)=(1.+xi)/2.;
|
||||
term=theta(1)*gm(1)+theta(2)*gm(3);
|
||||
gm(2)=gm(1)*(abs(term)-abs(theta(1)));
|
||||
gm(4)=gm(3)*(abs(term)-abs(theta(2)));
|
||||
t(j)=gm(1)*tmp1a+gm(2)*tmp1b+gm(3)*tmp2a+gm(4)*tmp2b;
|
||||
end
|
||||
end
|
||||
end
|
||||
vel=1.*(0.5/charlen)*(2*t(1)+t(2)-t(3)-2*t(4));
|
||||
vel=0.
|
||||
% Update interface position
|
||||
dpos=dpos+vel*dtime;
|
||||
stored(ts+1)=dpos;
|
||||
K=zeros(numNodes*ndof,numNodes*ndof);
|
||||
M=zeros(numNodes*ndof,numNodes*ndof);
|
||||
pforce=zeros(numNodes*ndof,1);
|
||||
% Loop Through Elements
|
||||
for e=1:numElem
|
||||
Ke=zeros(2*ndof);
|
||||
Me=zeros(2*ndof);
|
||||
crdn1=ndCoords(elemNodes(e,1));
|
||||
crdn2=ndCoords(elemNodes(e,2));
|
||||
theta(1)=abs(crdn1-dpos)*sign(crdn1-dpos);
|
||||
theta(2)=abs(crdn2-dpos)*sign(crdn2-dpos);
|
||||
enr=2;
|
||||
elen=abs(crdn2-crdn1);
|
||||
ajacob=elen/2.;
|
||||
if sign(theta(1))~=sign(theta(2))
|
||||
% enriched element
|
||||
enr=4;
|
||||
% get interface position on element
|
||||
point=(dpos-crdn1)/ajacob-1.;
|
||||
% devide element for sub integration
|
||||
len1=abs(-point-1.);
|
||||
len2=abs(1.-point);
|
||||
mid1=-1+len1/2.;
|
||||
mid2=1-len2/2.;
|
||||
gpx(1)=-(len1/2.)/sqrt(3.)+mid1;
|
||||
gpx(2)=(len1/2.)/sqrt(3.)+mid1;
|
||||
gpx(3)=-(len2/2.)/sqrt(3.)+mid2;
|
||||
gpx(4)=(len2/2.)/sqrt(3.)+mid2;
|
||||
w(1)=(len1/2.);
|
||||
w(2)=(len1/2.);
|
||||
w(3)=(len2/2.);
|
||||
w(4)=(len2/2.);
|
||||
else
|
||||
% regular element - fix extra dofs
|
||||
gpx(1)=-1/sqrt(3.);
|
||||
gpx(2)=1/sqrt(3.);
|
||||
w(1)=1.;
|
||||
w(2)=1.;
|
||||
end
|
||||
% Loop Through Int Points
|
||||
for i=1:enr;
|
||||
c=gpx(i);
|
||||
phi(1)=(1.-c)/2.;
|
||||
phi(3)=(1.+c)/2.;
|
||||
term=theta(1)*phi(1)+theta(2)*phi(3);
|
||||
if term<0
|
||||
cond=0.;
|
||||
spec=0.01;
|
||||
else
|
||||
cond=1.;
|
||||
spec=1.;
|
||||
end
|
||||
phi(2)=phi(1)*(abs(term)-abs(theta(1)));
|
||||
phi(4)=phi(3)*(abs(term)-abs(theta(2)));
|
||||
phic(1)=-0.5;
|
||||
phic(3)=0.5;
|
||||
dterm=sign(term)*(phic(1)*theta(1)+phic(3)*theta(2));
|
||||
phic(2)=phic(1)*(abs(term)-abs(theta(1)))+phi(1)*dterm;
|
||||
phic(4)=phic(3)*(abs(term)-abs(theta(2)))+phi(3)*dterm;
|
||||
phix(1)=phic(1)/ajacob;
|
||||
phix(2)=phic(2)/ajacob;
|
||||
phix(3)=phic(3)/ajacob;
|
||||
phix(4)=phic(4)/ajacob;
|
||||
we=ajacob*w(i);
|
||||
Ke=Ke+we*cond*phix'*phix;
|
||||
Me=Me+(we*rho*spec*phi'*phi)/dtime;
|
||||
end
|
||||
% Add penalty term and get temp gradient on interface
|
||||
if enr==4;
|
||||
xi=point;
|
||||
gm(1)=(1.-xi)/2.;
|
||||
gm(3)=(1.+xi)/2.;
|
||||
term=theta(1)*gm(1)+theta(2)*gm(3);
|
||||
gm(2)=gm(1)*(abs(term)-abs(theta(1)));
|
||||
gm(4)=gm(3)*(abs(term)-abs(theta(2)));
|
||||
tpos=gm(1)*Tnew(1)+gm(2)*Tnew(2)+gm(3)*Tnew(3)+gm(4)*Tnew(4);
|
||||
pen=beta*(gm'*gm);
|
||||
pfL=beta*1*gm';
|
||||
Ke=Ke+pen;
|
||||
else
|
||||
pen=zeros(4);
|
||||
pfL=zeros(4,1);
|
||||
end
|
||||
% Assemble Global Matrices
|
||||
gnum=2.*elemNodes(e,1)-1.;
|
||||
for i=1:4;
|
||||
for j=1:4;
|
||||
K(gnum+j-1,gnum+i-1)=K(gnum+j-1,gnum+i-1)+Ke(j,i);
|
||||
M(gnum+j-1,gnum+i-1)=M(gnum+j-1,gnum+i-1)+Me(j,i);
|
||||
end
|
||||
pforce(gnum+i-1)=pforce(gnum+i-1)+pfL(i);
|
||||
end
|
||||
end
|
||||
%Remove inactive DOFs(Reduce Matrices)
|
||||
RHS=M*Tnew;
|
||||
A=K+M;
|
||||
Sub=A*Bound;
|
||||
iindex=0;
|
||||
for i=1:ndof*numNodes;
|
||||
if Bound(i)==0.;
|
||||
iindex=iindex+1;
|
||||
RHSred(iindex)=RHS(i)-Sub(i)+pforce(i);
|
||||
jindex=0;
|
||||
for j=1:ndof*numNodes;
|
||||
if Bound(j)==0.;
|
||||
jindex=jindex+1;
|
||||
Ared(iindex,jindex)=A(i,j);
|
||||
end
|
||||
end
|
||||
end
|
||||
end
|
||||
%Solve
|
||||
Tnewr=(Ared^-1)*RHSred';
|
||||
iindex=0;
|
||||
for i=1:ndof*numNodes;
|
||||
if Bound(i)==0.;
|
||||
iindex=iindex+1;
|
||||
Tnew(i)=Tnewr(iindex);
|
||||
end
|
||||
end
|
||||
Tnew
|
||||
end
|
||||
stored'
|
||||
269
Unpublished/XFEM/Other/FESolveXT2.m
Normal file
269
Unpublished/XFEM/Other/FESolveXT2.m
Normal file
|
|
@ -0,0 +1,269 @@
|
|||
function [] = FESolveXT2()
|
||||
% MATLAB based 1-D XFEM Solver
|
||||
% J. Grogan (2012)
|
||||
clear all
|
||||
% Define Geometry
|
||||
len=1.;
|
||||
% Define Section Properties
|
||||
rho=1.;
|
||||
% Generate Mesh
|
||||
numElem=16;
|
||||
charlen=len/numElem;
|
||||
ndCoords=linspace(0,len,numElem+1);
|
||||
numNodes=size(ndCoords,2);
|
||||
indx=1:numElem;
|
||||
elemNodes(:,1)=indx;
|
||||
elemNodes(:,2)=indx+1;
|
||||
% dofs per node
|
||||
ndof=2;
|
||||
% initial interface position
|
||||
dpos=0.4;
|
||||
% Initial temperatures
|
||||
Tnew=zeros(numNodes*2,1);
|
||||
Bound=zeros(numNodes*2,1);
|
||||
%storage
|
||||
stored(1)=dpos;
|
||||
for e=1:numElem
|
||||
for n=1:2
|
||||
crdn1=ndCoords(elemNodes(e,n));
|
||||
if crdn1<=dpos
|
||||
Tnew(2*elemNodes(e,n)-1)=1.;
|
||||
end
|
||||
end
|
||||
end
|
||||
Bound(1)=1.;
|
||||
% Define Time Step
|
||||
dtime=0.001;
|
||||
tsteps=100;
|
||||
time=0.;
|
||||
% penalty term
|
||||
beta=100.;
|
||||
% Loop through time steps
|
||||
for ts=1:tsteps
|
||||
eNodes=zeros(2*numNodes,1);
|
||||
% Get interface velocity
|
||||
d(1)=dpos+charlen;
|
||||
d(2)=dpos+3*charlen/4;
|
||||
d(3)=dpos+charlen/4;
|
||||
d(4)=dpos;
|
||||
for e=1:numElem
|
||||
crdn1=ndCoords(elemNodes(e,1));
|
||||
crdn2=ndCoords(elemNodes(e,2));
|
||||
for j=1:4
|
||||
if d(j)>=crdn1 && d(j)<crdn2
|
||||
elen=abs(crdn2-crdn1);
|
||||
ajacob=elen/2.;
|
||||
point=(d(j)-crdn1)/ajacob-1.;
|
||||
theta(1)=abs(crdn1-dpos)*sign(crdn1-dpos);
|
||||
theta(2)=abs(crdn2-dpos)*sign(crdn2-dpos);
|
||||
tmp1a=Tnew(elemNodes(e,1)*2-1);
|
||||
tmp1b=Tnew(elemNodes(e,1)*2);
|
||||
tmp2a=Tnew(elemNodes(e,2)*2-1);
|
||||
tmp2b=Tnew(elemNodes(e,2)*2);
|
||||
xi=point;
|
||||
gm(1)=(1.-xi)/2.;
|
||||
gm(3)=(1.+xi)/2.;
|
||||
term=theta(1)*gm(1)+theta(2)*gm(3);
|
||||
gm(2)=gm(1)*(abs(term)-abs(theta(1)));
|
||||
gm(4)=gm(3)*(abs(term)-abs(theta(2)));
|
||||
t(j)=gm(1)*tmp1a+gm(2)*tmp1b+gm(3)*tmp2a+gm(4)*tmp2b;
|
||||
end
|
||||
end
|
||||
end
|
||||
vel=0.5*(0.5/charlen)*(2*t(1)+t(2)-t(3)-2*t(4));
|
||||
% Update interface position
|
||||
dpos=dpos+vel*dtime;
|
||||
stored(ts+1)=dpos;
|
||||
K=zeros(numNodes*ndof,numNodes*ndof);
|
||||
M=zeros(numNodes*ndof,numNodes*ndof);
|
||||
pforce=zeros(numNodes*ndof,1);
|
||||
% Loop Through Elements
|
||||
for e=1:numElem
|
||||
Ke=zeros(2*ndof);
|
||||
Me=zeros(2*ndof);
|
||||
crdn1=ndCoords(elemNodes(e,1));
|
||||
crdn2=ndCoords(elemNodes(e,2));
|
||||
theta(1)=abs(crdn1-dpos)*sign(crdn1-dpos);
|
||||
theta(2)=abs(crdn2-dpos)*sign(crdn2-dpos);
|
||||
enr=2;
|
||||
elen=abs(crdn2-crdn1);
|
||||
ajacob=elen/2.;
|
||||
if sign(theta(1))~=sign(theta(2))
|
||||
% enriched element
|
||||
eNodes(2*elemNodes(e,1))=1;
|
||||
eNodes(2*elemNodes(e,2))=1;
|
||||
enr=4;
|
||||
% get interface position on element
|
||||
point=(dpos-crdn1)/ajacob-1.;
|
||||
% devide element for sub integration
|
||||
len1=abs(-point-1.);
|
||||
len2=abs(1.-point);
|
||||
mid1=-1+len1/2.;
|
||||
mid2=1-len2/2.;
|
||||
gpx(1)=-(len1/2.)/sqrt(3.)+mid1;
|
||||
gpx(2)=(len1/2.)/sqrt(3.)+mid1;
|
||||
gpx(3)=-(len2/2.)/sqrt(3.)+mid2;
|
||||
gpx(4)=(len2/2.)/sqrt(3.)+mid2;
|
||||
w(1)=(len1/2.);
|
||||
w(2)=(len1/2.);
|
||||
w(3)=(len2/2.);
|
||||
w(4)=(len2/2.);
|
||||
else
|
||||
% regular element - fix extra dofs
|
||||
gpx(1)=-1/sqrt(3.);
|
||||
gpx(2)=1/sqrt(3.);
|
||||
w(1)=1.;
|
||||
w(2)=1.;
|
||||
end
|
||||
% Loop Through Int Points
|
||||
for i=1:enr;
|
||||
c=gpx(i);
|
||||
phi(1)=(1.-c)/2.;
|
||||
phi(3)=(1.+c)/2.;
|
||||
term=theta(1)*phi(1)+theta(2)*phi(3);
|
||||
% if term<0
|
||||
% cond=0.00;
|
||||
% spec=0.001;
|
||||
% else
|
||||
cond=1.;
|
||||
spec=1.;
|
||||
% end
|
||||
if enr==4
|
||||
phi(2)=phi(1)*(abs(term)-abs(theta(1)));
|
||||
phi(4)=phi(3)*(abs(term)-abs(theta(2)));
|
||||
else
|
||||
phi(2)=0.0;
|
||||
phi(4)=0.0;
|
||||
end
|
||||
phic(1)=-0.5;
|
||||
phic(3)=0.5;
|
||||
dterm=sign(term)*(phic(1)*theta(1)+phic(3)*theta(2));
|
||||
if enr==4
|
||||
phic(2)=phic(1)*(abs(term)-abs(theta(1)))+phi(1)*dterm;
|
||||
phic(4)=phic(3)*(abs(term)-abs(theta(2)))+phi(3)*dterm;
|
||||
else
|
||||
phic(2)=0.0;
|
||||
phic(4)=0.0;
|
||||
end
|
||||
phix(1)=phic(1)/ajacob;
|
||||
phix(2)=phic(2)/ajacob;
|
||||
phix(3)=phic(3)/ajacob;
|
||||
phix(4)=phic(4)/ajacob;
|
||||
we=ajacob*w(i);
|
||||
Ke=Ke+we*cond*phix'*phix;
|
||||
Me=Me+(we*rho*spec*phi'*phi)/dtime;
|
||||
end
|
||||
if enr==5;
|
||||
Ke(1,2)=0.;
|
||||
Me(1,2)=0.;
|
||||
Ke(2,1)=0.;
|
||||
Me(2,1)=0.;
|
||||
Ke(1,4)=0.;
|
||||
Me(1,4)=0.;
|
||||
Ke(4,1)=0.;
|
||||
Me(4,1)=0.;
|
||||
Ke(3,2)=0.;
|
||||
Me(3,2)=0.;
|
||||
Ke(2,3)=0.;
|
||||
Me(2,3)=0.;
|
||||
Ke(4,3)=0.;
|
||||
Me(4,3)=0.;
|
||||
Ke(3,4)=0.;
|
||||
Me(3,4)=0.;
|
||||
end
|
||||
% Add penalty term and get temp gradient on interface
|
||||
if enr==4;
|
||||
xi=point;
|
||||
gm(1)=(1.-xi)/2.;
|
||||
gm(3)=(1.+xi)/2.;
|
||||
term=theta(1)*gm(1)+theta(2)*gm(3);
|
||||
gm(2)=gm(1)*(abs(term)-abs(theta(1)));
|
||||
gm(4)=gm(3)*(abs(term)-abs(theta(2)));
|
||||
pen=beta*(gm'*gm);
|
||||
pfL=beta*1*gm';
|
||||
Ke=Ke+pen;
|
||||
else
|
||||
pen=zeros(4);
|
||||
pfL=zeros(4,1);
|
||||
end
|
||||
Ke;
|
||||
Me;
|
||||
% Assemble Global Matrices
|
||||
gnum=2.*elemNodes(e,1)-1.;
|
||||
for i=1:4;
|
||||
for j=1:4;
|
||||
K(gnum+j-1,gnum+i-1)=K(gnum+j-1,gnum+i-1)+Ke(j,i);
|
||||
M(gnum+j-1,gnum+i-1)=M(gnum+j-1,gnum+i-1)+Me(j,i);
|
||||
end
|
||||
pforce(gnum+i-1)=pforce(gnum+i-1)+pfL(i);
|
||||
end
|
||||
end
|
||||
%Remove NON-ENHANCED DOFs(Reduce Matrices)
|
||||
iindex=0.;
|
||||
for i=1:ndof*numNodes;
|
||||
check=0;
|
||||
if mod(i,2)==0 && eNodes(i)~=1
|
||||
check=1;
|
||||
end
|
||||
if check==0
|
||||
iindex=iindex+1;
|
||||
TR1(iindex)=Tnew(i);
|
||||
BR1(iindex)=Bound(i);
|
||||
pforceR1(iindex)=pforce(i);
|
||||
jindex=0;
|
||||
for j=1:ndof*numNodes;
|
||||
check=0;
|
||||
if mod(j,2)==0 && eNodes(j)~=1
|
||||
check=1;
|
||||
end
|
||||
if check==0
|
||||
jindex=jindex+1;
|
||||
MR1(iindex,jindex)=M(i,j);
|
||||
KR1(iindex,jindex)=K(i,j);
|
||||
end
|
||||
end
|
||||
end
|
||||
end
|
||||
AR1=KR1+MR1;
|
||||
SubR1=AR1*BR1';
|
||||
RHSR1=MR1*TR1'-SubR1+pforceR1';
|
||||
% Apply Boundary Conditions
|
||||
Biindex=0.;
|
||||
for i=1:iindex;
|
||||
if BR1(i)==0.;
|
||||
Biindex=Biindex+1;
|
||||
RHSR2(Biindex)=RHSR1(i);
|
||||
jindex=0;
|
||||
for j=1:iindex;
|
||||
check=0;
|
||||
if BR1(j)==0.;
|
||||
jindex=jindex+1;
|
||||
AR2(Biindex,jindex)=AR1(i,j);
|
||||
end
|
||||
end
|
||||
end
|
||||
end
|
||||
%Solve
|
||||
Tnewr=(AR2^-1)*RHSR2';
|
||||
% Restore Matrices
|
||||
Biindex=0;
|
||||
for i=1:iindex;
|
||||
if BR1(i)==0.;
|
||||
Biindex=Biindex+1;
|
||||
TR1(i)=Tnewr(Biindex);
|
||||
end
|
||||
end
|
||||
iindex=0;
|
||||
for i=1:ndof*numNodes;
|
||||
check=0;
|
||||
if mod(i,2)==0 && eNodes(i)~=1
|
||||
check=1;
|
||||
end
|
||||
if check==0
|
||||
iindex=iindex+1;
|
||||
Tnew(i)=TR1(iindex);
|
||||
end
|
||||
end
|
||||
Tnew
|
||||
end
|
||||
stored'
|
||||
128
Unpublished/XFEM/Other/GetF.m
Normal file
128
Unpublished/XFEM/Other/GetF.m
Normal file
|
|
@ -0,0 +1,128 @@
|
|||
function [] = GetF()
|
||||
% set up grid
|
||||
gd=0.;
|
||||
numElem=4;
|
||||
eLen=0.25;
|
||||
for i=1:numElem+1
|
||||
ndCrd(i)=gd;
|
||||
gd=gd+eLen;
|
||||
end
|
||||
for i=1:numElem
|
||||
elemNod(i,1)=i;
|
||||
elemNod(i,2)=i+1;
|
||||
end
|
||||
% Initial level set
|
||||
dpos=0.1;
|
||||
for i=1:numElem+1
|
||||
lSet(i)=sign(ndCrd(i)-dpos)*abs(dpos-ndCrd(i));
|
||||
end
|
||||
lSet'
|
||||
for tstep=1:120
|
||||
% Velocity BC
|
||||
F=zeros(numElem+1,1);
|
||||
for i=1:numElem
|
||||
if sign(lSet(elemNod(i,1)))~=sign(lSet(elemNod(i,2)))
|
||||
F(elemNod(i,1))= 0.0005;
|
||||
F(elemNod(i,2))= 0.0005;
|
||||
end
|
||||
end
|
||||
% Assemble 'Stiffness' Matrices
|
||||
A=zeros(numElem+1);
|
||||
for i=1:numElem
|
||||
pos(1)=-1/sqrt(3);
|
||||
pos(2)=1/sqrt(3);
|
||||
AfL=zeros(2);
|
||||
AfLGLS=zeros(2);
|
||||
for j=1:2
|
||||
shp(1)=(1-pos(j))/2.;
|
||||
shp(2)=(1+pos(j))/2.;
|
||||
dshp(1)=-0.5;
|
||||
dshp(2)=0.5;
|
||||
rset=shp(1)*lSet(elemNod(i,1))+shp(2)*lSet(elemNod(i,2));
|
||||
dls=dshp(1)*lSet(elemNod(i,1))+dshp(2)*lSet(elemNod(i,2));
|
||||
AfL=AfL+shp'*sign(rset)*(dls*dshp);
|
||||
AfLGLS=AfLGLS+(dshp'*dls)*(0.25/abs(dls))*(dls*dshp);
|
||||
end
|
||||
for k=1:2;
|
||||
for j=1:2;
|
||||
A(elemNod(i,j),elemNod(i,k))=A(elemNod(i,j),elemNod(i,k))+AfL(j,k)+AfLGLS(j,k);
|
||||
end
|
||||
end
|
||||
end
|
||||
% Apply BCs
|
||||
RHS=zeros(numElem+1,1);
|
||||
Sub=A*F;
|
||||
iindex=0;
|
||||
for i=1:numElem+1
|
||||
if F(i)==0.
|
||||
iindex=iindex+1;
|
||||
RHSred(iindex)=RHS(i)-Sub(i);
|
||||
Fred=0.;
|
||||
jindex=0;
|
||||
for j=1:numElem+1
|
||||
if F(j)==0.
|
||||
jindex=jindex+1;
|
||||
Ared(iindex,jindex)=A(i,j);
|
||||
end
|
||||
end
|
||||
end
|
||||
end
|
||||
% Solve for Fred
|
||||
Fred=(Ared^-1)*RHSred';
|
||||
% Get F
|
||||
iindex=0;
|
||||
for i=1:numElem+1
|
||||
if F(i)==0.
|
||||
iindex=iindex+1;
|
||||
F(i)=Fred(iindex);
|
||||
end
|
||||
end
|
||||
% Update level set
|
||||
mMat=zeros(numElem+1);
|
||||
mMatGLS=zeros(numElem+1);
|
||||
f1=zeros(numElem+1,1);
|
||||
f2=zeros(numElem+1,1);
|
||||
f3=zeros(numElem+1,1);
|
||||
h=0.25;
|
||||
visc=0.000;
|
||||
for i=1:numElem
|
||||
pos(1)=-1/sqrt(3);
|
||||
pos(2)=1/sqrt(3);
|
||||
mMatL=zeros(2);
|
||||
mMatGLSL=zeros(2);
|
||||
f1L=zeros(2,1);
|
||||
f2L=zeros(2,1);
|
||||
f3L=zeros(2,1);
|
||||
for j=1:2
|
||||
shp(1)=(1-pos(j))/2.;
|
||||
shp(2)=(1+pos(j))/2.;
|
||||
dshp(1)=-0.5;
|
||||
dshp(2)=0.5;
|
||||
Floc=shp(1)*F(elemNod(i,1))+shp(2)*F(elemNod(i,2));
|
||||
rset=shp(1)*lSet(elemNod(i,1))+shp(2)*lSet(elemNod(i,2));
|
||||
dls=dshp(1)*lSet(elemNod(i,1))+dshp(2)*lSet(elemNod(i,2));
|
||||
mMatL=mMatL+shp'*shp;
|
||||
mMatGLSL=mMatGLSL+((dshp'*(dls/abs(dls)))*Floc*(h/abs(Floc)))*shp;
|
||||
f1L=f1L+shp'*Floc*abs(dls);
|
||||
f2L=f2L+(dshp'*(dls/abs(dls))*Floc)*(h/abs(Floc))*Floc*abs(dls);
|
||||
vs=h*((abs(visc+Floc*abs(dls)))/(abs(Floc*dls)+h));
|
||||
f3L=f3L+vs*dshp'*dls;
|
||||
end
|
||||
for k=1:2;
|
||||
for j=1:2;
|
||||
mMat(elemNod(i,j),elemNod(i,k))=mMat(elemNod(i,j),elemNod(i,k))+mMatL(j,k);
|
||||
mMatGLS(elemNod(i,j),elemNod(i,k))=mMatGLS(elemNod(i,j),elemNod(i,k))+mMatGLSL(j,k);
|
||||
end
|
||||
f1(elemNod(i,k))=f1(elemNod(i,k))+f1L(k);
|
||||
f2(elemNod(i,k))=f2(elemNod(i,k))+f2L(k);
|
||||
f3(elemNod(i,k))=f3(elemNod(i,k))+f3L(k);
|
||||
end
|
||||
end
|
||||
dt=0.01;
|
||||
lSet=lSet-((((mMat+mMatGLS)^-1)/dt)*(f1+f2+f3))';
|
||||
lSet'
|
||||
end
|
||||
|
||||
|
||||
|
||||
|
||||
146
Unpublished/XFEM/Other/S2D.m
Normal file
146
Unpublished/XFEM/Other/S2D.m
Normal file
|
|
@ -0,0 +1,146 @@
|
|||
function [] = S2D()
|
||||
% MATLAB based 2-D XFEM Solver
|
||||
% J. Grogan (2012)
|
||||
clear all
|
||||
% Define Mesh
|
||||
NumX=10;
|
||||
NumY=1;
|
||||
delX=1.;
|
||||
delY=1.;
|
||||
for j=1:NumY+1
|
||||
for i=1:NumX+1
|
||||
index=i+(NumX+1)*(j-1);
|
||||
Node(index,1)=single((i-1.))*delX;
|
||||
Node(index,2)=single((j-1.))*delY;
|
||||
end
|
||||
end
|
||||
numNodes=(NumX+1)*(NumY+1);
|
||||
for j=1:NumY
|
||||
for i=1:NumX
|
||||
index=i+NumX*(j-1);
|
||||
Element(index,1)=i+(NumX+1)*(j-1);
|
||||
Element(index,2)=i+(NumX+1)*(j-1)+1;
|
||||
Element(index,3)=i+(NumX+1)*(j)+1;
|
||||
Element(index,4)=i+(NumX+1)*(j);
|
||||
end
|
||||
end
|
||||
numElem=(NumX)*(NumY);
|
||||
% Define Section Properties
|
||||
rho=1.;
|
||||
cond=1.;
|
||||
spec=1.;
|
||||
% initial interface position
|
||||
dpos=0.25;
|
||||
% Initial temperatures
|
||||
Tnew=zeros(numNodes,1);
|
||||
Bound=zeros(numNodes,1);
|
||||
for e=1:numElem
|
||||
for n=1:4
|
||||
crdn=Node(Element(e,n),1);
|
||||
if crdn<=dpos
|
||||
Tnew(Element(e,n))=1.;
|
||||
Bound(Element(e,n))=1.;
|
||||
end
|
||||
end
|
||||
end
|
||||
% Define Time Step
|
||||
dtime=0.1;
|
||||
tsteps=10;
|
||||
% Loop through time steps
|
||||
for ts=1:tsteps
|
||||
K=zeros(numNodes,numNodes);
|
||||
M=zeros(numNodes,numNodes);
|
||||
% Loop Through Elements
|
||||
for e=1:numElem
|
||||
Ke=zeros(4);
|
||||
Me=zeros(4);
|
||||
for icrd=1:4;
|
||||
crdnx(icrd)=Node(Element(e,icrd),1);
|
||||
crdny(icrd)=Node(Element(e,icrd),2);
|
||||
end
|
||||
gpos=1/sqrt(3.);
|
||||
gx(1)=-gpos;
|
||||
gx(2)=gpos;
|
||||
gx(3)=gpos;
|
||||
gx(4)=-gpos;
|
||||
hx(1)=-gpos;
|
||||
hx(2)=-gpos;
|
||||
hx(3)=gpos;
|
||||
hx(4)=gpos;
|
||||
% Loop Through Int Points
|
||||
for i=1:4;
|
||||
g=gx(i);
|
||||
h=hx(i);
|
||||
phi(1)=0.25*(1.-g)*(1.-h);
|
||||
phi(2)=0.25*(1.+g)*(1.-h);
|
||||
phi(3)=0.25*(1.+g)*(1.+h);
|
||||
phi(4)=0.25*(1.-g)*(1.+h);
|
||||
phig(1)=0.25*-(1.-h);
|
||||
phig(2)=0.25*(1.-h);
|
||||
phig(3)=0.25*(1.+h);
|
||||
phig(4)=0.25*-(1.+h);
|
||||
phih(1)=0.25*-(1.-g);
|
||||
phih(2)=0.25*-(1.+g);
|
||||
phih(3)=0.25*(1.+g);
|
||||
phih(4)=0.25*(1.-g);
|
||||
rjac=zeros(2,2);
|
||||
for iter=1:4
|
||||
rjac(1,1)=rjac(1,1)+phig(iter)*crdnx(iter);
|
||||
rjac(1,2)=rjac(1,2)+phig(iter)*crdny(iter);
|
||||
rjac(2,1)=rjac(2,1)+phih(iter)*crdnx(iter);
|
||||
rjac(2,2)=rjac(2,2)+phih(iter)*crdny(iter);
|
||||
end
|
||||
djac=rjac(1,1)*rjac(2,2)-rjac(1,2)*rjac(2,1);
|
||||
rjaci(1,1)= rjac(2,2)/djac;
|
||||
rjaci(2,2)= rjac(1,1)/djac;
|
||||
rjaci(1,2)=-rjac(1,2)/djac;
|
||||
rjaci(2,1)=-rjac(2,1)/djac ;
|
||||
for iter=1:4
|
||||
phix(iter)=rjaci(1,1)*phig(iter)+rjaci(1,2)*phih(iter);
|
||||
phiy(iter)=rjaci(2,1)*phig(iter)+rjaci(2,2)*phih(iter);
|
||||
end
|
||||
we=djac;
|
||||
Ke=Ke+we*cond*(phix'*phix+phiy'*phiy);
|
||||
Me=Me+(we*rho*spec*phi'*phi)/dtime;
|
||||
end
|
||||
% Assemble Global Matrices
|
||||
gnum(1)=Element(e,1);
|
||||
gnum(2)=Element(e,2);
|
||||
gnum(3)=Element(e,3);
|
||||
gnum(4)=Element(e,4);
|
||||
for i=1:4;
|
||||
for j=1:4;
|
||||
K(gnum(j),gnum(i))=K(gnum(j),gnum(i))+Ke(j,i);
|
||||
M(gnum(j),gnum(i))=M(gnum(j),gnum(i))+Me(j,i);
|
||||
end
|
||||
end
|
||||
end
|
||||
%Remove inactive DOFs(Reduce Matrices)
|
||||
RHS=M*Tnew;
|
||||
A=K+M;
|
||||
Sub=A*Bound;
|
||||
iindex=0;
|
||||
for i=1:numNodes;
|
||||
if Bound(i)==0.;
|
||||
iindex=iindex+1;
|
||||
RHSred(iindex)=RHS(i)-Sub(i);
|
||||
jindex=0;
|
||||
for j=1:numNodes;
|
||||
if Bound(j)==0.;
|
||||
jindex=jindex+1;
|
||||
Ared(iindex,jindex)=A(i,j);
|
||||
end
|
||||
end
|
||||
end
|
||||
end
|
||||
%Solve
|
||||
Tnewr=(Ared^-1)*RHSred';
|
||||
iindex=0;
|
||||
for i=1:numNodes;
|
||||
if Bound(i)==0.;
|
||||
iindex=iindex+1;
|
||||
Tnew(i)=Tnewr(iindex);
|
||||
end
|
||||
end
|
||||
Tnew
|
||||
end
|
||||
270
Unpublished/XFEM/Other/XCOR1D.m
Normal file
270
Unpublished/XFEM/Other/XCOR1D.m
Normal file
|
|
@ -0,0 +1,270 @@
|
|||
function [] = XCOR1D()
|
||||
% MATLAB based 1-D XFEM Solver
|
||||
% J. Grogan (2012)
|
||||
clear all
|
||||
% Define Geometry
|
||||
len=1.;
|
||||
% Define Section Properties
|
||||
rho=1.;
|
||||
% Generate Mesh
|
||||
numElem=4;
|
||||
charlen=len/numElem;
|
||||
ndCoords=linspace(0,len,numElem+1);
|
||||
numNodes=size(ndCoords,2);
|
||||
indx=1:numElem;
|
||||
elemNodes(:,1)=indx;
|
||||
elemNodes(:,2)=indx+1;
|
||||
% dofs per node
|
||||
ndof=2;
|
||||
% initial interface position
|
||||
dpos=0.6;
|
||||
% Initial temperatures
|
||||
Tnew=zeros(numNodes*2,1);
|
||||
Bound=zeros(numNodes*2,1);
|
||||
%storage
|
||||
stored(1)=dpos;
|
||||
for e=1:numElem
|
||||
for n=1:2
|
||||
crdn1=ndCoords(elemNodes(e,n));
|
||||
if crdn1<=dpos
|
||||
Tnew(2*elemNodes(e,n)-1)=1.;
|
||||
end
|
||||
end
|
||||
end
|
||||
Bound(1)=1.;
|
||||
% Define Time Step
|
||||
dtime=0.01;
|
||||
tsteps=10;
|
||||
time=0.;
|
||||
% penalty term
|
||||
beta=100.;
|
||||
% Loop through time steps
|
||||
for ts=1:tsteps
|
||||
eNodes=zeros(2*numNodes,1);
|
||||
% Get interface velocity
|
||||
d(1)=dpos+charlen;
|
||||
d(2)=dpos+3*charlen/4;
|
||||
d(3)=dpos+charlen/4;
|
||||
d(4)=dpos;
|
||||
for e=1:numElem
|
||||
crdn1=ndCoords(elemNodes(e,1));
|
||||
crdn2=ndCoords(elemNodes(e,2));
|
||||
for j=1:4
|
||||
if d(j)>=crdn1 && d(j)<crdn2
|
||||
elen=abs(crdn2-crdn1);
|
||||
ajacob=elen/2.;
|
||||
point=(d(j)-crdn1)/ajacob-1.;
|
||||
theta(1)=abs(crdn1-dpos)*sign(crdn1-dpos);
|
||||
theta(2)=abs(crdn2-dpos)*sign(crdn2-dpos);
|
||||
tmp1a=Tnew(elemNodes(e,1)*2-1);
|
||||
tmp1b=Tnew(elemNodes(e,1)*2);
|
||||
tmp2a=Tnew(elemNodes(e,2)*2-1);
|
||||
tmp2b=Tnew(elemNodes(e,2)*2);
|
||||
xi=point;
|
||||
gm(1)=(1.-xi)/2.;
|
||||
gm(3)=(1.+xi)/2.;
|
||||
term=theta(1)*gm(1)+theta(2)*gm(3);
|
||||
gm(2)=gm(1)*(abs(term)-abs(theta(1)));
|
||||
gm(4)=gm(3)*(abs(term)-abs(theta(2)));
|
||||
t(j)=gm(1)*tmp1a+gm(2)*tmp1b+gm(3)*tmp2a+gm(4)*tmp2b;
|
||||
end
|
||||
end
|
||||
end
|
||||
vel=0.5*(0.5/charlen)*(2*t(1)+t(2)-t(3)-2*t(4));
|
||||
vel=0.
|
||||
% Update interface position
|
||||
dpos=dpos+vel*dtime;
|
||||
stored(ts+1)=dpos;
|
||||
K=zeros(numNodes*ndof,numNodes*ndof);
|
||||
M=zeros(numNodes*ndof,numNodes*ndof);
|
||||
pforce=zeros(numNodes*ndof,1);
|
||||
% Loop Through Elements
|
||||
for e=1:numElem
|
||||
Ke=zeros(2*ndof);
|
||||
Me=zeros(2*ndof);
|
||||
crdn1=ndCoords(elemNodes(e,1));
|
||||
crdn2=ndCoords(elemNodes(e,2));
|
||||
theta(1)=abs(crdn1-dpos)*sign(crdn1-dpos);
|
||||
theta(2)=abs(crdn2-dpos)*sign(crdn2-dpos);
|
||||
enr=2;
|
||||
elen=abs(crdn2-crdn1);
|
||||
ajacob=elen/2.;
|
||||
if sign(theta(1))~=sign(theta(2))
|
||||
% enriched element
|
||||
eNodes(2*elemNodes(e,1))=1;
|
||||
eNodes(2*elemNodes(e,2))=1;
|
||||
enr=4;
|
||||
% get interface position on element
|
||||
point=(dpos-crdn1)/ajacob-1.;
|
||||
% devide element for sub integration
|
||||
len1=abs(-point-1.);
|
||||
len2=abs(1.-point);
|
||||
mid1=-1+len1/2.;
|
||||
mid2=1-len2/2.;
|
||||
gpx(1)=-(len1/2.)/sqrt(3.)+mid1;
|
||||
gpx(2)=(len1/2.)/sqrt(3.)+mid1;
|
||||
gpx(3)=-(len2/2.)/sqrt(3.)+mid2;
|
||||
gpx(4)=(len2/2.)/sqrt(3.)+mid2;
|
||||
w(1)=(len1/2.);
|
||||
w(2)=(len1/2.);
|
||||
w(3)=(len2/2.);
|
||||
w(4)=(len2/2.);
|
||||
else
|
||||
% regular element - fix extra dofs
|
||||
gpx(1)=-1/sqrt(3.);
|
||||
gpx(2)=1/sqrt(3.);
|
||||
w(1)=1.;
|
||||
w(2)=1.;
|
||||
end
|
||||
% Loop Through Int Points
|
||||
for i=1:enr;
|
||||
c=gpx(i);
|
||||
phi(1)=(1.-c)/2.;
|
||||
phi(3)=(1.+c)/2.;
|
||||
term=theta(1)*phi(1)+theta(2)*phi(3);
|
||||
% if term<0
|
||||
% cond=0.00;
|
||||
% spec=0.001;
|
||||
% else
|
||||
cond=1.;
|
||||
spec=1.;
|
||||
% end
|
||||
if enr==4
|
||||
phi(2)=phi(1)*(abs(term)-abs(theta(1)));
|
||||
phi(4)=phi(3)*(abs(term)-abs(theta(2)));
|
||||
else
|
||||
phi(2)=0.0;
|
||||
phi(4)=0.0;
|
||||
end
|
||||
phic(1)=-0.5;
|
||||
phic(3)=0.5;
|
||||
dterm=sign(term)*(phic(1)*theta(1)+phic(3)*theta(2));
|
||||
if enr==4
|
||||
phic(2)=phic(1)*(abs(term)-abs(theta(1)))+phi(1)*dterm;
|
||||
phic(4)=phic(3)*(abs(term)-abs(theta(2)))+phi(3)*dterm;
|
||||
else
|
||||
phic(2)=0.0;
|
||||
phic(4)=0.0;
|
||||
end
|
||||
phix(1)=phic(1)/ajacob;
|
||||
phix(2)=phic(2)/ajacob;
|
||||
phix(3)=phic(3)/ajacob;
|
||||
phix(4)=phic(4)/ajacob;
|
||||
we=ajacob*w(i);
|
||||
Ke=Ke+we*cond*phix'*phix;
|
||||
Me=Me+(we*rho*spec*phi'*phi)/dtime;
|
||||
end
|
||||
if enr==5;
|
||||
Ke(1,2)=0.;
|
||||
Me(1,2)=0.;
|
||||
Ke(2,1)=0.;
|
||||
Me(2,1)=0.;
|
||||
Ke(1,4)=0.;
|
||||
Me(1,4)=0.;
|
||||
Ke(4,1)=0.;
|
||||
Me(4,1)=0.;
|
||||
Ke(3,2)=0.;
|
||||
Me(3,2)=0.;
|
||||
Ke(2,3)=0.;
|
||||
Me(2,3)=0.;
|
||||
Ke(4,3)=0.;
|
||||
Me(4,3)=0.;
|
||||
Ke(3,4)=0.;
|
||||
Me(3,4)=0.;
|
||||
end
|
||||
% Add penalty term and get temp gradient on interface
|
||||
if enr==4;
|
||||
xi=point;
|
||||
gm(1)=(1.-xi)/2.;
|
||||
gm(3)=(1.+xi)/2.;
|
||||
term=theta(1)*gm(1)+theta(2)*gm(3);
|
||||
gm(2)=gm(1)*(abs(term)-abs(theta(1)));
|
||||
gm(4)=gm(3)*(abs(term)-abs(theta(2)));
|
||||
pen=beta*(gm'*gm);
|
||||
pfL=beta*1*gm';
|
||||
Ke=Ke+pen;
|
||||
else
|
||||
pen=zeros(4);
|
||||
pfL=zeros(4,1);
|
||||
end
|
||||
Ke;
|
||||
Me;
|
||||
% Assemble Global Matrices
|
||||
gnum=2.*elemNodes(e,1)-1.;
|
||||
for i=1:4;
|
||||
for j=1:4;
|
||||
K(gnum+j-1,gnum+i-1)=K(gnum+j-1,gnum+i-1)+Ke(j,i);
|
||||
M(gnum+j-1,gnum+i-1)=M(gnum+j-1,gnum+i-1)+Me(j,i);
|
||||
end
|
||||
pforce(gnum+i-1)=pforce(gnum+i-1)+pfL(i);
|
||||
end
|
||||
end
|
||||
%Remove NON-ENHANCED DOFs(Reduce Matrices)
|
||||
iindex=0.;
|
||||
for i=1:ndof*numNodes;
|
||||
check=0;
|
||||
if mod(i,2)==0 && eNodes(i)~=1
|
||||
check=1;
|
||||
end
|
||||
if check==0
|
||||
iindex=iindex+1;
|
||||
TR1(iindex)=Tnew(i);
|
||||
BR1(iindex)=Bound(i);
|
||||
pforceR1(iindex)=pforce(i);
|
||||
jindex=0;
|
||||
for j=1:ndof*numNodes;
|
||||
check=0;
|
||||
if mod(j,2)==0 && eNodes(j)~=1
|
||||
check=1;
|
||||
end
|
||||
if check==0
|
||||
jindex=jindex+1;
|
||||
MR1(iindex,jindex)=M(i,j);
|
||||
KR1(iindex,jindex)=K(i,j);
|
||||
end
|
||||
end
|
||||
end
|
||||
end
|
||||
AR1=KR1+MR1;
|
||||
SubR1=AR1*BR1';
|
||||
RHSR1=MR1*TR1'-SubR1+pforceR1';
|
||||
% Apply Boundary Conditions
|
||||
Biindex=0.;
|
||||
for i=1:iindex;
|
||||
if BR1(i)==0.;
|
||||
Biindex=Biindex+1;
|
||||
RHSR2(Biindex)=RHSR1(i);
|
||||
jindex=0;
|
||||
for j=1:iindex;
|
||||
check=0;
|
||||
if BR1(j)==0.;
|
||||
jindex=jindex+1;
|
||||
AR2(Biindex,jindex)=AR1(i,j);
|
||||
end
|
||||
end
|
||||
end
|
||||
end
|
||||
%Solve
|
||||
Tnewr=(AR2^-1)*RHSR2';
|
||||
% Restore Matrices
|
||||
Biindex=0;
|
||||
for i=1:iindex;
|
||||
if BR1(i)==0.;
|
||||
Biindex=Biindex+1;
|
||||
TR1(i)=Tnewr(Biindex);
|
||||
end
|
||||
end
|
||||
iindex=0;
|
||||
for i=1:ndof*numNodes;
|
||||
check=0;
|
||||
if mod(i,2)==0 && eNodes(i)~=1
|
||||
check=1;
|
||||
end
|
||||
if check==0
|
||||
iindex=iindex+1;
|
||||
Tnew(i)=TR1(iindex);
|
||||
end
|
||||
end
|
||||
Tnew
|
||||
end
|
||||
stored';
|
||||
197
Unpublished/XFEM/Other/XCOR1Db.m
Normal file
197
Unpublished/XFEM/Other/XCOR1Db.m
Normal file
|
|
@ -0,0 +1,197 @@
|
|||
function [] = XCOR1Db()
|
||||
% MATLAB based 1-D XFEM Solver
|
||||
% J. Grogan (2012)
|
||||
clear all
|
||||
% Define Geometry
|
||||
len=1.;
|
||||
% Define Section Properties
|
||||
rho=1.;
|
||||
% Generate Mesh
|
||||
numElem=4;
|
||||
charlen=len/numElem;
|
||||
ndCoords=linspace(0,len,numElem+1);
|
||||
numNodes=size(ndCoords,2);
|
||||
indx=1:numElem;
|
||||
elemNodes(:,1)=indx;
|
||||
elemNodes(:,2)=indx+1;
|
||||
% dofs per node
|
||||
ndof=2;
|
||||
% initial interface position
|
||||
dpos=0.6;
|
||||
% Initial temperatures
|
||||
Tnew=zeros(numNodes*2,1);
|
||||
Bound=zeros(numNodes*2,1);
|
||||
%storage
|
||||
stored(1)=dpos;
|
||||
for e=1:numElem
|
||||
for n=1:2
|
||||
crdn1=ndCoords(elemNodes(e,n));
|
||||
if crdn1<=dpos
|
||||
Tnew(2*elemNodes(e,n)-1)=1.;
|
||||
end
|
||||
end
|
||||
end
|
||||
Bound(1)=1.;
|
||||
% Define Time Step
|
||||
dtime=0.01;
|
||||
tsteps=10;
|
||||
time=0.;
|
||||
% penalty term
|
||||
beta=100.;
|
||||
% Loop through time steps
|
||||
for ts=1:tsteps
|
||||
eNodes=zeros(2*numNodes,1);
|
||||
% Get interface velocity
|
||||
d(1)=dpos+charlen;
|
||||
d(2)=dpos+3*charlen/4;
|
||||
d(3)=dpos+charlen/4;
|
||||
d(4)=dpos;
|
||||
for e=1:numElem
|
||||
crdn1=ndCoords(elemNodes(e,1));
|
||||
crdn2=ndCoords(elemNodes(e,2));
|
||||
for j=1:4
|
||||
if d(j)>=crdn1 && d(j)<crdn2
|
||||
elen=abs(crdn2-crdn1);
|
||||
ajacob=elen/2.;
|
||||
point=(d(j)-crdn1)/ajacob-1.;
|
||||
theta(1)=abs(crdn1-dpos)*sign(crdn1-dpos);
|
||||
theta(2)=abs(crdn2-dpos)*sign(crdn2-dpos);
|
||||
tmp1a=Tnew(elemNodes(e,1)*2-1);
|
||||
tmp1b=Tnew(elemNodes(e,1)*2);
|
||||
tmp2a=Tnew(elemNodes(e,2)*2-1);
|
||||
tmp2b=Tnew(elemNodes(e,2)*2);
|
||||
xi=point;
|
||||
gm(1)=(1.-xi)/2.;
|
||||
gm(3)=(1.+xi)/2.;
|
||||
term=theta(1)*gm(1)+theta(2)*gm(3);
|
||||
gm(2)=gm(1)*(abs(term)-abs(theta(1)));
|
||||
gm(4)=gm(3)*(abs(term)-abs(theta(2)));
|
||||
t(j)=gm(1)*tmp1a+gm(2)*tmp1b+gm(3)*tmp2a+gm(4)*tmp2b;
|
||||
end
|
||||
end
|
||||
end
|
||||
vel=0.5*(0.5/charlen)*(2*t(1)+t(2)-t(3)-2*t(4));
|
||||
vel=0.
|
||||
% Update interface position
|
||||
dpos=dpos+vel*dtime;
|
||||
stored(ts+1)=dpos;
|
||||
K=zeros(numNodes*ndof,numNodes*ndof);
|
||||
M=zeros(numNodes*ndof,numNodes*ndof);
|
||||
pforce=zeros(numNodes*ndof,1);
|
||||
% Loop Through Elements
|
||||
for e=1:numElem
|
||||
Ke=zeros(2*ndof);
|
||||
Me=zeros(2*ndof);
|
||||
crdn1=ndCoords(elemNodes(e,1));
|
||||
crdn2=ndCoords(elemNodes(e,2));
|
||||
theta(1)=abs(crdn1-dpos)*sign(crdn1-dpos);
|
||||
theta(2)=abs(crdn2-dpos)*sign(crdn2-dpos);
|
||||
enr=2;
|
||||
elen=abs(crdn2-crdn1);
|
||||
ajacob=elen/2.;
|
||||
if sign(theta(1))~=sign(theta(2))
|
||||
% enriched element
|
||||
eNodes(2*elemNodes(e,1))=1;
|
||||
eNodes(2*elemNodes(e,2))=1;
|
||||
enr=4;
|
||||
% get interface position on element
|
||||
point=(dpos-crdn1)/ajacob-1.;
|
||||
% devide element for sub integration
|
||||
len1=abs(-point-1.);
|
||||
len2=abs(1.-point);
|
||||
mid1=-1+len1/2.;
|
||||
mid2=1-len2/2.;
|
||||
gpx(1)=-(len1/2.)/sqrt(3.)+mid1;
|
||||
gpx(2)=(len1/2.)/sqrt(3.)+mid1;
|
||||
gpx(3)=-(len2/2.)/sqrt(3.)+mid2;
|
||||
gpx(4)=(len2/2.)/sqrt(3.)+mid2;
|
||||
w(1)=(len1/2.);
|
||||
w(2)=(len1/2.);
|
||||
w(3)=(len2/2.);
|
||||
w(4)=(len2/2.);
|
||||
else
|
||||
% regular element - fix extra dofs
|
||||
gpx(1)=-1/sqrt(3.);
|
||||
gpx(2)=1/sqrt(3.);
|
||||
w(1)=1.;
|
||||
w(2)=1.;
|
||||
end
|
||||
% Loop Through Int Points
|
||||
for i=1:enr;
|
||||
c=gpx(i);
|
||||
phi(1)=(1.-c)/2.;
|
||||
phi(3)=(1.+c)/2.;
|
||||
term=theta(1)*phi(1)+theta(2)*phi(3);
|
||||
cond=1.;
|
||||
spec=1.;
|
||||
phi(2)=phi(1)*(abs(term)-abs(theta(1)));
|
||||
phi(4)=phi(3)*(abs(term)-abs(theta(2)));
|
||||
phic(1)=-0.5;
|
||||
phic(3)=0.5;
|
||||
dterm=sign(term)*(phic(1)*theta(1)+phic(3)*theta(2));
|
||||
phic(2)=phic(1)*(abs(term)-abs(theta(1)))+phi(1)*dterm;
|
||||
phic(4)=phic(3)*(abs(term)-abs(theta(2)))+phi(3)*dterm;
|
||||
phix(1)=phic(1)/ajacob;
|
||||
phix(2)=phic(2)/ajacob;
|
||||
phix(3)=phic(3)/ajacob;
|
||||
phix(4)=phic(4)/ajacob;
|
||||
we=ajacob*w(i);
|
||||
Ke=Ke+we*cond*phix'*phix;
|
||||
Me=Me+(we*rho*spec*phi'*phi)/dtime;
|
||||
end
|
||||
% Add penalty term and get temp gradient on interface
|
||||
if enr==4;
|
||||
xi=point;
|
||||
gm(1)=(1.-xi)/2.;
|
||||
gm(3)=(1.+xi)/2.;
|
||||
term=theta(1)*gm(1)+theta(2)*gm(3);
|
||||
gm(2)=gm(1)*(abs(term)-abs(theta(1)));
|
||||
gm(4)=gm(3)*(abs(term)-abs(theta(2)));
|
||||
pen=beta*(gm'*gm);
|
||||
pfL=beta*1*gm';
|
||||
Ke=Ke+pen;
|
||||
else
|
||||
pen=zeros(4);
|
||||
pfL=zeros(4,1);
|
||||
end
|
||||
% Assemble Global Matrices
|
||||
gnum=2.*elemNodes(e,1)-1.;
|
||||
for i=1:4;
|
||||
for j=1:4;
|
||||
K(gnum+j-1,gnum+i-1)=K(gnum+j-1,gnum+i-1)+Ke(j,i);
|
||||
M(gnum+j-1,gnum+i-1)=M(gnum+j-1,gnum+i-1)+Me(j,i);
|
||||
end
|
||||
pforce(gnum+i-1)=pforce(gnum+i-1)+pfL(i);
|
||||
end
|
||||
end
|
||||
A=K+M;
|
||||
Sub=A*Bound;
|
||||
RHS=M*Tnew-Sub+pforce;
|
||||
% Apply Boundary Conditions
|
||||
Biindex=0.;
|
||||
for i=1:ndof*numNodes;
|
||||
if Bound(i)==0.;
|
||||
Biindex=Biindex+1;
|
||||
RHSR(Biindex)=RHS(i);
|
||||
jindex=0;
|
||||
for j=1:ndof*numNodes;
|
||||
if Bound(j)==0.;
|
||||
jindex=jindex+1;
|
||||
AR(Biindex,jindex)=A(i,j);
|
||||
end
|
||||
end
|
||||
end
|
||||
end
|
||||
%Solve
|
||||
Tnewr=(AR^-1)*RHSR';
|
||||
% Restore Matrices
|
||||
Biindex=0;
|
||||
for i=1:ndof*numNodes;
|
||||
if Bound(i)==0.;
|
||||
Biindex=Biindex+1;
|
||||
Tnew(i)=Tnewr(Biindex);
|
||||
end
|
||||
end
|
||||
Tnew
|
||||
end
|
||||
stored';
|
||||
234
Unpublished/XFEM2/1D_Solver/2DLevelSet.m
Normal file
234
Unpublished/XFEM2/1D_Solver/2DLevelSet.m
Normal file
|
|
@ -0,0 +1,234 @@
|
|||
function [] = 2DLevelSet()
|
||||
clear all
|
||||
% Define Main Solution Mesh
|
||||
NumX=8;
|
||||
NumY=8;
|
||||
delX=1.;
|
||||
delY=1.;
|
||||
for j=1:NumY+1
|
||||
for i=1:NumX+1
|
||||
index=i+(NumX+1)*(j-1);
|
||||
Node(index,1)=single((i-1.))*delX;
|
||||
Node(index,2)=single((j-1.))*delY;
|
||||
end
|
||||
end
|
||||
numNodes=(NumX+1)*(NumY+1);
|
||||
for j=1:NumY
|
||||
for i=1:NumX
|
||||
index=i+NumX*(j-1);
|
||||
Element(index,1)=i+(NumX+1)*(j-1);
|
||||
Element(index,2)=i+(NumX+1)*(j-1)+1;
|
||||
Element(index,3)=i+(NumX+1)*(j)+1;
|
||||
Element(index,4)=i+(NumX+1)*(j);
|
||||
end
|
||||
end
|
||||
numElem=(NumX)*(NumY);
|
||||
% Define Initial Level Set
|
||||
centx=4.;
|
||||
centy=4.;
|
||||
rad=2.1;
|
||||
for i=1:numNodes;
|
||||
dist=sqrt((Node(i,1)-centx)*(Node(i,1)-centx)+(Node(i,2)-centy)*(Node(i,2)-centy));
|
||||
lSet(i)=dist-rad;
|
||||
end
|
||||
%for i=1:numNodes;
|
||||
% dist=Node(i,1)-0.1;
|
||||
% lSet(i)=dist;
|
||||
%end
|
||||
% Plot initial level set
|
||||
[X Y]=meshgrid(0:1.:8);
|
||||
Z=zeros(9);
|
||||
for i=1:81
|
||||
Z(i)=lSet(i);
|
||||
end
|
||||
surf(X,Y,Z)
|
||||
% LS Algorithm Parameters
|
||||
lSet'
|
||||
bandwidth=10.;
|
||||
% Loop through timesteps
|
||||
for tstep=1:100
|
||||
% Identify Narrow Band Elements
|
||||
NBindex=0;
|
||||
for i=1:numElem
|
||||
check=0;
|
||||
for iNd=1:4
|
||||
if abs(lSet(Element(i,iNd)))<=bandwidth*delX
|
||||
check=1;
|
||||
end
|
||||
end
|
||||
% If an element is in the narrow band split it into triangles
|
||||
if check==1
|
||||
NBindex=NBindex+1;
|
||||
NBelem(NBindex,1)=Element(i,1);
|
||||
NBelem(NBindex,2)=Element(i,2);
|
||||
NBelem(NBindex,3)=Element(i,3);
|
||||
NBindex=NBindex+1;
|
||||
NBelem(NBindex,1)=Element(i,1);
|
||||
NBelem(NBindex,2)=Element(i,3);
|
||||
NBelem(NBindex,3)=Element(i,4);
|
||||
end
|
||||
end
|
||||
% Velocity BC
|
||||
F=zeros(numNodes,1);
|
||||
for i=1:NBindex
|
||||
if sign(lSet(NBelem(i,1)))~=sign(lSet(NBelem(i,2)))||sign(lSet(NBelem(i,1)))~=sign(lSet(NBelem(i,3)))
|
||||
F(NBelem(i,1))= 1.;
|
||||
F(NBelem(i,2))= 1.;
|
||||
F(NBelem(i,3))= 1.;
|
||||
end
|
||||
end
|
||||
% Assemble 'Stiffness' Matrices
|
||||
A=zeros(numNodes);
|
||||
for i=1:NBindex
|
||||
gx(1)=2./3.;
|
||||
gx(2)=1./6.;
|
||||
gx(3)=1./6.;
|
||||
hx(1)=1./6.;
|
||||
hx(2)=1./6.;
|
||||
hx(3)=2./3.;
|
||||
AfL=zeros(3);
|
||||
AfLGLS=zeros(3);
|
||||
x1=Node(NBelem(i,1),1);
|
||||
y1=Node(NBelem(i,1),2);
|
||||
x2=Node(NBelem(i,2),1);
|
||||
y2=Node(NBelem(i,2),2);
|
||||
x3=Node(NBelem(i,3),1);
|
||||
y3=Node(NBelem(i,3),2);
|
||||
for j=1:3
|
||||
g=gx(j);
|
||||
h=hx(j);
|
||||
phi(1)=1.-g-h;
|
||||
phi(2)=g;
|
||||
phi(3)=h;
|
||||
phig(1)=-1.;
|
||||
phig(2)=1.;
|
||||
phig(3)=0.;
|
||||
phih(1)=-1.;
|
||||
phih(2)=0.;
|
||||
phih(3)=1.;
|
||||
djac=2*abs(x1*(y2-y3)+x2*(y3-y1)+x3*(y1-y2));
|
||||
for k=1:3
|
||||
phix(k)=(1./djac)*((-y1+y3)*phig(k)+(y1-y2)*phih(k));
|
||||
phiy(k)=(1./djac)*((x1-x3)*phig(k)+(-x1+x2)*phih(k));
|
||||
end
|
||||
delphi=[phix;phiy];
|
||||
nodalLset=[lSet(NBelem(i,1));lSet(NBelem(i,2));lSet(NBelem(i,3))];
|
||||
set=phi*nodalLset;
|
||||
delset=delphi*nodalLset;
|
||||
AfL=AfL+(phi'*sign(set))*(delset'*delphi)/3.;
|
||||
AfLGLS=AfLGLS+(delphi'*delset)*(1./norm(delset))*(delset'*delphi)/3.;
|
||||
end
|
||||
sum=AfL+AfLGLS;
|
||||
for k=1:3;
|
||||
for j=1:3;
|
||||
A(NBelem(i,j),NBelem(i,k))=A(NBelem(i,j),NBelem(i,k))+sum(j,k);
|
||||
end
|
||||
end
|
||||
end
|
||||
% Apply BCs
|
||||
RHS=zeros(numNodes,1);
|
||||
Sub=A*F;
|
||||
iindex=0;
|
||||
for i=1:numNodes
|
||||
if F(i)==0.
|
||||
iindex=iindex+1;
|
||||
RHSred(iindex)=RHS(i)-Sub(i);
|
||||
Fred=0.;
|
||||
jindex=0;
|
||||
for j=1:numNodes
|
||||
if F(j)==0.
|
||||
jindex=jindex+1;
|
||||
Ared(iindex,jindex)=A(i,j);
|
||||
end
|
||||
end
|
||||
end
|
||||
end
|
||||
% Solve for Fred
|
||||
Fred=(Ared^-1)*RHSred';
|
||||
% Get F
|
||||
iindex=0;
|
||||
for i=1:numNodes
|
||||
if F(i)==0.
|
||||
iindex=iindex+1;
|
||||
F(i)=Fred(iindex);
|
||||
end
|
||||
end
|
||||
% Update level set
|
||||
mMat=zeros(numNodes);
|
||||
mMatGLS=zeros(numNodes);
|
||||
f1=zeros(numNodes,1);
|
||||
f2=zeros(numNodes,1);
|
||||
f3=zeros(numNodes,1);
|
||||
h2=0.00001;
|
||||
visc=0.0005;
|
||||
for i=1:NBindex
|
||||
mMatL=zeros(3);
|
||||
mMatGLSL=zeros(3);
|
||||
f1L=zeros(3,1);
|
||||
f2L=zeros(3,1);
|
||||
f3L=zeros(3,1);
|
||||
gx(1)=2./3.;
|
||||
gx(2)=1./6.;
|
||||
gx(3)=1./6.;
|
||||
hx(1)=1./6.;
|
||||
hx(2)=1./6.;
|
||||
hx(3)=2./3.;
|
||||
x1=Node(NBelem(i,1),1);
|
||||
y1=Node(NBelem(i,1),2);
|
||||
x2=Node(NBelem(i,2),1);
|
||||
y2=Node(NBelem(i,2),2);
|
||||
x3=Node(NBelem(i,3),1);
|
||||
y3=Node(NBelem(i,3),2);
|
||||
for j=1:3
|
||||
g=gx(j);
|
||||
h=hx(j);
|
||||
phi(1)=1.-g-h;
|
||||
phi(2)=g;
|
||||
phi(3)=h;
|
||||
phig(1)=-1.;
|
||||
phig(2)=1.;
|
||||
phig(3)=0.;
|
||||
phih(1)=-1.;
|
||||
phih(2)=0.;
|
||||
phih(3)=1.;
|
||||
djac=abs(x1*(y2-y3)+x2*(y3-y1)+x3*(y1-y2));
|
||||
for k=1:3
|
||||
phix(k)=(1./djac)*((-y1+y3)*phig(k)+(y1-y2)*phih(k));
|
||||
phiy(k)=(1./djac)*((x1-x3)*phig(k)+(-x1+x2)*phih(k));
|
||||
end
|
||||
delphi=[phix;phiy];
|
||||
nodalLset=[lSet(NBelem(i,1));lSet(NBelem(i,2));lSet(NBelem(i,3))];
|
||||
nodalF=[F(NBelem(i,1));F(NBelem(i,2));F(NBelem(i,3))];
|
||||
delset=delphi*nodalLset;
|
||||
Floc=phi*nodalF;
|
||||
mMatL=mMatL+(phi'*phi)/3.;
|
||||
mMatGLSL=mMatGLSL+((delphi'*(delset/norm(delset)))*Floc*(h2/abs(Floc)))*phi/3.;
|
||||
f1L=f1L+phi'*Floc*norm(delset)/3.;
|
||||
f2L=f2L+(delphi'*(delset/norm(delset))*Floc)*(h2/abs(Floc))*Floc*norm(delset)/3.;
|
||||
vs=h2*((abs(visc+Floc*norm(delset)))/(norm(Floc*delset)+h2));
|
||||
f3L=f3L+vs*delphi'*delset/3.;
|
||||
end
|
||||
for k=1:3;
|
||||
for j=1:3;
|
||||
mMat(NBelem(i,j),NBelem(i,k))=mMat(NBelem(i,j),NBelem(i,k))+mMatL(j,k);
|
||||
mMatGLS(NBelem(i,j),NBelem(i,k))=mMatGLS(NBelem(i,j),NBelem(i,k))+mMatGLSL(j,k);
|
||||
end
|
||||
f1(NBelem(i,k))=f1(NBelem(i,k))+f1L(k);
|
||||
f2(NBelem(i,k))=f2(NBelem(i,k))+f2L(k);
|
||||
f3(NBelem(i,k))=f3(NBelem(i,k))+f3L(k);
|
||||
end
|
||||
end
|
||||
dt=0.01;
|
||||
lSet=lSet-((((mMat+mMatGLS)^-1)*dt)*(f1+f2+f3))';
|
||||
end
|
||||
lSet'
|
||||
%[X Y]=meshgrid(0:1.:8);
|
||||
%Z=zeros(9);
|
||||
%for i=1:81
|
||||
% Z(i)=lSet(i);
|
||||
%end
|
||||
%surf(X,Y,Z)
|
||||
|
||||
|
||||
|
||||
|
||||
234
Unpublished/XFEM2/1D_Solver/2DLevelSetFMM.m
Normal file
234
Unpublished/XFEM2/1D_Solver/2DLevelSetFMM.m
Normal file
|
|
@ -0,0 +1,234 @@
|
|||
function [] = 2DLevelSetFMM()
|
||||
clear all
|
||||
% Define Main Solution Mesh
|
||||
NumX=3;
|
||||
NumY=1;
|
||||
delX=1.;
|
||||
delY=1.;
|
||||
for j=1:NumY+1
|
||||
for i=1:NumX+1
|
||||
index=i+(NumX+1)*(j-1);
|
||||
Node(index,1)=single((i-1.))*delX;
|
||||
Node(index,2)=single((j-1.))*delY;
|
||||
end
|
||||
end
|
||||
numNodes=(NumX+1)*(NumY+1);
|
||||
for j=1:NumY
|
||||
for i=1:NumX
|
||||
index=i+NumX*(j-1);
|
||||
Element(index,1)=i+(NumX+1)*(j-1);
|
||||
Element(index,2)=i+(NumX+1)*(j-1)+1;
|
||||
Element(index,3)=i+(NumX+1)*(j)+1;
|
||||
Element(index,4)=i+(NumX+1)*(j);
|
||||
end
|
||||
end
|
||||
numElem=(NumX)*(NumY);
|
||||
% Define Initial Level Set
|
||||
%centx=4.;
|
||||
%centy=4.;
|
||||
%rad=2.1;
|
||||
%for i=1:numNodes;
|
||||
% dist=sqrt((Node(i,1)-centx)*(Node(i,1)-centx)+(Node(i,2)-centy)*(Node(i,2)-centy));
|
||||
% lSet(i)=dist-rad;
|
||||
%end
|
||||
for i=1:numNodes;
|
||||
dist=Node(i,1)-0.1;
|
||||
lSet(i)=dist;
|
||||
end
|
||||
% Plot initial level set
|
||||
%[X Y]=meshgrid(0:1.:8);
|
||||
%Z=zeros(9);
|
||||
%for i=1:81
|
||||
% Z(i)=lSet(i);
|
||||
%end
|
||||
%surf(X,Y,Z)
|
||||
% LS Algorithm Parameters
|
||||
lSet'
|
||||
bandwidth=10.;
|
||||
% Loop through timesteps
|
||||
for tstep=1:1
|
||||
% Identify Narrow Band Elements
|
||||
NBindex=0;
|
||||
for i=1:numElem
|
||||
check=0;
|
||||
for iNd=1:4
|
||||
if abs(lSet(Element(i,iNd)))<=bandwidth*delX
|
||||
check=1;
|
||||
end
|
||||
end
|
||||
% If an element is in the narrow band split it into triangles
|
||||
if check==1
|
||||
NBindex=NBindex+1;
|
||||
NBelem(NBindex,1)=Element(i,1);
|
||||
NBelem(NBindex,2)=Element(i,2);
|
||||
NBelem(NBindex,3)=Element(i,3);
|
||||
NBindex=NBindex+1;
|
||||
NBelem(NBindex,1)=Element(i,1);
|
||||
NBelem(NBindex,2)=Element(i,3);
|
||||
NBelem(NBindex,3)=Element(i,4);
|
||||
end
|
||||
end
|
||||
% Velocity BC
|
||||
F=zeros(numNodes,1);
|
||||
for i=1:NBindex
|
||||
if sign(lSet(NBelem(i,1)))~=sign(lSet(NBelem(i,2)))||sign(lSet(NBelem(i,1)))~=sign(lSet(NBelem(i,3)))
|
||||
F(NBelem(i,1))= 1.;
|
||||
F(NBelem(i,2))= 1.;
|
||||
F(NBelem(i,3))= 1.;
|
||||
end
|
||||
end
|
||||
% Assemble 'Stiffness' Matrices
|
||||
A=zeros(numNodes);
|
||||
for i=1:NBindex
|
||||
gx(1)=2./3.;
|
||||
gx(2)=1./6.;
|
||||
gx(3)=1./6.;
|
||||
hx(1)=1./6.;
|
||||
hx(2)=1./6.;
|
||||
hx(3)=2./3.;
|
||||
AfL=zeros(3);
|
||||
AfLGLS=zeros(3);
|
||||
x1=Node(NBelem(i,1),1);
|
||||
y1=Node(NBelem(i,1),2);
|
||||
x2=Node(NBelem(i,2),1);
|
||||
y2=Node(NBelem(i,2),2);
|
||||
x3=Node(NBelem(i,3),1);
|
||||
y3=Node(NBelem(i,3),2);
|
||||
for j=1:3
|
||||
g=gx(j);
|
||||
h=hx(j);
|
||||
phi(1)=1.-g-h;
|
||||
phi(2)=g;
|
||||
phi(3)=h;
|
||||
phig(1)=-1.;
|
||||
phig(2)=1.;
|
||||
phig(3)=0.;
|
||||
phih(1)=-1.;
|
||||
phih(2)=0.;
|
||||
phih(3)=1.;
|
||||
djac=2*abs(x1*(y2-y3)+x2*(y3-y1)+x3*(y1-y2));
|
||||
for k=1:3
|
||||
phix(k)=(1./djac)*((-y1+y3)*phig(k)+(y1-y2)*phih(k));
|
||||
phiy(k)=(1./djac)*((x1-x3)*phig(k)+(-x1+x2)*phih(k));
|
||||
end
|
||||
delphi=[phix;phiy];
|
||||
nodalLset=[lSet(NBelem(i,1));lSet(NBelem(i,2));lSet(NBelem(i,3))];
|
||||
set=phi*nodalLset;
|
||||
delset=delphi*nodalLset;
|
||||
AfL=AfL+(phi'*sign(set))*(delset'*delphi)/3.;
|
||||
AfLGLS=AfLGLS+(delphi'*delset)*(1./norm(delset))*(delset'*delphi)/3.;
|
||||
end
|
||||
sum=AfL+AfLGLS;
|
||||
for k=1:3;
|
||||
for j=1:3;
|
||||
A(NBelem(i,j),NBelem(i,k))=A(NBelem(i,j),NBelem(i,k))+sum(j,k);
|
||||
end
|
||||
end
|
||||
end
|
||||
% Apply BCs
|
||||
RHS=zeros(numNodes,1);
|
||||
Sub=A*F;
|
||||
iindex=0;
|
||||
for i=1:numNodes
|
||||
if F(i)==0.
|
||||
iindex=iindex+1;
|
||||
RHSred(iindex)=RHS(i)-Sub(i);
|
||||
Fred=0.;
|
||||
jindex=0;
|
||||
for j=1:numNodes
|
||||
if F(j)==0.
|
||||
jindex=jindex+1;
|
||||
Ared(iindex,jindex)=A(i,j);
|
||||
end
|
||||
end
|
||||
end
|
||||
end
|
||||
% Solve for Fred
|
||||
Fred=(Ared^-1)*RHSred';
|
||||
% Get F
|
||||
iindex=0;
|
||||
for i=1:numNodes
|
||||
if F(i)==0.
|
||||
iindex=iindex+1;
|
||||
F(i)=Fred(iindex);
|
||||
end
|
||||
end
|
||||
% Update level set
|
||||
mMat=zeros(numNodes);
|
||||
mMatGLS=zeros(numNodes);
|
||||
f1=zeros(numNodes,1);
|
||||
f2=zeros(numNodes,1);
|
||||
f3=zeros(numNodes,1);
|
||||
h2=0.00001;
|
||||
visc=0.0005;
|
||||
for i=1:NBindex
|
||||
mMatL=zeros(3);
|
||||
mMatGLSL=zeros(3);
|
||||
f1L=zeros(3,1);
|
||||
f2L=zeros(3,1);
|
||||
f3L=zeros(3,1);
|
||||
gx(1)=2./3.;
|
||||
gx(2)=1./6.;
|
||||
gx(3)=1./6.;
|
||||
hx(1)=1./6.;
|
||||
hx(2)=1./6.;
|
||||
hx(3)=2./3.;
|
||||
x1=Node(NBelem(i,1),1);
|
||||
y1=Node(NBelem(i,1),2);
|
||||
x2=Node(NBelem(i,2),1);
|
||||
y2=Node(NBelem(i,2),2);
|
||||
x3=Node(NBelem(i,3),1);
|
||||
y3=Node(NBelem(i,3),2);
|
||||
for j=1:3
|
||||
g=gx(j);
|
||||
h=hx(j);
|
||||
phi(1)=1.-g-h;
|
||||
phi(2)=g;
|
||||
phi(3)=h;
|
||||
phig(1)=-1.;
|
||||
phig(2)=1.;
|
||||
phig(3)=0.;
|
||||
phih(1)=-1.;
|
||||
phih(2)=0.;
|
||||
phih(3)=1.;
|
||||
djac=abs(x1*(y2-y3)+x2*(y3-y1)+x3*(y1-y2));
|
||||
for k=1:3
|
||||
phix(k)=(1./djac)*((-y1+y3)*phig(k)+(y1-y2)*phih(k));
|
||||
phiy(k)=(1./djac)*((x1-x3)*phig(k)+(-x1+x2)*phih(k));
|
||||
end
|
||||
delphi=[phix;phiy];
|
||||
nodalLset=[lSet(NBelem(i,1));lSet(NBelem(i,2));lSet(NBelem(i,3))];
|
||||
nodalF=[F(NBelem(i,1));F(NBelem(i,2));F(NBelem(i,3))];
|
||||
delset=delphi*nodalLset;
|
||||
Floc=phi*nodalF;
|
||||
mMatL=mMatL+(phi'*phi)/3.;
|
||||
mMatGLSL=mMatGLSL+((delphi'*(delset/norm(delset)))*Floc*(h2/abs(Floc)))*phi/3.;
|
||||
f1L=f1L+phi'*Floc*norm(delset)/3.;
|
||||
f2L=f2L+(delphi'*(delset/norm(delset))*Floc)*(h2/abs(Floc))*Floc*norm(delset)/3.;
|
||||
vs=h2*((abs(visc+Floc*norm(delset)))/(norm(Floc*delset)+h2));
|
||||
f3L=f3L+vs*delphi'*delset/3.;
|
||||
end
|
||||
for k=1:3;
|
||||
for j=1:3;
|
||||
mMat(NBelem(i,j),NBelem(i,k))=mMat(NBelem(i,j),NBelem(i,k))+mMatL(j,k);
|
||||
mMatGLS(NBelem(i,j),NBelem(i,k))=mMatGLS(NBelem(i,j),NBelem(i,k))+mMatGLSL(j,k);
|
||||
end
|
||||
f1(NBelem(i,k))=f1(NBelem(i,k))+f1L(k);
|
||||
f2(NBelem(i,k))=f2(NBelem(i,k))+f2L(k);
|
||||
f3(NBelem(i,k))=f3(NBelem(i,k))+f3L(k);
|
||||
end
|
||||
end
|
||||
dt=0.01;
|
||||
lSet=lSet-((((mMat+mMatGLS)^-1)*dt)*(f1+f2+f3))';
|
||||
end
|
||||
lSet'
|
||||
%[X Y]=meshgrid(0:1.:8);
|
||||
%Z=zeros(9);
|
||||
%for i=1:81
|
||||
% Z(i)=lSet(i);
|
||||
%end
|
||||
%surf(X,Y,Z)
|
||||
|
||||
|
||||
|
||||
|
||||
322
Unpublished/XFEM2/1D_Solver/F2DLevelSetFMM.asv
Normal file
322
Unpublished/XFEM2/1D_Solver/F2DLevelSetFMM.asv
Normal file
|
|
@ -0,0 +1,322 @@
|
|||
function [] = F2DLevelSetFMM()
|
||||
clear all
|
||||
% Define Main Solution Mesh
|
||||
NumX=5;
|
||||
NumY=1;
|
||||
delX=1.;
|
||||
delY=1.;
|
||||
for j=1:NumY+1
|
||||
for i=1:NumX+1
|
||||
index=i+(NumX+1)*(j-1);
|
||||
Node(index,1)=single((i-1.))*delX;
|
||||
Node(index,2)=single((j-1.))*delY;
|
||||
end
|
||||
end
|
||||
numNodes=(NumX+1)*(NumY+1);
|
||||
for j=1:NumY
|
||||
for i=1:NumX
|
||||
index=i+NumX*(j-1);
|
||||
Element(index,1)=i+(NumX+1)*(j-1);
|
||||
Element(index,2)=i+(NumX+1)*(j-1)+1;
|
||||
Element(index,3)=i+(NumX+1)*(j)+1;
|
||||
Element(index,4)=i+(NumX+1)*(j);
|
||||
end
|
||||
end
|
||||
numElem=(NumX)*(NumY);
|
||||
% Define Initial Level Set
|
||||
%centx=4.;
|
||||
%centy=4.;
|
||||
%rad=2.1;
|
||||
%for i=1:numNodes;
|
||||
% dist=sqrt((Node(i,1)-centx)*(Node(i,1)-centx)+(Node(i,2)-centy)*(Node(i,2)-centy));
|
||||
% lSet(i)=dist-rad;
|
||||
%end
|
||||
for i=1:numNodes;
|
||||
dist=Node(i,1)-0.1;
|
||||
lSet(i)=dist;
|
||||
end
|
||||
% Plot initial level set
|
||||
%[X Y]=meshgrid(0:1.:8);
|
||||
%Z=zeros(9);
|
||||
%for i=1:81
|
||||
% Z(i)=lSet(i);
|
||||
%end
|
||||
%surf(X,Y,Z)
|
||||
% LS Algorithm Parameters
|
||||
lSet'
|
||||
bandwidth=3.;
|
||||
% Loop through timesteps
|
||||
for tstep=1:1
|
||||
% Identify Narrow Band Elements
|
||||
NBElems=0;
|
||||
NBNodes=0;
|
||||
NGlobal=zeros(NumNodes);
|
||||
for i=1:numElem
|
||||
check=0;
|
||||
for iNd=1:4
|
||||
if abs(lSet(Element(i,iNd)))<=bandwidth*delX
|
||||
check=1;
|
||||
end
|
||||
end
|
||||
% If an element is in the narrow band split it into triangles
|
||||
if check==1
|
||||
for j=1:4
|
||||
if NewNums(Element(i,j))==0
|
||||
NBNodes=NBNodes+1
|
||||
NGlobal(Element(i,j))=NBNodes;
|
||||
NLocal(NBNodes)=Element(i,j);
|
||||
end
|
||||
end
|
||||
NBElems=NBElems+1;
|
||||
NBelem(NBElems,1)=NGlobal(Element(i,1));
|
||||
NBelem(NBElems,2)=NGlobal(Element(i,2));
|
||||
NBelem(NBElems,3)=NGlobal(Element(i,3));
|
||||
NBElems=NBElems+1;
|
||||
NBelem(NBElems,1)=NGlobal(Element(i,1));
|
||||
NBelem(NBElems,2)=NGlobal(Element(i,3));
|
||||
NBelem(NBElems,3)=NGlobal(Element(i,4));
|
||||
end
|
||||
end
|
||||
% Get local Level Set
|
||||
for i=1:NBNodes
|
||||
lSetLocal(i)=lSet(NLocal(i));
|
||||
end
|
||||
% Velocity BC
|
||||
F=zeros(NBNodes,1);
|
||||
for i=1:NBElems
|
||||
L1=sign(lSetLocal(NBelem(i,1)));
|
||||
L2=sign(lSetLocal(NBelem(i,2)));
|
||||
L3=sign(lSetLocal(NBelem(i,3)));
|
||||
if L1 ~= L2 || L1 ~= L3
|
||||
F(NBelem(i,1))= 1.;
|
||||
F(NBelem(i,2))= 1.;
|
||||
F(NBelem(i,3))= 1.;
|
||||
end
|
||||
end
|
||||
% Assemble 'Stiffness' Matrices
|
||||
A=zeros(NBNodes);
|
||||
for i=1:NBElems
|
||||
gx(1)=2./3.;
|
||||
gx(2)=1./6.;
|
||||
gx(3)=1./6.;
|
||||
hx(1)=1./6.;
|
||||
hx(2)=1./6.;
|
||||
hx(3)=2./3.;
|
||||
AfL=zeros(3);
|
||||
AfLGLS=zeros(3);
|
||||
x1=Node(NLocal(NBelem(i,1)),1);
|
||||
y1=Node(NLocal(NBelem(i,1)),2);
|
||||
x2=Node(NLocal(NBelem(i,2)),1);
|
||||
y2=Node(NLocal(NBelem(i,2)),2);
|
||||
x3=Node(NLocal(NBelem(i,3)),1);
|
||||
y3=Node(NLocal(NBelem(i,3)),2);
|
||||
for j=1:3
|
||||
g=gx(j);
|
||||
h=hx(j);
|
||||
phi(1)=1.-g-h;
|
||||
phi(2)=g;
|
||||
phi(3)=h;
|
||||
phig(1)=-1.;
|
||||
phig(2)=1.;
|
||||
phig(3)=0.;
|
||||
phih(1)=-1.;
|
||||
phih(2)=0.;
|
||||
phih(3)=1.;
|
||||
djac=2*abs(x1*(y2-y3)+x2*(y3-y1)+x3*(y1-y2));
|
||||
for k=1:3
|
||||
phix(k)=(1./djac)*((-y1+y3)*phig(k)+(y1-y2)*phih(k));
|
||||
phiy(k)=(1./djac)*((x1-x3)*phig(k)+(-x1+x2)*phih(k));
|
||||
end
|
||||
delphi=[phix;phiy];
|
||||
nodalLset=[lSetLocal(NBelem(i,1));lSetLocal(NBelem(i,2));lSetLocal(NBelem(i,3))];
|
||||
set=phi*nodalLset;
|
||||
delset=delphi*nodalLset;
|
||||
AfL=AfL+(phi'*sign(set))*(delset'*delphi)/3.;
|
||||
AfLGLS=AfLGLS+(delphi'*delset)*(1./norm(delset))*(delset'*delphi)/3.;
|
||||
end
|
||||
sum=AfL+AfLGLS;
|
||||
for k=1:3;
|
||||
for j=1:3;
|
||||
A(NBelem(i,j),NBelem(i,k))=A(NBelem(i,j),NBelem(i,k))+sum(j,k);
|
||||
end
|
||||
end
|
||||
end
|
||||
% Apply BCs
|
||||
RHS=zeros(NBNodes,1);
|
||||
Sub=A*F;
|
||||
iindex=0;
|
||||
for i=1:NBNodes
|
||||
if F(i)==0.
|
||||
iindex=iindex+1;
|
||||
RHSred(iindex)=RHS(i)-Sub(i);
|
||||
Fred=0.;
|
||||
jindex=0;
|
||||
for j=1:NBNodes
|
||||
if F(j)==0.
|
||||
jindex=jindex+1;
|
||||
Ared(iindex,jindex)=A(i,j);
|
||||
end
|
||||
end
|
||||
end
|
||||
end
|
||||
% Solve for Fred
|
||||
Fred=(Ared^-1)*RHSred';
|
||||
% Get F
|
||||
iindex=0;
|
||||
for i=1:NBNodes
|
||||
if F(i)==0.
|
||||
iindex=iindex+1;
|
||||
F(i)=Fred(iindex);
|
||||
end
|
||||
end
|
||||
% Update level set
|
||||
mMat=zeros(NBNodes);
|
||||
mMatGLS=zeros(NBNodes);
|
||||
f1=zeros(NBNodes,1);
|
||||
f2=zeros(NBNodes,1);
|
||||
f3=zeros(NBNodes,1);
|
||||
h2=0.00001;
|
||||
visc=0.0005;
|
||||
for i=1:NBElems
|
||||
mMatL=zeros(3);
|
||||
mMatGLSL=zeros(3);
|
||||
f1L=zeros(3,1);
|
||||
f2L=zeros(3,1);
|
||||
f3L=zeros(3,1);
|
||||
gx(1)=2./3.;
|
||||
gx(2)=1./6.;
|
||||
gx(3)=1./6.;
|
||||
hx(1)=1./6.;
|
||||
hx(2)=1./6.;
|
||||
hx(3)=2./3.;
|
||||
x1=Node(NLocal(NBelem(i,1)),1);
|
||||
y1=Node(NLocal(NBelem(i,1)),2);
|
||||
x2=Node(NLocal(NBelem(i,2)),1);
|
||||
y2=Node(NLocal(NBelem(i,2)),2);
|
||||
x3=Node(NLocal(NBelem(i,3)),1);
|
||||
y3=Node(NLocal(NBelem(i,3)),2);
|
||||
for j=1:3
|
||||
g=gx(j);
|
||||
h=hx(j);
|
||||
phi(1)=1.-g-h;
|
||||
phi(2)=g;
|
||||
phi(3)=h;
|
||||
phig(1)=-1.;
|
||||
phig(2)=1.;
|
||||
phig(3)=0.;
|
||||
phih(1)=-1.;
|
||||
phih(2)=0.;
|
||||
phih(3)=1.;
|
||||
djac=abs(x1*(y2-y3)+x2*(y3-y1)+x3*(y1-y2));
|
||||
for k=1:3
|
||||
phix(k)=(1./djac)*((-y1+y3)*phig(k)+(y1-y2)*phih(k));
|
||||
phiy(k)=(1./djac)*((x1-x3)*phig(k)+(-x1+x2)*phih(k));
|
||||
end
|
||||
delphi=[phix;phiy];
|
||||
nodalLset=[lSetLocal(NBelem(i,1));lSetLocal(NBelem(i,2));lSetLocal(NBelem(i,3))];
|
||||
nodalF=[F(NBelem(i,1));F(NBelem(i,2));F(NBelem(i,3))];
|
||||
delset=delphi*nodalLset;
|
||||
Floc=phi*nodalF;
|
||||
mMatL=mMatL+(phi'*phi)/3.;
|
||||
mMatGLSL=mMatGLSL+((delphi'*(delset/norm(delset)))*Floc*(h2/abs(Floc)))*phi/3.;
|
||||
f1L=f1L+phi'*Floc*norm(delset)/3.;
|
||||
f2L=f2L+(delphi'*(delset/norm(delset))*Floc)*(h2/abs(Floc))*Floc*norm(delset)/3.;
|
||||
vs=h2*((abs(visc+Floc*norm(delset)))/(norm(Floc*delset)+h2));
|
||||
f3L=f3L+vs*delphi'*delset/3.;
|
||||
end
|
||||
for k=1:3;
|
||||
for j=1:3;
|
||||
mMat(NBelem(i,j),NBelem(i,k))=mMat(NBelem(i,j),NBelem(i,k))+mMatL(j,k);
|
||||
mMatGLS(NBelem(i,j),NBelem(i,k))=mMatGLS(NBelem(i,j),NBelem(i,k))+mMatGLSL(j,k);
|
||||
end
|
||||
f1(NBelem(i,k))=f1(NBelem(i,k))+f1L(k);
|
||||
f2(NBelem(i,k))=f2(NBelem(i,k))+f2L(k);
|
||||
f3(NBelem(i,k))=f3(NBelem(i,k))+f3L(k);
|
||||
end
|
||||
end
|
||||
dt=0.01;
|
||||
lSetLocal=lSetLocal-((((mMat+mMatGLS)^-1)*dt)*(f1+f2+f3))';
|
||||
newlSet=lSetLocal;
|
||||
% Reinitialize LS
|
||||
nstat=zeros(NBNodes,1);
|
||||
for i=1:NBelems
|
||||
L1=sign(lSetLocal(NBelem(i,1)));
|
||||
L2=sign(lSetLocal(NBelem(i,2)));
|
||||
L3=sign(lSetLocal(NBelem(i,3)));
|
||||
if L1 ~= L2 || L1 ~= L3
|
||||
for j=1:3
|
||||
nstat(NBelem(i,j))=1;
|
||||
end
|
||||
end
|
||||
end
|
||||
maincheck=0;
|
||||
while(maincheck==0)
|
||||
lmin=1000.;
|
||||
avlmin=1000.;
|
||||
eindex=0;
|
||||
nindex=0;
|
||||
maincheck=1;
|
||||
for i=1:NBindex
|
||||
if nstat(NBelem(i,1))+nstat(NBelem(i,2))+nstat(NBelem(i,3))==2
|
||||
maincheck=0;
|
||||
check=0;
|
||||
ltot=0.;
|
||||
for j=1:3
|
||||
if nstat(NBelem(i,j))==0
|
||||
if abs(lSet(NBelem(i,j)))<=lmin
|
||||
check=1;
|
||||
tempindex=j;
|
||||
end
|
||||
end
|
||||
ltot=ltot+abs(lSet(NBelem(i,j)));
|
||||
end
|
||||
if check==1 & ltot/3.<=avlmin
|
||||
eindex=i;
|
||||
nindex=tempindex;
|
||||
lmin=lSet(NBelem(eindex,nindex));
|
||||
avlmin=ltot/3.;
|
||||
end
|
||||
end
|
||||
end
|
||||
if maincheck==0
|
||||
% Find New LS for point
|
||||
xp=Node(NBelem(eindex,nindex),1);
|
||||
yp=Node(NBelem(eindex,nindex),2);
|
||||
count=0;
|
||||
for i=1:3
|
||||
if i~=nindex
|
||||
count=count+1;
|
||||
x(count)=Node(NBelem(eindex,i),1);
|
||||
y(count)=Node(NBelem(eindex,i),2);
|
||||
lloc(count)=newlSet(NBelem(eindex,i));
|
||||
end
|
||||
end
|
||||
delxa=x(1)-xp;
|
||||
delya=y(1)-yp;
|
||||
delxb=x(2)-xp;
|
||||
delyb=y(2)-yp;
|
||||
N=[delxa delya; delxb delyb];
|
||||
M=N^-1;
|
||||
A=(M(1)*M(1)+M(2)*M(2));
|
||||
B=(M(3)*M(3)+M(4)*M(4));
|
||||
C=2.*(M(1)*M(3)+M(2)*M(4));
|
||||
a=A+B+C;
|
||||
b=-2.*lloc(1)*A-2.*lloc(2)*B-C*(lloc(1)+lloc(2));
|
||||
c=lloc(1)*lloc(1)*A+lloc(2)*lloc(2)*B+lloc(1)*lloc(2)*C-1.;
|
||||
templ1=(-b+sqrt(b*b-4.*a*c))/(2.*a);
|
||||
templ2=(-b-sqrt(b*b-4.*a*c))/(2.*a);
|
||||
if abs(templ1)>abs(templ2)
|
||||
newlSet(NBelem(eindex,nindex))=templ1;
|
||||
else
|
||||
newlSet(NBelem(eindex,nindex))=templ2;
|
||||
end
|
||||
nstat(NBelem(eindex,nindex))=1;
|
||||
end
|
||||
end
|
||||
% lSet=newlSet;
|
||||
end
|
||||
lSet'
|
||||
|
||||
|
||||
|
||||
|
||||
331
Unpublished/XFEM2/1D_Solver/F2DLevelSetFMM.m
Normal file
331
Unpublished/XFEM2/1D_Solver/F2DLevelSetFMM.m
Normal file
|
|
@ -0,0 +1,331 @@
|
|||
function [] = F2DLevelSetFMM()
|
||||
clear all
|
||||
% Define Main Solution Mesh
|
||||
NumX=32;
|
||||
NumY=32;
|
||||
delX=0.25;
|
||||
delY=0.25;
|
||||
for j=1:NumY+1
|
||||
for i=1:NumX+1
|
||||
index=i+(NumX+1)*(j-1);
|
||||
Node(index,1)=single((i-1.))*delX;
|
||||
Node(index,2)=single((j-1.))*delY;
|
||||
end
|
||||
end
|
||||
numNodes=(NumX+1)*(NumY+1);
|
||||
for j=1:NumY
|
||||
for i=1:NumX
|
||||
index=i+NumX*(j-1);
|
||||
Element(index,1)=i+(NumX+1)*(j-1);
|
||||
Element(index,2)=i+(NumX+1)*(j-1)+1;
|
||||
Element(index,3)=i+(NumX+1)*(j)+1;
|
||||
Element(index,4)=i+(NumX+1)*(j);
|
||||
end
|
||||
end
|
||||
numElem=(NumX)*(NumY);
|
||||
% Define Initial Level Set
|
||||
centx=4.;
|
||||
centy=4.;
|
||||
rad=2.1;
|
||||
for i=1:numNodes;
|
||||
dist=sqrt((Node(i,1)-centx)*(Node(i,1)-centx)+(Node(i,2)-centy)*(Node(i,2)-centy));
|
||||
lSet(i)=dist-rad;
|
||||
end
|
||||
%for i=1:numNodes;
|
||||
% dist=Node(i,1)-0.1;
|
||||
% lSet(i)=dist;
|
||||
%end
|
||||
% Plot initial level set
|
||||
[X Y]=meshgrid(0:0.25:8);
|
||||
Z=zeros(33);
|
||||
for i=1:1089
|
||||
Z(i)=lSet(i);
|
||||
end
|
||||
surf(X,Y,Z)
|
||||
% LS Algorithm Parameters
|
||||
lSet'
|
||||
bandwidth=10;
|
||||
% Loop through timesteps
|
||||
for tstep=1:10
|
||||
% Identify Narrow Band Elements
|
||||
NBElems=0;
|
||||
NBNodes=0;
|
||||
NGlobal=zeros(numNodes);
|
||||
for i=1:numElem
|
||||
check=0;
|
||||
for iNd=1:4
|
||||
if abs(lSet(Element(i,iNd)))<=bandwidth*delX
|
||||
check=1;
|
||||
end
|
||||
end
|
||||
% If an element is in the narrow band split it into triangles
|
||||
if check==1
|
||||
for j=1:4
|
||||
if NGlobal(Element(i,j))==0
|
||||
NBNodes=NBNodes+1;
|
||||
NGlobal(Element(i,j))=NBNodes;
|
||||
NLocal(NBNodes)=Element(i,j);
|
||||
end
|
||||
end
|
||||
NBElems=NBElems+1;
|
||||
NBelem(NBElems,1)=NGlobal(Element(i,1));
|
||||
NBelem(NBElems,2)=NGlobal(Element(i,2));
|
||||
NBelem(NBElems,3)=NGlobal(Element(i,3));
|
||||
NBElems=NBElems+1;
|
||||
NBelem(NBElems,1)=NGlobal(Element(i,1));
|
||||
NBelem(NBElems,2)=NGlobal(Element(i,3));
|
||||
NBelem(NBElems,3)=NGlobal(Element(i,4));
|
||||
end
|
||||
end
|
||||
% Get local Level Set
|
||||
for i=1:NBNodes
|
||||
lSetLocal(i)=lSet(NLocal(i));
|
||||
end
|
||||
% Velocity BC
|
||||
F=zeros(NBNodes,1);
|
||||
for i=1:NBElems
|
||||
L1=sign(lSetLocal(NBelem(i,1)));
|
||||
L2=sign(lSetLocal(NBelem(i,2)));
|
||||
L3=sign(lSetLocal(NBelem(i,3)));
|
||||
if L1 ~= L2 || L1 ~= L3
|
||||
F(NBelem(i,1))= 1.;
|
||||
F(NBelem(i,2))= 1.;
|
||||
F(NBelem(i,3))= 1.;
|
||||
end
|
||||
end
|
||||
% Assemble 'Stiffness' Matrices
|
||||
A=zeros(NBNodes);
|
||||
for i=1:NBElems
|
||||
gx(1)=2./3.;
|
||||
gx(2)=1./6.;
|
||||
gx(3)=1./6.;
|
||||
hx(1)=1./6.;
|
||||
hx(2)=1./6.;
|
||||
hx(3)=2./3.;
|
||||
AfL=zeros(3);
|
||||
AfLGLS=zeros(3);
|
||||
x1=Node(NLocal(NBelem(i,1)),1);
|
||||
y1=Node(NLocal(NBelem(i,1)),2);
|
||||
x2=Node(NLocal(NBelem(i,2)),1);
|
||||
y2=Node(NLocal(NBelem(i,2)),2);
|
||||
x3=Node(NLocal(NBelem(i,3)),1);
|
||||
y3=Node(NLocal(NBelem(i,3)),2);
|
||||
for j=1:3
|
||||
g=gx(j);
|
||||
h=hx(j);
|
||||
phi(1)=1.-g-h;
|
||||
phi(2)=g;
|
||||
phi(3)=h;
|
||||
phig(1)=-1.;
|
||||
phig(2)=1.;
|
||||
phig(3)=0.;
|
||||
phih(1)=-1.;
|
||||
phih(2)=0.;
|
||||
phih(3)=1.;
|
||||
djac=2*abs(x1*(y2-y3)+x2*(y3-y1)+x3*(y1-y2));
|
||||
for k=1:3
|
||||
phix(k)=(1./djac)*((-y1+y3)*phig(k)+(y1-y2)*phih(k));
|
||||
phiy(k)=(1./djac)*((x1-x3)*phig(k)+(-x1+x2)*phih(k));
|
||||
end
|
||||
delphi=[phix;phiy];
|
||||
nodalLset=[lSetLocal(NBelem(i,1));lSetLocal(NBelem(i,2));lSetLocal(NBelem(i,3))];
|
||||
set=phi*nodalLset;
|
||||
delset=delphi*nodalLset;
|
||||
AfL=AfL+(phi'*sign(set))*(delset'*delphi)/3.;
|
||||
AfLGLS=AfLGLS+(delphi'*delset)*(1./norm(delset))*(delset'*delphi)/3.;
|
||||
end
|
||||
sum=AfL+AfLGLS;
|
||||
for k=1:3;
|
||||
for j=1:3;
|
||||
A(NBelem(i,j),NBelem(i,k))=A(NBelem(i,j),NBelem(i,k))+sum(j,k);
|
||||
end
|
||||
end
|
||||
end
|
||||
% Apply BCs
|
||||
RHS=zeros(NBNodes,1);
|
||||
Sub=A*F;
|
||||
iindex=0;
|
||||
for i=1:NBNodes
|
||||
if F(i)==0.
|
||||
iindex=iindex+1;
|
||||
RHSred(iindex)=RHS(i)-Sub(i);
|
||||
Fred=0.;
|
||||
jindex=0;
|
||||
for j=1:NBNodes
|
||||
if F(j)==0.
|
||||
jindex=jindex+1;
|
||||
Ared(iindex,jindex)=A(i,j);
|
||||
end
|
||||
end
|
||||
end
|
||||
end
|
||||
% Solve for Fred
|
||||
Fred=(Ared^-1)*RHSred';
|
||||
% Get F
|
||||
iindex=0;
|
||||
for i=1:NBNodes
|
||||
if F(i)==0.
|
||||
iindex=iindex+1;
|
||||
F(i)=Fred(iindex);
|
||||
end
|
||||
end
|
||||
% Update level set
|
||||
mMat=zeros(NBNodes);
|
||||
mMatGLS=zeros(NBNodes);
|
||||
f1=zeros(NBNodes,1);
|
||||
f2=zeros(NBNodes,1);
|
||||
f3=zeros(NBNodes,1);
|
||||
h2=0.00001;
|
||||
visc=0.0005;
|
||||
for i=1:NBElems
|
||||
mMatL=zeros(3);
|
||||
mMatGLSL=zeros(3);
|
||||
f1L=zeros(3,1);
|
||||
f2L=zeros(3,1);
|
||||
f3L=zeros(3,1);
|
||||
gx(1)=2./3.;
|
||||
gx(2)=1./6.;
|
||||
gx(3)=1./6.;
|
||||
hx(1)=1./6.;
|
||||
hx(2)=1./6.;
|
||||
hx(3)=2./3.;
|
||||
x1=Node(NLocal(NBelem(i,1)),1);
|
||||
y1=Node(NLocal(NBelem(i,1)),2);
|
||||
x2=Node(NLocal(NBelem(i,2)),1);
|
||||
y2=Node(NLocal(NBelem(i,2)),2);
|
||||
x3=Node(NLocal(NBelem(i,3)),1);
|
||||
y3=Node(NLocal(NBelem(i,3)),2);
|
||||
for j=1:3
|
||||
g=gx(j);
|
||||
h=hx(j);
|
||||
phi(1)=1.-g-h;
|
||||
phi(2)=g;
|
||||
phi(3)=h;
|
||||
phig(1)=-1.;
|
||||
phig(2)=1.;
|
||||
phig(3)=0.;
|
||||
phih(1)=-1.;
|
||||
phih(2)=0.;
|
||||
phih(3)=1.;
|
||||
djac=abs(x1*(y2-y3)+x2*(y3-y1)+x3*(y1-y2));
|
||||
for k=1:3
|
||||
phix(k)=(1./djac)*((-y1+y3)*phig(k)+(y1-y2)*phih(k));
|
||||
phiy(k)=(1./djac)*((x1-x3)*phig(k)+(-x1+x2)*phih(k));
|
||||
end
|
||||
delphi=[phix;phiy];
|
||||
nodalLset=[lSetLocal(NBelem(i,1));lSetLocal(NBelem(i,2));lSetLocal(NBelem(i,3))];
|
||||
nodalF=[F(NBelem(i,1));F(NBelem(i,2));F(NBelem(i,3))];
|
||||
delset=delphi*nodalLset;
|
||||
Floc=phi*nodalF;
|
||||
mMatL=mMatL+(phi'*phi)/3.;
|
||||
mMatGLSL=mMatGLSL+((delphi'*(delset/norm(delset)))*Floc*(h2/abs(Floc)))*phi/3.;
|
||||
f1L=f1L+phi'*Floc*norm(delset)/3.;
|
||||
f2L=f2L+(delphi'*(delset/norm(delset))*Floc)*(h2/abs(Floc))*Floc*norm(delset)/3.;
|
||||
vs=h2*((abs(visc+Floc*norm(delset)))/(norm(Floc*delset)+h2));
|
||||
f3L=f3L+vs*delphi'*delset/3.;
|
||||
end
|
||||
for k=1:3;
|
||||
for j=1:3;
|
||||
mMat(NBelem(i,j),NBelem(i,k))=mMat(NBelem(i,j),NBelem(i,k))+mMatL(j,k);
|
||||
mMatGLS(NBelem(i,j),NBelem(i,k))=mMatGLS(NBelem(i,j),NBelem(i,k))+mMatGLSL(j,k);
|
||||
end
|
||||
f1(NBelem(i,k))=f1(NBelem(i,k))+f1L(k);
|
||||
f2(NBelem(i,k))=f2(NBelem(i,k))+f2L(k);
|
||||
f3(NBelem(i,k))=f3(NBelem(i,k))+f3L(k);
|
||||
end
|
||||
end
|
||||
dt=0.01;
|
||||
lSetLocal=lSetLocal-((((mMat+mMatGLS)^-1)*dt)*(f1+f2+f3))';
|
||||
newlSet=lSetLocal;
|
||||
% Reinitialize LS
|
||||
nstat=zeros(NBNodes,1);
|
||||
for i=1:NBElems
|
||||
L1=sign(lSetLocal(NBelem(i,1)));
|
||||
L2=sign(lSetLocal(NBelem(i,2)));
|
||||
L3=sign(lSetLocal(NBelem(i,3)));
|
||||
if L1 ~= L2 || L1 ~= L3
|
||||
for j=1:3
|
||||
nstat(NBelem(i,j))=1;
|
||||
end
|
||||
end
|
||||
end
|
||||
maincheck=0;
|
||||
while(maincheck==0)
|
||||
lmin=1000.;
|
||||
avlmin=1000.;
|
||||
eindex=0;
|
||||
nindex=0;
|
||||
maincheck=1;
|
||||
for i=1:NBElems
|
||||
if nstat(NBelem(i,1))+nstat(NBelem(i,2))+nstat(NBelem(i,3))==2
|
||||
maincheck=0;
|
||||
check=0;
|
||||
ltot=0.;
|
||||
for j=1:3
|
||||
if nstat(NBelem(i,j))==0
|
||||
if abs(lSetLocal(NBelem(i,j)))<=lmin
|
||||
check=1;
|
||||
tempindex=j;
|
||||
end
|
||||
end
|
||||
ltot=ltot+abs(lSetLocal(NBelem(i,j)));
|
||||
end
|
||||
if check==1 & ltot/3.<=avlmin
|
||||
eindex=i;
|
||||
nindex=tempindex;
|
||||
lmin=lSetLocal(NBelem(eindex,nindex));
|
||||
avlmin=ltot/3.;
|
||||
end
|
||||
end
|
||||
end
|
||||
if maincheck==0
|
||||
% Find New LS for point
|
||||
xp=Node(NLocal(NBelem(eindex,nindex)),1);
|
||||
yp=Node(NLocal(NBelem(eindex,nindex)),2);
|
||||
count=0;
|
||||
for i=1:3
|
||||
if i~=nindex
|
||||
count=count+1;
|
||||
x(count)=Node(NLocal(NBelem(eindex,i)),1);
|
||||
y(count)=Node(NLocal(NBelem(eindex,i)),2);
|
||||
lloc(count)=newlSet(NBelem(eindex,i));
|
||||
end
|
||||
end
|
||||
delxa=x(1)-xp;
|
||||
delya=y(1)-yp;
|
||||
delxb=x(2)-xp;
|
||||
delyb=y(2)-yp;
|
||||
N=[delxa delya; delxb delyb];
|
||||
M=N^-1;
|
||||
A=(M(1)*M(1)+M(2)*M(2));
|
||||
B=(M(3)*M(3)+M(4)*M(4));
|
||||
C=2.*(M(1)*M(3)+M(2)*M(4));
|
||||
a=A+B+C;
|
||||
b=-2.*lloc(1)*A-2.*lloc(2)*B-C*(lloc(1)+lloc(2));
|
||||
c=lloc(1)*lloc(1)*A+lloc(2)*lloc(2)*B+lloc(1)*lloc(2)*C-1.;
|
||||
templ1=(-b+sqrt(b*b-4.*a*c))/(2.*a);
|
||||
templ2=(-b-sqrt(b*b-4.*a*c))/(2.*a);
|
||||
if abs(templ1)>abs(templ2)
|
||||
newlSet(NBelem(eindex,nindex))=templ1;
|
||||
else
|
||||
newlSet(NBelem(eindex,nindex))=templ2;
|
||||
end
|
||||
nstat(NBelem(eindex,nindex))=1;
|
||||
end
|
||||
end
|
||||
% lSetLocal=newlSet;
|
||||
% Update Global Level Set
|
||||
for i=1:NBNodes
|
||||
lSet(NLocal(i))=lSetLocal(i);
|
||||
end
|
||||
end
|
||||
lSet'
|
||||
[X Y]=meshgrid(0:0.25:8);
|
||||
Z=zeros(33);
|
||||
for i=1:1089
|
||||
Z(i)=lSet(i);
|
||||
end
|
||||
surf(X,Y,Z)
|
||||
|
||||
|
||||
|
||||
221
Unpublished/XFEM2/1D_Solver/FESolveX.m
Normal file
221
Unpublished/XFEM2/1D_Solver/FESolveX.m
Normal file
|
|
@ -0,0 +1,221 @@
|
|||
function [] = FESolveX()
|
||||
% MATLAB based XFEM Solver
|
||||
% J. Grogan (2012)
|
||||
clear all
|
||||
% Define Geometry
|
||||
len=10.;
|
||||
% Define Section Properties
|
||||
rho=1.;
|
||||
% Generate Mesh
|
||||
numElem=10;
|
||||
charlen=len/numElem;
|
||||
ndCoords=linspace(0,len,numElem+1);
|
||||
numNodes=size(ndCoords,2);
|
||||
indx=1:numElem;
|
||||
elemNodes(:,1)=indx;
|
||||
elemNodes(:,2)=indx+1;
|
||||
% dofs per node
|
||||
ndof=2;
|
||||
% initial interface position
|
||||
dpos=5.;
|
||||
% Initial temperatures
|
||||
Tnew=zeros(numNodes*2,1);
|
||||
%storage
|
||||
stored(1)=dpos;
|
||||
for e=1:numElem
|
||||
crdn1=ndCoords(elemNodes(e,1));
|
||||
if crdn1<=dpos
|
||||
Tnew(2*elemNodes(e,1)-1)=1.;
|
||||
end
|
||||
end
|
||||
% Define Time Step
|
||||
dtime=0.05;
|
||||
tsteps=20;
|
||||
time=0.;
|
||||
% penalty term
|
||||
beta=40.;
|
||||
% Loop through time steps
|
||||
for ts=1:tsteps
|
||||
% Get interface velocity
|
||||
d(1)=dpos+charlen;
|
||||
d(2)=dpos+3*charlen/4;
|
||||
d(3)=dpos+charlen/4;
|
||||
d(4)=dpos;
|
||||
for e=1:numElem
|
||||
crdn1=ndCoords(elemNodes(e,1));
|
||||
crdn2=ndCoords(elemNodes(e,2));
|
||||
for j=1:4
|
||||
if d(j)>=crdn1 & d(j)<crdn2
|
||||
elen=abs(crdn2-crdn1);
|
||||
ajacob=elen/2.;
|
||||
point=(d(j)-crdn1)/ajacob-1.;
|
||||
theta(1)=abs(crdn1-dpos)*sign(crdn1-dpos);
|
||||
theta(2)=abs(crdn2-dpos)*sign(crdn2-dpos);
|
||||
tmp1a=Tnew(elemNodes(e,1)*2-1);
|
||||
tmp1b=Tnew(elemNodes(e,1)*2);
|
||||
tmp2a=Tnew(elemNodes(e,2)*2-1);
|
||||
tmp2b=Tnew(elemNodes(e,2)*2);
|
||||
xi=point;
|
||||
gm(1)=(1.-xi)/2.;
|
||||
gm(3)=(1.+xi)/2.;
|
||||
term=theta(1)*gm(1)+theta(2)*gm(3);
|
||||
gm(2)=gm(1)*(abs(term)-abs(theta(1)));
|
||||
gm(4)=gm(3)*(abs(term)-abs(theta(2)));
|
||||
t(j)=gm(1)*tmp1a+gm(2)*tmp1b+gm(3)*tmp2a+gm(4)*tmp2b;
|
||||
end
|
||||
end
|
||||
end
|
||||
vel=(0.5/charlen)*(2*t(1)+t(2)-t(3)-2*t(4));
|
||||
% Update interface position
|
||||
dpos=dpos+vel*dtime;
|
||||
stored(ts+1)=dpos;
|
||||
K=zeros(numNodes*ndof,numNodes*ndof);
|
||||
M=zeros(numNodes*ndof,numNodes*ndof);
|
||||
pforce=zeros(numNodes*ndof,1);
|
||||
% Loop Through Elements
|
||||
for e=1:numElem
|
||||
Ke=zeros(2*ndof);
|
||||
Me=zeros(2*ndof);
|
||||
crdn1=ndCoords(elemNodes(e,1));
|
||||
crdn2=ndCoords(elemNodes(e,2));
|
||||
theta(1)=abs(crdn1-dpos)*sign(crdn1-dpos);
|
||||
theta(2)=abs(crdn2-dpos)*sign(crdn2-dpos);
|
||||
enr=2;
|
||||
elen=abs(crdn2-crdn1);
|
||||
ajacob=elen/2.;
|
||||
if sign(theta(1))~=sign(theta(2))
|
||||
% enriched element
|
||||
enr=4;
|
||||
% get interface position on element
|
||||
point=(dpos-crdn1)/ajacob-1.;
|
||||
% devide element for sub integration
|
||||
len1=abs(-point-1.);
|
||||
len2=abs(1.-point);
|
||||
mid1=-1+len1/2.;
|
||||
mid2=1-len2/2.;
|
||||
gpx(1)=-(len1/2.)/sqrt(3.)+mid1;
|
||||
gpx(2)=(len1/2.)/sqrt(3.)+mid1;
|
||||
gpx(3)=-(len2/2.)/sqrt(3.)+mid2;
|
||||
gpx(4)=(len2/2.)/sqrt(3.)+mid2;
|
||||
w(1)=(len1/2.);
|
||||
w(2)=(len1/2.);
|
||||
w(3)=(len2/2.);
|
||||
w(4)=(len2/2.);
|
||||
fdofs(1)=2*elemNodes(e,1);
|
||||
fdofs(2)=2*elemNodes(e,2);
|
||||
else
|
||||
% regular element - fix extra dofs
|
||||
gpx(1)=-1/sqrt(3.);
|
||||
gpx(2)=1/sqrt(3.);
|
||||
w(1)=1.;
|
||||
w(2)=1.;
|
||||
end
|
||||
% Loop Through Int Points
|
||||
for i=1:enr;
|
||||
c=gpx(i);
|
||||
phi(1)=(1.-c)/2.;
|
||||
phi(3)=(1.+c)/2.;
|
||||
term=theta(1)*phi(1)+theta(2)*phi(3);
|
||||
if term<0
|
||||
cond=0.;
|
||||
spec=0.01;
|
||||
else
|
||||
cond=1.;
|
||||
spec=1.;
|
||||
end
|
||||
phi(2)=phi(1)*(abs(term)-abs(theta(1)));
|
||||
phi(4)=phi(3)*(abs(term)-abs(theta(2)));
|
||||
phic(1)=-0.5;
|
||||
phic(3)=0.5;
|
||||
dterm=sign(term)*(phic(1)*theta(1)+phic(3)*theta(2));
|
||||
phic(2)=phic(1)*(abs(term)-abs(theta(1)))+phi(1)*dterm;
|
||||
phic(4)=phic(3)*(abs(term)-abs(theta(2)))+phi(3)*dterm;
|
||||
phix(1)=phic(1)/ajacob;
|
||||
phix(2)=phic(2)/ajacob;
|
||||
phix(3)=phic(3)/ajacob;
|
||||
phix(4)=phic(4)/ajacob;
|
||||
we=ajacob*w(i);
|
||||
Ke=Ke+we*cond*phix'*phix;
|
||||
Me=Me+(we*rho*spec*phi'*phi)/dtime;
|
||||
end
|
||||
% Add penalty term and get temp gradient on interface
|
||||
if enr==4;
|
||||
xi=point;
|
||||
gm(1)=(1.-xi)/2.;
|
||||
gm(3)=(1.+xi)/2.;
|
||||
term=theta(1)*gm(1)+theta(2)*gm(3);
|
||||
gm(2)=gm(1)*(abs(term)-abs(theta(1)));
|
||||
gm(4)=gm(3)*(abs(term)-abs(theta(2)));
|
||||
tpos=gm(1)*Tnew(1)+gm(2)*Tnew(2)+gm(3)*Tnew(3)+gm(4)*Tnew(4);
|
||||
pen=beta*(gm'*gm);
|
||||
pfL=beta*1*gm';
|
||||
Ke=Ke+pen;
|
||||
else
|
||||
pen=zeros(4);
|
||||
pfL=zeros(4,1);
|
||||
end
|
||||
% Assemble Global Matrices
|
||||
gnum=2.*elemNodes(e,1)-1.;
|
||||
for i=1:4;
|
||||
for j=1:4;
|
||||
K(gnum+j-1,gnum+i-1)=K(gnum+j-1,gnum+i-1)+Ke(j,i);
|
||||
M(gnum+j-1,gnum+i-1)=M(gnum+j-1,gnum+i-1)+Me(j,i);
|
||||
end
|
||||
pforce(gnum+i-1)=pforce(gnum+i-1)+pfL(i);
|
||||
end
|
||||
end
|
||||
%Remove inactive DOFs(Reduce Matrices)
|
||||
T1=1;
|
||||
RHS=M*Tnew;
|
||||
iindex=0;
|
||||
for i=1:ndof*numNodes;
|
||||
check=1;
|
||||
if i==fdofs(1)|i==fdofs(2)
|
||||
check=0;
|
||||
elseif mod(i,2)~=0 & i~=1
|
||||
check=0;
|
||||
end
|
||||
if check==0
|
||||
jindex=0;
|
||||
iindex=iindex+1;
|
||||
for j=1:ndof*numNodes;
|
||||
check=1;
|
||||
if j==fdofs(1)|j==fdofs(2)
|
||||
check=0;
|
||||
elseif mod(j,2)~=0 & j~=1
|
||||
check=0;
|
||||
end
|
||||
if check==0
|
||||
jindex=jindex+1;
|
||||
Kred(iindex,jindex)=K(i,j);
|
||||
Mred(iindex,jindex)=M(i,j);
|
||||
end
|
||||
end
|
||||
Subr(iindex)=(K(i,1)+M(i,1))*T1;
|
||||
RHSr(iindex)=RHS(i);
|
||||
pforcer(iindex)=pforce(i);
|
||||
end
|
||||
end
|
||||
%Solve
|
||||
Mred+Kred;
|
||||
StiffI=(Mred+Kred)^-1;
|
||||
Tnewr=StiffI*(RHSr'-Subr'+pforcer');
|
||||
iindex=0.;
|
||||
for i=1:ndof*numNodes;
|
||||
check=1;
|
||||
if i==fdofs(1)|i==fdofs(2)
|
||||
check=0;
|
||||
elseif mod(i,2)~=0 & i~=1
|
||||
check=0;
|
||||
end
|
||||
if check==0
|
||||
iindex=iindex+1;
|
||||
Tnew(i)=Tnewr(iindex);
|
||||
else
|
||||
Tnew(i)=0.;
|
||||
end
|
||||
end
|
||||
Tnew(1)=1.;
|
||||
Tnew
|
||||
end
|
||||
stored'
|
||||
128
Unpublished/XFEM2/1D_Solver/GetF.m
Normal file
128
Unpublished/XFEM2/1D_Solver/GetF.m
Normal file
|
|
@ -0,0 +1,128 @@
|
|||
function [] = GetF()
|
||||
% set up grid
|
||||
gd=0.;
|
||||
numElem=4;
|
||||
eLen=0.25;
|
||||
for i=1:numElem+1
|
||||
ndCrd(i)=gd;
|
||||
gd=gd+eLen;
|
||||
end
|
||||
for i=1:numElem
|
||||
elemNod(i,1)=i;
|
||||
elemNod(i,2)=i+1;
|
||||
end
|
||||
% Initial level set
|
||||
dpos=0.1;
|
||||
for i=1:numElem+1
|
||||
lSet(i)=sign(ndCrd(i)-dpos)*abs(dpos-ndCrd(i));
|
||||
end
|
||||
lSet'
|
||||
for tstep=1:1
|
||||
% Velocity BC
|
||||
F=zeros(numElem+1,1);
|
||||
for i=1:numElem
|
||||
if sign(lSet(elemNod(i,1)))~=sign(lSet(elemNod(i,2)))
|
||||
F(elemNod(i,1))= 0.0005;
|
||||
F(elemNod(i,2))= 0.0005;
|
||||
end
|
||||
end
|
||||
% Assemble 'Stiffness' Matrices
|
||||
A=zeros(numElem+1);
|
||||
for i=1:numElem
|
||||
pos(1)=-1/sqrt(3);
|
||||
pos(2)=1/sqrt(3);
|
||||
AfL=zeros(2);
|
||||
AfLGLS=zeros(2);
|
||||
for j=1:2
|
||||
shp(1)=(1-pos(j))/2.;
|
||||
shp(2)=(1+pos(j))/2.;
|
||||
dshp(1)=-0.5;
|
||||
dshp(2)=0.5;
|
||||
rset=shp(1)*lSet(elemNod(i,1))+shp(2)*lSet(elemNod(i,2));
|
||||
dls=dshp(1)*lSet(elemNod(i,1))+dshp(2)*lSet(elemNod(i,2));
|
||||
AfL=AfL+shp'*sign(rset)*(dls*dshp);
|
||||
AfLGLS=AfLGLS+(dshp'*dls)*(0.25/abs(dls))*(dls*dshp);
|
||||
end
|
||||
for k=1:2;
|
||||
for j=1:2;
|
||||
A(elemNod(i,j),elemNod(i,k))=A(elemNod(i,j),elemNod(i,k))+AfL(j,k)+AfLGLS(j,k)
|
||||
end
|
||||
end
|
||||
end
|
||||
% Apply BCs
|
||||
RHS=zeros(numElem+1,1);
|
||||
Sub=A*F;
|
||||
iindex=0;
|
||||
for i=1:numElem+1
|
||||
if F(i)==0.
|
||||
iindex=iindex+1;
|
||||
RHSred(iindex)=RHS(i)-Sub(i);
|
||||
Fred=0.;
|
||||
jindex=0;
|
||||
for j=1:numElem+1
|
||||
if F(j)==0.
|
||||
jindex=jindex+1;
|
||||
Ared(iindex,jindex)=A(i,j);
|
||||
end
|
||||
end
|
||||
end
|
||||
end
|
||||
% Solve for Fred
|
||||
Fred=(Ared^-1)*RHSred';
|
||||
% Get F
|
||||
iindex=0;
|
||||
for i=1:numElem+1
|
||||
if F(i)==0.
|
||||
iindex=iindex+1;
|
||||
F(i)=Fred(iindex);
|
||||
end
|
||||
end
|
||||
% Update level set
|
||||
mMat=zeros(numElem+1);
|
||||
mMatGLS=zeros(numElem+1);
|
||||
f1=zeros(numElem+1,1);
|
||||
f2=zeros(numElem+1,1);
|
||||
f3=zeros(numElem+1,1);
|
||||
h=0.25;
|
||||
visc=0.000;
|
||||
for i=1:numElem
|
||||
pos(1)=-1/sqrt(3);
|
||||
pos(2)=1/sqrt(3);
|
||||
mMatL=zeros(2);
|
||||
mMatGLSL=zeros(2);
|
||||
f1L=zeros(2,1);
|
||||
f2L=zeros(2,1);
|
||||
f3L=zeros(2,1);
|
||||
for j=1:2
|
||||
shp(1)=(1-pos(j))/2.;
|
||||
shp(2)=(1+pos(j))/2.;
|
||||
dshp(1)=-0.5;
|
||||
dshp(2)=0.5;
|
||||
Floc=shp(1)*F(elemNod(i,1))+shp(2)*F(elemNod(i,2));
|
||||
rset=shp(1)*lSet(elemNod(i,1))+shp(2)*lSet(elemNod(i,2));
|
||||
dls=dshp(1)*lSet(elemNod(i,1))+dshp(2)*lSet(elemNod(i,2));
|
||||
mMatL=mMatL+shp'*shp;
|
||||
mMatGLSL=mMatGLSL+((dshp'*(dls/abs(dls)))*Floc*(h/abs(Floc)))*shp;
|
||||
f1L=f1L+shp'*Floc*abs(dls);
|
||||
f2L=f2L+(dshp'*(dls/abs(dls))*Floc)*(h/abs(Floc))*Floc*abs(dls);
|
||||
vs=h*((abs(visc+Floc*abs(dls)))/(abs(Floc*dls)+h));
|
||||
f3L=f3L+vs*dshp'*dls;
|
||||
end
|
||||
for k=1:2;
|
||||
for j=1:2;
|
||||
mMat(elemNod(i,j),elemNod(i,k))=mMat(elemNod(i,j),elemNod(i,k))+mMatL(j,k);
|
||||
mMatGLS(elemNod(i,j),elemNod(i,k))=mMatGLS(elemNod(i,j),elemNod(i,k))+mMatGLSL(j,k);
|
||||
end
|
||||
f1(elemNod(i,k))=f1(elemNod(i,k))+f1L(k);
|
||||
f2(elemNod(i,k))=f2(elemNod(i,k))+f2L(k);
|
||||
f3(elemNod(i,k))=f3(elemNod(i,k))+f3L(k);
|
||||
end
|
||||
end
|
||||
dt=0.01;
|
||||
lSet=lSet-((((mMat+mMatGLS)^-1)/dt)*(f1+f2+f3))';
|
||||
lSet';
|
||||
end
|
||||
|
||||
|
||||
|
||||
|
||||
200
Unpublished/XFEM2/1D_Solver/GetF2D.asv
Normal file
200
Unpublished/XFEM2/1D_Solver/GetF2D.asv
Normal file
|
|
@ -0,0 +1,200 @@
|
|||
function [] = GetF2D_()
|
||||
clear all
|
||||
% Define Main Solution Mesh
|
||||
NumX=10;
|
||||
NumY=10;
|
||||
delX=1.;
|
||||
delY=1.;
|
||||
for j=1:NumY+1
|
||||
for i=1:NumX+1
|
||||
index=i+(NumX+1)*(j-1);
|
||||
Node(index,1)=single((i-1.))*delX;
|
||||
Node(index,2)=single((j-1.))*delY;
|
||||
end
|
||||
end
|
||||
numNodes=(NumX+1)*(NumY+1);
|
||||
for j=1:NumY
|
||||
for i=1:NumX
|
||||
index=i+NumX*(j-1);
|
||||
Element(index,1)=i+(NumX+1)*(j-1);
|
||||
Element(index,2)=i+(NumX+1)*(j-1)+1;
|
||||
Element(index,3)=i+(NumX+1)*(j)+1;
|
||||
Element(index,4)=i+(NumX+1)*(j);
|
||||
end
|
||||
end
|
||||
numElem=(NumX)*(NumY);
|
||||
% Define Initial Level Set
|
||||
centx=5.;
|
||||
centy=5.;
|
||||
rad=2.5;
|
||||
for i=1:numNodes;
|
||||
dist=sqrt((Node(i,1)-centx)*(Node(i,1)-centx)+(Node(i,2)-centy)*(Node(i,2)-centy));
|
||||
lSet(i)=dist-rad;
|
||||
end
|
||||
% Plot initial level set
|
||||
[X,Y]=meshgrid(0:1.:10);
|
||||
Z=zeros(11);
|
||||
for i=1:numNodes
|
||||
Z(i)=lSet(i);
|
||||
end
|
||||
surf(X,Y,Z)
|
||||
% LS Algorithm Parameters
|
||||
bandwith=10.;
|
||||
% Loop through timesteps
|
||||
for tstep=1:1
|
||||
% Identify Narrow Band Elements
|
||||
NBindex=0;
|
||||
for i=1:numElem
|
||||
check=0;
|
||||
for iNd=1:4
|
||||
if abs(lSet(Element(i,iNd)))<=bandwidth*delX
|
||||
check=1;
|
||||
end
|
||||
end
|
||||
% If an element is in the narrow band split it into triangles
|
||||
if check==1
|
||||
NBindex=NBindex+1;
|
||||
NBelem(NBindex,1)=Element(i,1);
|
||||
NBelem(NBindex,2)=Element(i,2);
|
||||
NBelem(NBindex,3)=Element(i,3);
|
||||
NBindex=NBindex+1;
|
||||
NBelem(NBindex,1)=Element(i,1);
|
||||
NBelem(NBindex,2)=Element(i,3);
|
||||
NBelem(NBindex,3)=Element(i,4);
|
||||
end
|
||||
end
|
||||
% Velocity BC
|
||||
F=zeros(numNodes,1);
|
||||
for i=1:NBindex
|
||||
if lSet(NBelem(i,1))~=lSet(NBelem(i,2)) || lSet(NBelem(i,1))~=lSet(NBelem(i,3))
|
||||
F(NBelem(i,1))= 0.0005;
|
||||
F(NBelem(i,2))= 0.0005;
|
||||
F(NBelem(i,3))= 0.0005;
|
||||
end
|
||||
end
|
||||
% Assemble 'Stiffness' Matrices
|
||||
A=zeros(numNodes);
|
||||
for i=1:NBindex
|
||||
gpos=1/sqrt(3.);
|
||||
gx(1)=-gpos;
|
||||
gx(2)=gpos;
|
||||
gx(3)=gpos;
|
||||
gx(4)=-gpos;
|
||||
hx(1)=-gpos;
|
||||
hx(2)=-gpos;
|
||||
hx(3)=gpos;
|
||||
hx(4)=gpos;
|
||||
AfL=zeros(4);
|
||||
AfLGLS=zeros(4);
|
||||
for j=1:4
|
||||
g=gx(j);
|
||||
h=hx(j);
|
||||
phi(1)=0.25*(1.-g)*(1.-h);
|
||||
phi(2)=0.25*(1.+g)*(1.-h);
|
||||
phi(3)=0.25*(1.+g)*(1.+h);
|
||||
phi(4)=0.25*(1.-g)*(1.+h);
|
||||
phig(1)=0.25*-(1.-h);
|
||||
phig(2)=0.25*(1.-h);
|
||||
phig(3)=0.25*(1.+h);
|
||||
phig(4)=0.25*-(1.+h);
|
||||
rset=phi(1)*lSet(Element(i,1))+phi(2)*lSet(Element(i,2))+phi(3)*lSet(Element(i,3))+phi(4)*lSet(Element(i,4));
|
||||
dls=phig(1)*lSet(Element(i,1))+phig(2)*lSet(Element(i,2))+phig(3)*lSet(Element(i,3))+phig(4)*lSet(Element(i,4));
|
||||
AfL=AfL+(phi'*sign(rset))*(dls*phig);
|
||||
AfLGLS=AfLGLS+(phig'*dls)*(1./abs(dls))*(dls*phig);
|
||||
end
|
||||
for k=1:4;
|
||||
for j=1:4;
|
||||
A(Element(i,j),Element(i,k))=A(Element(i,j),Element(i,k))+AfL(j,k)+AfLGLS(j,k);
|
||||
end
|
||||
end
|
||||
end
|
||||
% Apply BCs
|
||||
RHS=zeros(numNodes,1);
|
||||
Sub=A*F;
|
||||
iindex=0;
|
||||
for i=1:numNodes
|
||||
if F(i)==0.
|
||||
iindex=iindex+1;
|
||||
RHSred(iindex)=RHS(i)-Sub(i);
|
||||
Fred=0.;
|
||||
jindex=0;
|
||||
for j=1:numNodes
|
||||
if F(j)==0.
|
||||
jindex=jindex+1;
|
||||
Ared(iindex,jindex)=A(i,j);
|
||||
end
|
||||
end
|
||||
end
|
||||
end
|
||||
% Solve for Fred
|
||||
Fred=(Ared^-1)*RHSred';
|
||||
% Get F
|
||||
iindex=0;
|
||||
for i=1:numNodes
|
||||
if F(i)==0.
|
||||
iindex=iindex+1;
|
||||
F(i)=Fred(iindex);
|
||||
end
|
||||
end
|
||||
% Update level set
|
||||
mMat=zeros(numNodes);
|
||||
mMatGLS=zeros(numNodes);
|
||||
f1=zeros(numNodes,1);
|
||||
f2=zeros(numNodes,1);
|
||||
f3=zeros(numNodes,1);
|
||||
h=1.;
|
||||
visc=0.000;
|
||||
for i=1:numElem
|
||||
gpos=1/sqrt(3.);
|
||||
gx(1)=-gpos;
|
||||
gx(2)=gpos;
|
||||
gx(3)=gpos;
|
||||
gx(4)=-gpos;
|
||||
hx(1)=-gpos;
|
||||
hx(2)=-gpos;
|
||||
hx(3)=gpos;
|
||||
hx(4)=gpos;
|
||||
mMatL=zeros(4);
|
||||
mMatGLSL=zeros(4);
|
||||
f1L=zeros(4,1);
|
||||
f2L=zeros(4,1);
|
||||
f3L=zeros(4,1);
|
||||
for j=1:4
|
||||
g=gx(j);
|
||||
h=hx(j);
|
||||
phi(1)=0.25*(1.-g)*(1.-h);
|
||||
phi(2)=0.25*(1.+g)*(1.-h);
|
||||
phi(3)=0.25*(1.+g)*(1.+h);
|
||||
phi(4)=0.25*(1.-g)*(1.+h);
|
||||
phig(1)=0.25*-(1.-h);
|
||||
phig(2)=0.25*(1.-h);
|
||||
phig(3)=0.25*(1.+h);
|
||||
phig(4)=0.25*-(1.+h);
|
||||
Floc=phi(1)*F(Element(i,1))+phi(2)*F(Element(i,2))+phi(3)*F(Element(i,3))+phi(4)*F(Element(i,4));
|
||||
rset=phi(1)*lSet(Element(i,1))+phi(2)*lSet(Element(i,2))+phi(3)*lSet(Element(i,3))+phi(4)*lSet(Element(i,4));
|
||||
dls=phig(1)*lSet(Element(i,1))+phig(2)*lSet(Element(i,2))+phig(3)*lSet(Element(i,3))+phig(4)*lSet(Element(i,4));
|
||||
mMatL=mMatL+phi'*phi;
|
||||
mMatGLSL=mMatGLSL+((phig'*(dls/abs(dls)))*Floc*(h/abs(Floc)))*phi;
|
||||
f1L=f1L+phi'*Floc*abs(dls);
|
||||
f2L=f2L+(phig'*(dls/abs(dls))*Floc)*(h/abs(Floc))*Floc*abs(dls);
|
||||
vs=h*((abs(visc+Floc*abs(dls)))/(abs(Floc*dls)+h));
|
||||
f3L=f3L+vs*phig'*dls;
|
||||
end
|
||||
for k=1:4;
|
||||
for j=1:4;
|
||||
mMat(Element(i,j),Element(i,k))=mMat(Element(i,j),Element(i,k))+mMatL(j,k);
|
||||
mMatGLS(Element(i,j),Element(i,k))=mMatGLS(Element(i,j),Element(i,k))+mMatGLSL(j,k);
|
||||
end
|
||||
f1(Element(i,k))=f1(Element(i,k))+f1L(k);
|
||||
f2(Element(i,k))=f2(Element(i,k))+f2L(k);
|
||||
f3(Element(i,k))=f3(Element(i,k))+f3L(k);
|
||||
end
|
||||
end
|
||||
dt=0.01;
|
||||
lSet=lSet-((((mMat+mMatGLS)^-1)/dt)*(f1+f2+f3))';
|
||||
end
|
||||
%scatter3(Node(:,1), Node(:,2), lSet');
|
||||
|
||||
|
||||
|
||||
|
||||
200
Unpublished/XFEM2/1D_Solver/GetF2D.m
Normal file
200
Unpublished/XFEM2/1D_Solver/GetF2D.m
Normal file
|
|
@ -0,0 +1,200 @@
|
|||
function [] = GetF2D()
|
||||
clear all
|
||||
% Define Main Solution Mesh
|
||||
NumX=10;
|
||||
NumY=10;
|
||||
delX=1.;
|
||||
delY=1.;
|
||||
for j=1:NumY+1
|
||||
for i=1:NumX+1
|
||||
index=i+(NumX+1)*(j-1);
|
||||
Node(index,1)=single((i-1.))*delX;
|
||||
Node(index,2)=single((j-1.))*delY;
|
||||
end
|
||||
end
|
||||
numNodes=(NumX+1)*(NumY+1);
|
||||
for j=1:NumY
|
||||
for i=1:NumX
|
||||
index=i+NumX*(j-1);
|
||||
Element(index,1)=i+(NumX+1)*(j-1);
|
||||
Element(index,2)=i+(NumX+1)*(j-1)+1;
|
||||
Element(index,3)=i+(NumX+1)*(j)+1;
|
||||
Element(index,4)=i+(NumX+1)*(j);
|
||||
end
|
||||
end
|
||||
numElem=(NumX)*(NumY);
|
||||
% Define Initial Level Set
|
||||
centx=5.;
|
||||
centy=5.;
|
||||
rad=2.5;
|
||||
for i=1:numNodes;
|
||||
dist=sqrt((Node(i,1)-centx)*(Node(i,1)-centx)+(Node(i,2)-centy)*(Node(i,2)-centy));
|
||||
lSet(i)=dist-rad;
|
||||
end
|
||||
% Plot initial level set
|
||||
[X,Y]=meshgrid(0:1.:10);
|
||||
Z=zeros(11);
|
||||
for i=1:numNodes
|
||||
Z(i)=lSet(i);
|
||||
end
|
||||
surf(X,Y,Z)
|
||||
% LS Algorithm Parameters
|
||||
bandwith=10.;
|
||||
% Loop through timesteps
|
||||
for tstep=1:1
|
||||
% Identify Narrow Band Elements
|
||||
NBindex=0;
|
||||
for i=1:numElem
|
||||
check=0;
|
||||
for iNd=1:4
|
||||
if abs(lSet(Element(i,iNd)))<=bandwidth*delX
|
||||
check=1;
|
||||
end
|
||||
end
|
||||
% If an element is in the narrow band split it into triangles
|
||||
if check==1
|
||||
NBindex=NBindex+1;
|
||||
NBelem(NBindex,1)=Element(i,1);
|
||||
NBelem(NBindex,2)=Element(i,2);
|
||||
NBelem(NBindex,3)=Element(i,3);
|
||||
NBindex=NBindex+1;
|
||||
NBelem(NBindex,1)=Element(i,1);
|
||||
NBelem(NBindex,2)=Element(i,3);
|
||||
NBelem(NBindex,3)=Element(i,4);
|
||||
end
|
||||
end
|
||||
% Velocity BC
|
||||
F=zeros(numNodes,1);
|
||||
for i=1:NBindex
|
||||
if lSet(NBelem(i,1))~=lSet(NBelem(i,2)) || lSet(NBelem(i,1))~=lSet(NBelem(i,3))
|
||||
F(NBelem(i,1))= 0.0005;
|
||||
F(NBelem(i,2))= 0.0005;
|
||||
F(NBelem(i,3))= 0.0005;
|
||||
end
|
||||
end
|
||||
% Assemble 'Stiffness' Matrices
|
||||
A=zeros(numNodes);
|
||||
for i=1:NBindex
|
||||
gpos=1/sqrt(3.);
|
||||
gx(1)=-gpos;
|
||||
gx(2)=gpos;
|
||||
gx(3)=gpos;
|
||||
gx(4)=-gpos;
|
||||
hx(1)=-gpos;
|
||||
hx(2)=-gpos;
|
||||
hx(3)=gpos;
|
||||
hx(4)=gpos;
|
||||
AfL=zeros(4);
|
||||
AfLGLS=zeros(4);
|
||||
for j=1:4
|
||||
g=gx(j);
|
||||
h=hx(j);
|
||||
phi(1)=0.25*(1.-g)*(1.-h);
|
||||
phi(2)=0.25*(1.+g)*(1.-h);
|
||||
phi(3)=0.25*(1.+g)*(1.+h);
|
||||
phi(4)=0.25*(1.-g)*(1.+h);
|
||||
phig(1)=0.25*-(1.-h);
|
||||
phig(2)=0.25*(1.-h);
|
||||
phig(3)=0.25*(1.+h);
|
||||
phig(4)=0.25*-(1.+h);
|
||||
rset=phi(1)*lSet(Element(i,1))+phi(2)*lSet(Element(i,2))+phi(3)*lSet(Element(i,3))+phi(4)*lSet(Element(i,4));
|
||||
dls=phig(1)*lSet(Element(i,1))+phig(2)*lSet(Element(i,2))+phig(3)*lSet(Element(i,3))+phig(4)*lSet(Element(i,4));
|
||||
AfL=AfL+(phi'*sign(rset))*(dls*phig);
|
||||
AfLGLS=AfLGLS+(phig'*dls)*(1./abs(dls))*(dls*phig);
|
||||
end
|
||||
for k=1:4;
|
||||
for j=1:4;
|
||||
A(Element(i,j),Element(i,k))=A(Element(i,j),Element(i,k))+AfL(j,k)+AfLGLS(j,k)
|
||||
end
|
||||
end
|
||||
end
|
||||
% Apply BCs
|
||||
RHS=zeros(numNodes,1);
|
||||
Sub=A*F;
|
||||
iindex=0;
|
||||
for i=1:numNodes
|
||||
if F(i)==0.
|
||||
iindex=iindex+1;
|
||||
RHSred(iindex)=RHS(i)-Sub(i);
|
||||
Fred=0.;
|
||||
jindex=0;
|
||||
for j=1:numNodes
|
||||
if F(j)==0.
|
||||
jindex=jindex+1;
|
||||
Ared(iindex,jindex)=A(i,j);
|
||||
end
|
||||
end
|
||||
end
|
||||
end
|
||||
% Solve for Fred
|
||||
Fred=(Ared^-1)*RHSred';
|
||||
% Get F
|
||||
iindex=0;
|
||||
for i=1:numNodes
|
||||
if F(i)==0.
|
||||
iindex=iindex+1;
|
||||
F(i)=Fred(iindex);
|
||||
end
|
||||
end
|
||||
% Update level set
|
||||
mMat=zeros(numNodes);
|
||||
mMatGLS=zeros(numNodes);
|
||||
f1=zeros(numNodes,1);
|
||||
f2=zeros(numNodes,1);
|
||||
f3=zeros(numNodes,1);
|
||||
h=1.;
|
||||
visc=0.000;
|
||||
for i=1:numElem
|
||||
gpos=1/sqrt(3.);
|
||||
gx(1)=-gpos;
|
||||
gx(2)=gpos;
|
||||
gx(3)=gpos;
|
||||
gx(4)=-gpos;
|
||||
hx(1)=-gpos;
|
||||
hx(2)=-gpos;
|
||||
hx(3)=gpos;
|
||||
hx(4)=gpos;
|
||||
mMatL=zeros(4);
|
||||
mMatGLSL=zeros(4);
|
||||
f1L=zeros(4,1);
|
||||
f2L=zeros(4,1);
|
||||
f3L=zeros(4,1);
|
||||
for j=1:4
|
||||
g=gx(j);
|
||||
h=hx(j);
|
||||
phi(1)=0.25*(1.-g)*(1.-h);
|
||||
phi(2)=0.25*(1.+g)*(1.-h);
|
||||
phi(3)=0.25*(1.+g)*(1.+h);
|
||||
phi(4)=0.25*(1.-g)*(1.+h);
|
||||
phig(1)=0.25*-(1.-h);
|
||||
phig(2)=0.25*(1.-h);
|
||||
phig(3)=0.25*(1.+h);
|
||||
phig(4)=0.25*-(1.+h);
|
||||
Floc=phi(1)*F(Element(i,1))+phi(2)*F(Element(i,2))+phi(3)*F(Element(i,3))+phi(4)*F(Element(i,4));
|
||||
rset=phi(1)*lSet(Element(i,1))+phi(2)*lSet(Element(i,2))+phi(3)*lSet(Element(i,3))+phi(4)*lSet(Element(i,4));
|
||||
dls=phig(1)*lSet(Element(i,1))+phig(2)*lSet(Element(i,2))+phig(3)*lSet(Element(i,3))+phig(4)*lSet(Element(i,4));
|
||||
mMatL=mMatL+phi'*phi;
|
||||
mMatGLSL=mMatGLSL+((phig'*(dls/abs(dls)))*Floc*(h/abs(Floc)))*phi;
|
||||
f1L=f1L+phi'*Floc*abs(dls);
|
||||
f2L=f2L+(phig'*(dls/abs(dls))*Floc)*(h/abs(Floc))*Floc*abs(dls);
|
||||
vs=h*((abs(visc+Floc*abs(dls)))/(abs(Floc*dls)+h));
|
||||
f3L=f3L+vs*phig'*dls;
|
||||
end
|
||||
for k=1:4;
|
||||
for j=1:4;
|
||||
mMat(Element(i,j),Element(i,k))=mMat(Element(i,j),Element(i,k))+mMatL(j,k);
|
||||
mMatGLS(Element(i,j),Element(i,k))=mMatGLS(Element(i,j),Element(i,k))+mMatGLSL(j,k);
|
||||
end
|
||||
f1(Element(i,k))=f1(Element(i,k))+f1L(k);
|
||||
f2(Element(i,k))=f2(Element(i,k))+f2L(k);
|
||||
f3(Element(i,k))=f3(Element(i,k))+f3L(k);
|
||||
end
|
||||
end
|
||||
dt=0.01;
|
||||
lSet=lSet-((((mMat+mMatGLS)^-1)/dt)*(f1+f2+f3))';
|
||||
end
|
||||
%scatter3(Node(:,1), Node(:,2), lSet');
|
||||
|
||||
|
||||
|
||||
|
||||
232
Unpublished/XFEM2/1D_Solver/GetF2D_T.asv
Normal file
232
Unpublished/XFEM2/1D_Solver/GetF2D_T.asv
Normal file
|
|
@ -0,0 +1,232 @@
|
|||
function [] = GetF2D_T()
|
||||
clear all
|
||||
% Define Main Solution Mesh
|
||||
NumX=2;
|
||||
NumY=1;
|
||||
delX=1.;
|
||||
delY=1.;
|
||||
for j=1:NumY+1
|
||||
for i=1:NumX+1
|
||||
index=i+(NumX+1)*(j-1);
|
||||
Node(index,1)=single((i-1.))*delX;
|
||||
Node(index,2)=single((j-1.))*delY;
|
||||
end
|
||||
end
|
||||
numNodes=(NumX+1)*(NumY+1);
|
||||
for j=1:NumY
|
||||
for i=1:NumX
|
||||
index=i+NumX*(j-1);
|
||||
Element(index,1)=i+(NumX+1)*(j-1);
|
||||
Element(index,2)=i+(NumX+1)*(j-1)+1;
|
||||
Element(index,3)=i+(NumX+1)*(j)+1;
|
||||
Element(index,4)=i+(NumX+1)*(j);
|
||||
end
|
||||
end
|
||||
numElem=(NumX)*(NumY);
|
||||
% Define Initial Level Set
|
||||
%centx=5.;
|
||||
%centy=5.;
|
||||
%rad=2.5;
|
||||
%for i=1:numNodes;
|
||||
% dist=sqrt((Node(i,1)-centx)*(Node(i,1)-centx)+(Node(i,2)-centy)*(Node(i,2)-centy));
|
||||
% lSet(i)=dist-rad;
|
||||
%end
|
||||
for i=1:numNodes;
|
||||
dist=Node(i,1)-0.1;
|
||||
lSet(i)=dist;
|
||||
end
|
||||
% Plot initial level set
|
||||
%[X]=meshgrid(0:1.:10);
|
||||
%Z=zeros(11);
|
||||
%for i=1:numNodes
|
||||
% Z(i)=lSet(i);
|
||||
%end
|
||||
%surf(X,Z)
|
||||
% LS Algorithm Parameters
|
||||
bandwidth=10.;
|
||||
% Loop through timesteps
|
||||
for tstep=1:1
|
||||
% Identify Narrow Band Elements
|
||||
NBindex=0;
|
||||
for i=1:numElem
|
||||
check=0;
|
||||
for iNd=1:4
|
||||
if abs(lSet(Element(i,iNd)))<=bandwidth*delX
|
||||
check=1;
|
||||
end
|
||||
end
|
||||
% If an element is in the narrow band split it into triangles
|
||||
if check==1
|
||||
NBindex=NBindex+1;
|
||||
NBelem(NBindex,1)=Element(i,1);
|
||||
NBelem(NBindex,2)=Element(i,2);
|
||||
NBelem(NBindex,3)=Element(i,3);
|
||||
NBindex=NBindex+1;
|
||||
NBelem(NBindex,1)=Element(i,1);
|
||||
NBelem(NBindex,2)=Element(i,3);
|
||||
NBelem(NBindex,3)=Element(i,4);
|
||||
end
|
||||
end
|
||||
% Velocity BC
|
||||
F=zeros(numNodes,1);
|
||||
for i=1:NBindex
|
||||
if sign(lSet(NBelem(i,1)))~=sign(lSet(NBelem(i,2)))||sign(lSet(NBelem(i,1)))~=sign(lSet(NBelem(i,3)))
|
||||
F(NBelem(i,1))= 0.05;
|
||||
F(NBelem(i,2))= 0.05;
|
||||
F(NBelem(i,3))= 0.05;
|
||||
end
|
||||
end
|
||||
% Assemble 'Stiffness' Matrices
|
||||
A=zeros(numNodes);
|
||||
for i=1:NBindex
|
||||
gx(1)=2./3.;
|
||||
gx(2)=1./6.;
|
||||
gx(3)=1./6.;
|
||||
hx(1)=1./6.;
|
||||
hx(2)=1./6.;
|
||||
hx(3)=2./3.;
|
||||
AfL=zeros(3);
|
||||
AfLGLS=zeros(3);
|
||||
x1=Node(NBelem(i,1),1);
|
||||
y1=Node(NBelem(i,1),2);
|
||||
x2=Node(NBelem(i,2),1);
|
||||
y2=Node(NBelem(i,2),2);
|
||||
x3=Node(NBelem(i,3),1);
|
||||
y3=Node(NBelem(i,3),2);
|
||||
for j=1:3
|
||||
g=gx(j);
|
||||
h=hx(j);
|
||||
phi(1)=1.-g-h;
|
||||
phi(2)=g;
|
||||
phi(3)=h;
|
||||
phig(1)=-1.;
|
||||
phig(2)=1.;
|
||||
phig(3)=0.;
|
||||
phih(1)=-1.;
|
||||
phih(2)=0.;
|
||||
phih(3)=1.;
|
||||
djac=2*abs(x1*(y2-y3)+x2*(y3-y1)+x3*(y1-y2));
|
||||
for k=1:3
|
||||
phix(k)=(1./djac)*((-y1+y3)*phig(k)+(y1-y2)*phih(k));
|
||||
phiy(k)=(1./djac)*((x1-x3)*phig(k)+(-x1+x2)*phih(k));
|
||||
end
|
||||
delphi=[phix;phiy];
|
||||
nodalLset=[lSet(NBelem(i,1));lSet(NBelem(i,2));lSet(NBelem(i,3))];
|
||||
set=phi*nodalLset;
|
||||
delset=delphi*nodalLset;
|
||||
AfL=AfL+(phi'*sign(set))*(delset'*delphi)/3.;
|
||||
AfLGLS=AfLGLS+(delphi'*delset)*(1./norm(delset))*(delset'*delphi)/3.;
|
||||
end
|
||||
sum=AfL+AfLGLS;
|
||||
for k=1:3;
|
||||
for j=1:3;
|
||||
A(NBelem(i,j),NBelem(i,k))=A(NBelem(i,j),NBelem(i,k))+sum(j,k);
|
||||
end
|
||||
end
|
||||
end
|
||||
% Apply BCs
|
||||
RHS=zeros(numNodes,1);
|
||||
Sub=A*F;
|
||||
iindex=0;
|
||||
for i=1:numNodes
|
||||
if F(i)==0.
|
||||
iindex=iindex+1;
|
||||
RHSred(iindex)=RHS(i)-Sub(i);
|
||||
Fred=0.;
|
||||
jindex=0;
|
||||
for j=1:numNodes
|
||||
if F(j)==0.
|
||||
jindex=jindex+1;
|
||||
Ared(iindex,jindex)=A(i,j);
|
||||
end
|
||||
end
|
||||
end
|
||||
end
|
||||
% Solve for Fred
|
||||
Fred=(Ared^-1)*RHSred';
|
||||
% Get F
|
||||
iindex=0;
|
||||
for i=1:numNodes
|
||||
if F(i)==0.
|
||||
iindex=iindex+1;
|
||||
F(i)=Fred(iindex);
|
||||
end
|
||||
end
|
||||
% Update level set
|
||||
mMat=zeros(numNodes);
|
||||
mMatGLS=zeros(numNodes);
|
||||
f1=zeros(numNodes,1);
|
||||
f2=zeros(numNodes,1);
|
||||
f3=zeros(numNodes,1);
|
||||
h=1.;
|
||||
visc=0.001;
|
||||
for i=1:NBindex
|
||||
mMatL=zeros(3);
|
||||
mMatGLSL=zeros(3);
|
||||
f1L=zeros(3,1);
|
||||
f2L=zeros(3,1);
|
||||
f3L=zeros(3,1);
|
||||
gx(1)=2./3.;
|
||||
gx(2)=1./6.;
|
||||
gx(3)=1./6.;
|
||||
hx(1)=1./6.;
|
||||
hx(2)=1./6.;
|
||||
hx(3)=2./3.;
|
||||
x1=Node(NBelem(i,1),1);
|
||||
y1=Node(NBelem(i,1),2);
|
||||
x2=Node(NBelem(i,2),1);
|
||||
y2=Node(NBelem(i,2),2);
|
||||
x3=Node(NBelem(i,3),1);
|
||||
y3=Node(NBelem(i,3),2);
|
||||
for j=1:3
|
||||
g=gx(j);
|
||||
h=hx(j);
|
||||
phi(1)=1.-g-h;
|
||||
phi(2)=g;
|
||||
phi(3)=h;
|
||||
phig(1)=-1.;
|
||||
phig(2)=1.;
|
||||
phig(3)=0.;
|
||||
phih(1)=-1.;
|
||||
phih(2)=0.;
|
||||
phih(3)=1.;
|
||||
djac=abs(x1*(y2-y3)+x2*(y3-y1)+x3*(y1-y2));
|
||||
for k=1:3
|
||||
phix(k)=(1./djac)*((-y1+y3)*phig(k)+(y1-y2)*phih(k));
|
||||
phiy(k)=(1./djac)*((x1-x3)*phig(k)+(-x1+x2)*phih(k));
|
||||
end
|
||||
delphi=[phix;phiy];
|
||||
nodalLset=[lSet(NBelem(i,1));lSet(NBelem(i,2));lSet(NBelem(i,3))];
|
||||
nodalF=[F(NBelem(i,1));F(NBelem(i,2));F(NBelem(i,3))];
|
||||
delset=delphi*nodalLset;
|
||||
Floc=phi*nodalF;
|
||||
mMatL=mMatL+(phi'*phi)/3.;
|
||||
mMatGLSL=mMatGLSL+((delphi'*(delset/norm(delset)))*Floc*(h/abs(Floc)))*phi/3.;
|
||||
f1L=f1L+phi'*Floc*norm(delset)/3.;
|
||||
f2L=f2L+(delphi'*(delset/norm(delset))*Floc)*(h/abs(Floc))*Floc*norm(delset)/3.;
|
||||
vs=h*((abs(visc+Floc*norm(delset)))/(norm(Floc*delset)+h));
|
||||
f3L=f3L+vs*delphi'*delset/3.;
|
||||
end
|
||||
for k=1:3;
|
||||
for j=1:3;
|
||||
mMat(NBelem(i,j),NBelem(i,k))=mMat(NBelem(i,j),NBelem(i,k))+mMatL(j,k);
|
||||
mMatGLS(NBelem(i,j),NBelem(i,k))=mMatGLS(NBelem(i,j),NBelem(i,k))+mMatGLSL(j,k);
|
||||
end
|
||||
f1(NBelem(i,k))=f1(NBelem(i,k))+f1L(k);
|
||||
f2(NBelem(i,k))=f2(NBelem(i,k))+f2L(k);
|
||||
f3(NBelem(i,k))=f3(NBelem(i,k))+f3L(k);
|
||||
end
|
||||
end
|
||||
|
||||
(mMat+mMatGLS)^-1
|
||||
f1+f2+f3
|
||||
dt=0.0001;
|
||||
-((((mMat+mMatGLS)^-1)*dt)*(f1+f2+f3))'
|
||||
lSet=lSet-((((mMat+mMatGLS)^-1)*dt)*(f1+f2+f3))';
|
||||
end
|
||||
lSet';
|
||||
%scatter3(Node(:,1), Node(:,2), lSet');
|
||||
|
||||
|
||||
|
||||
|
||||
233
Unpublished/XFEM2/1D_Solver/GetF2D_T.m
Normal file
233
Unpublished/XFEM2/1D_Solver/GetF2D_T.m
Normal file
|
|
@ -0,0 +1,233 @@
|
|||
function [] = GetF2D_T()
|
||||
clear all
|
||||
% Define Main Solution Mesh
|
||||
NumX=2;
|
||||
NumY=1;
|
||||
delX=1.;
|
||||
delY=1.;
|
||||
for j=1:NumY+1
|
||||
for i=1:NumX+1
|
||||
index=i+(NumX+1)*(j-1);
|
||||
Node(index,1)=single((i-1.))*delX;
|
||||
Node(index,2)=single((j-1.))*delY;
|
||||
end
|
||||
end
|
||||
numNodes=(NumX+1)*(NumY+1);
|
||||
for j=1:NumY
|
||||
for i=1:NumX
|
||||
index=i+NumX*(j-1);
|
||||
Element(index,1)=i+(NumX+1)*(j-1);
|
||||
Element(index,2)=i+(NumX+1)*(j-1)+1;
|
||||
Element(index,3)=i+(NumX+1)*(j)+1;
|
||||
Element(index,4)=i+(NumX+1)*(j);
|
||||
end
|
||||
end
|
||||
numElem=(NumX)*(NumY);
|
||||
% Define Initial Level Set
|
||||
%centx=5.;
|
||||
%centy=5.;
|
||||
%rad=2.5;
|
||||
%for i=1:numNodes;
|
||||
% dist=sqrt((Node(i,1)-centx)*(Node(i,1)-centx)+(Node(i,2)-centy)*(Node(i,2)-centy));
|
||||
% lSet(i)=dist-rad;
|
||||
%end
|
||||
for i=1:numNodes;
|
||||
dist=Node(i,1)-1.5;
|
||||
lSet(i)=dist;
|
||||
end
|
||||
% Plot initial level set
|
||||
%[X]=meshgrid(0:1.:10);
|
||||
%Z=zeros(11);
|
||||
%for i=1:numNodes
|
||||
% Z(i)=lSet(i);
|
||||
%end
|
||||
%surf(X,Z)
|
||||
% LS Algorithm Parameters
|
||||
bandwidth=10.;
|
||||
% Loop through timesteps
|
||||
for tstep=1:1
|
||||
% Identify Narrow Band Elements
|
||||
NBindex=0;
|
||||
for i=1:numElem
|
||||
check=0;
|
||||
for iNd=1:4
|
||||
if abs(lSet(Element(i,iNd)))<=bandwidth*delX
|
||||
check=1;
|
||||
end
|
||||
end
|
||||
% If an element is in the narrow band split it into triangles
|
||||
if check==1
|
||||
NBindex=NBindex+1;
|
||||
NBelem(NBindex,1)=Element(i,1);
|
||||
NBelem(NBindex,2)=Element(i,2);
|
||||
NBelem(NBindex,3)=Element(i,3);
|
||||
NBindex=NBindex+1;
|
||||
NBelem(NBindex,1)=Element(i,1);
|
||||
NBelem(NBindex,2)=Element(i,3);
|
||||
NBelem(NBindex,3)=Element(i,4);
|
||||
end
|
||||
end
|
||||
% Velocity BC
|
||||
F=zeros(numNodes,1);
|
||||
for i=1:NBindex
|
||||
if sign(lSet(NBelem(i,1)))~=sign(lSet(NBelem(i,2)))||sign(lSet(NBelem(i,1)))~=sign(lSet(NBelem(i,3)))
|
||||
F(NBelem(i,1))= 0.05;
|
||||
F(NBelem(i,2))= 0.05;
|
||||
F(NBelem(i,3))= 0.05;
|
||||
end
|
||||
end
|
||||
% Assemble 'Stiffness' Matrices
|
||||
A=zeros(numNodes);
|
||||
for i=1:NBindex
|
||||
gx(1)=2./3.;
|
||||
gx(2)=1./6.;
|
||||
gx(3)=1./6.;
|
||||
hx(1)=1./6.;
|
||||
hx(2)=1./6.;
|
||||
hx(3)=2./3.;
|
||||
AfL=zeros(3);
|
||||
AfLGLS=zeros(3);
|
||||
x1=Node(NBelem(i,1),1);
|
||||
y1=Node(NBelem(i,1),2);
|
||||
x2=Node(NBelem(i,2),1);
|
||||
y2=Node(NBelem(i,2),2);
|
||||
x3=Node(NBelem(i,3),1);
|
||||
y3=Node(NBelem(i,3),2);
|
||||
for j=1:3
|
||||
g=gx(j);
|
||||
h=hx(j);
|
||||
phi(1)=1.-g-h;
|
||||
phi(2)=g;
|
||||
phi(3)=h;
|
||||
phig(1)=-1.;
|
||||
phig(2)=1.;
|
||||
phig(3)=0.;
|
||||
phih(1)=-1.;
|
||||
phih(2)=0.;
|
||||
phih(3)=1.;
|
||||
djac=2*abs(x1*(y2-y3)+x2*(y3-y1)+x3*(y1-y2));
|
||||
for k=1:3
|
||||
phix(k)=(1./djac)*((-y1+y3)*phig(k)+(y1-y2)*phih(k));
|
||||
phiy(k)=(1./djac)*((x1-x3)*phig(k)+(-x1+x2)*phih(k));
|
||||
end
|
||||
delphi=[phix;phiy];
|
||||
nodalLset=[lSet(NBelem(i,1));lSet(NBelem(i,2));lSet(NBelem(i,3))];
|
||||
set=phi*nodalLset;
|
||||
delset=delphi*nodalLset;
|
||||
AfL=AfL+(phi'*sign(set))*(delset'*delphi)/3.;
|
||||
AfLGLS=AfLGLS+(delphi'*delset)*(1./norm(delset))*(delset'*delphi)/3.;
|
||||
end
|
||||
sum=AfL+AfLGLS;
|
||||
for k=1:3;
|
||||
for j=1:3;
|
||||
A(NBelem(i,j),NBelem(i,k))=A(NBelem(i,j),NBelem(i,k))+sum(j,k);
|
||||
end
|
||||
end
|
||||
end
|
||||
% Apply BCs
|
||||
RHS=zeros(numNodes,1);
|
||||
Sub=A*F;
|
||||
iindex=0;
|
||||
for i=1:numNodes
|
||||
if F(i)==0.
|
||||
iindex=iindex+1;
|
||||
RHSred(iindex)=RHS(i)-Sub(i);
|
||||
Fred=0.;
|
||||
jindex=0;
|
||||
for j=1:numNodes
|
||||
if F(j)==0.
|
||||
jindex=jindex+1;
|
||||
Ared(iindex,jindex)=A(i,j);
|
||||
end
|
||||
end
|
||||
end
|
||||
end
|
||||
% Solve for Fred
|
||||
Fred=(Ared^-1)*RHSred';
|
||||
% Get F
|
||||
iindex=0;
|
||||
for i=1:numNodes
|
||||
if F(i)==0.
|
||||
iindex=iindex+1;
|
||||
F(i)=Fred(iindex);
|
||||
end
|
||||
end
|
||||
% Update level set
|
||||
mMat=zeros(numNodes);
|
||||
mMatGLS=zeros(numNodes);
|
||||
f1=zeros(numNodes,1);
|
||||
f2=zeros(numNodes,1);
|
||||
f3=zeros(numNodes,1);
|
||||
h=1.;
|
||||
visc=0.0005;
|
||||
for i=1:NBindex
|
||||
mMatL=zeros(3);
|
||||
mMatGLSL=zeros(3);
|
||||
f1L=zeros(3,1);
|
||||
f2L=zeros(3,1);
|
||||
f3L=zeros(3,1);
|
||||
gx(1)=2./3.;
|
||||
gx(2)=1./6.;
|
||||
gx(3)=1./6.;
|
||||
hx(1)=1./6.;
|
||||
hx(2)=1./6.;
|
||||
hx(3)=2./3.;
|
||||
x1=Node(NBelem(i,1),1);
|
||||
y1=Node(NBelem(i,1),2);
|
||||
x2=Node(NBelem(i,2),1);
|
||||
y2=Node(NBelem(i,2),2);
|
||||
x3=Node(NBelem(i,3),1);
|
||||
y3=Node(NBelem(i,3),2);
|
||||
for j=1:3
|
||||
g=gx(j);
|
||||
h=hx(j);
|
||||
phi(1)=1.-g-h;
|
||||
phi(2)=g;
|
||||
phi(3)=h;
|
||||
phig(1)=-1.;
|
||||
phig(2)=1.;
|
||||
phig(3)=0.;
|
||||
phih(1)=-1.;
|
||||
phih(2)=0.;
|
||||
phih(3)=1.;
|
||||
djac=abs(x1*(y2-y3)+x2*(y3-y1)+x3*(y1-y2));
|
||||
for k=1:3
|
||||
phix(k)=(1./djac)*((-y1+y3)*phig(k)+(y1-y2)*phih(k));
|
||||
phiy(k)=(1./djac)*((x1-x3)*phig(k)+(-x1+x2)*phih(k));
|
||||
end
|
||||
delphi=[phix;phiy];
|
||||
nodalLset=[lSet(NBelem(i,1));lSet(NBelem(i,2));lSet(NBelem(i,3))];
|
||||
nodalF=[F(NBelem(i,1));F(NBelem(i,2));F(NBelem(i,3))];
|
||||
delset=delphi*nodalLset;
|
||||
Floc=phi*nodalF;
|
||||
mMatL=mMatL+(phi'*phi)/3.;
|
||||
mMatGLSL=mMatGLSL+((delphi'*(delset/norm(delset)))*Floc*(h/abs(Floc)))*phi/3.;
|
||||
f1L=f1L+phi'*Floc*norm(delset)/3.;
|
||||
f2L=f2L+(delphi'*(delset/norm(delset))*Floc)*(h/abs(Floc))*Floc*norm(delset)/3.;
|
||||
vs=h*((abs(visc+Floc*norm(delset)))/(norm(Floc*delset)+h));
|
||||
f3L=f3L+vs*delphi'*delset/3.;
|
||||
end
|
||||
for k=1:3;
|
||||
for j=1:3;
|
||||
mMat(NBelem(i,j),NBelem(i,k))=mMat(NBelem(i,j),NBelem(i,k))+mMatL(j,k);
|
||||
mMatGLS(NBelem(i,j),NBelem(i,k))=mMatGLS(NBelem(i,j),NBelem(i,k))+mMatGLSL(j,k);
|
||||
end
|
||||
f1(NBelem(i,k))=f1(NBelem(i,k))+f1L(k);
|
||||
f2(NBelem(i,k))=f2(NBelem(i,k))+f2L(k);
|
||||
f3(NBelem(i,k))=f3(NBelem(i,k))+f3L(k);
|
||||
end
|
||||
end
|
||||
mMat
|
||||
mMatGLS
|
||||
(mMat+mMatGLS)^-1
|
||||
f1+f2+f3
|
||||
dt=0.1;
|
||||
-((((mMat+mMatGLS)^-1)*dt)*(f1+f2+f3))'
|
||||
lSet=lSet-((((mMat+mMatGLS)^-1)*dt)*(f1+f2+f3))';
|
||||
end
|
||||
lSet';
|
||||
%scatter3(Node(:,1), Node(:,2), lSet');
|
||||
|
||||
|
||||
|
||||
|
||||
234
Unpublished/XFEM2/1D_Solver/GetF2D_Z.m
Normal file
234
Unpublished/XFEM2/1D_Solver/GetF2D_Z.m
Normal file
|
|
@ -0,0 +1,234 @@
|
|||
function [] = GetF2D_Z()
|
||||
clear all
|
||||
% Define Main Solution Mesh
|
||||
NumX=8;
|
||||
NumY=8;
|
||||
delX=1.;
|
||||
delY=1.;
|
||||
for j=1:NumY+1
|
||||
for i=1:NumX+1
|
||||
index=i+(NumX+1)*(j-1);
|
||||
Node(index,1)=single((i-1.))*delX;
|
||||
Node(index,2)=single((j-1.))*delY;
|
||||
end
|
||||
end
|
||||
numNodes=(NumX+1)*(NumY+1);
|
||||
for j=1:NumY
|
||||
for i=1:NumX
|
||||
index=i+NumX*(j-1);
|
||||
Element(index,1)=i+(NumX+1)*(j-1);
|
||||
Element(index,2)=i+(NumX+1)*(j-1)+1;
|
||||
Element(index,3)=i+(NumX+1)*(j)+1;
|
||||
Element(index,4)=i+(NumX+1)*(j);
|
||||
end
|
||||
end
|
||||
numElem=(NumX)*(NumY);
|
||||
% Define Initial Level Set
|
||||
centx=4.;
|
||||
centy=4.;
|
||||
rad=2.1;
|
||||
for i=1:numNodes;
|
||||
dist=sqrt((Node(i,1)-centx)*(Node(i,1)-centx)+(Node(i,2)-centy)*(Node(i,2)-centy));
|
||||
lSet(i)=dist-rad;
|
||||
end
|
||||
%for i=1:numNodes;
|
||||
% dist=Node(i,1)-0.1;
|
||||
% lSet(i)=dist;
|
||||
%end
|
||||
% Plot initial level set
|
||||
[X Y]=meshgrid(0:1.:8);
|
||||
Z=zeros(9);
|
||||
for i=1:81
|
||||
Z(i)=lSet(i);
|
||||
end
|
||||
surf(X,Y,Z)
|
||||
% LS Algorithm Parameters
|
||||
lSet'
|
||||
bandwidth=10.;
|
||||
% Loop through timesteps
|
||||
for tstep=1:100
|
||||
% Identify Narrow Band Elements
|
||||
NBindex=0;
|
||||
for i=1:numElem
|
||||
check=0;
|
||||
for iNd=1:4
|
||||
if abs(lSet(Element(i,iNd)))<=bandwidth*delX
|
||||
check=1;
|
||||
end
|
||||
end
|
||||
% If an element is in the narrow band split it into triangles
|
||||
if check==1
|
||||
NBindex=NBindex+1;
|
||||
NBelem(NBindex,1)=Element(i,1);
|
||||
NBelem(NBindex,2)=Element(i,2);
|
||||
NBelem(NBindex,3)=Element(i,3);
|
||||
NBindex=NBindex+1;
|
||||
NBelem(NBindex,1)=Element(i,1);
|
||||
NBelem(NBindex,2)=Element(i,3);
|
||||
NBelem(NBindex,3)=Element(i,4);
|
||||
end
|
||||
end
|
||||
% Velocity BC
|
||||
F=zeros(numNodes,1);
|
||||
for i=1:NBindex
|
||||
if sign(lSet(NBelem(i,1)))~=sign(lSet(NBelem(i,2)))||sign(lSet(NBelem(i,1)))~=sign(lSet(NBelem(i,3)))
|
||||
F(NBelem(i,1))= 1.;
|
||||
F(NBelem(i,2))= 1.;
|
||||
F(NBelem(i,3))= 1.;
|
||||
end
|
||||
end
|
||||
% Assemble 'Stiffness' Matrices
|
||||
A=zeros(numNodes);
|
||||
for i=1:NBindex
|
||||
gx(1)=2./3.;
|
||||
gx(2)=1./6.;
|
||||
gx(3)=1./6.;
|
||||
hx(1)=1./6.;
|
||||
hx(2)=1./6.;
|
||||
hx(3)=2./3.;
|
||||
AfL=zeros(3);
|
||||
AfLGLS=zeros(3);
|
||||
x1=Node(NBelem(i,1),1);
|
||||
y1=Node(NBelem(i,1),2);
|
||||
x2=Node(NBelem(i,2),1);
|
||||
y2=Node(NBelem(i,2),2);
|
||||
x3=Node(NBelem(i,3),1);
|
||||
y3=Node(NBelem(i,3),2);
|
||||
for j=1:3
|
||||
g=gx(j);
|
||||
h=hx(j);
|
||||
phi(1)=1.-g-h;
|
||||
phi(2)=g;
|
||||
phi(3)=h;
|
||||
phig(1)=-1.;
|
||||
phig(2)=1.;
|
||||
phig(3)=0.;
|
||||
phih(1)=-1.;
|
||||
phih(2)=0.;
|
||||
phih(3)=1.;
|
||||
djac=2*abs(x1*(y2-y3)+x2*(y3-y1)+x3*(y1-y2));
|
||||
for k=1:3
|
||||
phix(k)=(1./djac)*((-y1+y3)*phig(k)+(y1-y2)*phih(k));
|
||||
phiy(k)=(1./djac)*((x1-x3)*phig(k)+(-x1+x2)*phih(k));
|
||||
end
|
||||
delphi=[phix;phiy];
|
||||
nodalLset=[lSet(NBelem(i,1));lSet(NBelem(i,2));lSet(NBelem(i,3))];
|
||||
set=phi*nodalLset;
|
||||
delset=delphi*nodalLset;
|
||||
AfL=AfL+(phi'*sign(set))*(delset'*delphi)/3.;
|
||||
AfLGLS=AfLGLS+(delphi'*delset)*(1./norm(delset))*(delset'*delphi)/3.;
|
||||
end
|
||||
sum=AfL+AfLGLS;
|
||||
for k=1:3;
|
||||
for j=1:3;
|
||||
A(NBelem(i,j),NBelem(i,k))=A(NBelem(i,j),NBelem(i,k))+sum(j,k);
|
||||
end
|
||||
end
|
||||
end
|
||||
% Apply BCs
|
||||
RHS=zeros(numNodes,1);
|
||||
Sub=A*F;
|
||||
iindex=0;
|
||||
for i=1:numNodes
|
||||
if F(i)==0.
|
||||
iindex=iindex+1;
|
||||
RHSred(iindex)=RHS(i)-Sub(i);
|
||||
Fred=0.;
|
||||
jindex=0;
|
||||
for j=1:numNodes
|
||||
if F(j)==0.
|
||||
jindex=jindex+1;
|
||||
Ared(iindex,jindex)=A(i,j);
|
||||
end
|
||||
end
|
||||
end
|
||||
end
|
||||
% Solve for Fred
|
||||
Fred=(Ared^-1)*RHSred';
|
||||
% Get F
|
||||
iindex=0;
|
||||
for i=1:numNodes
|
||||
if F(i)==0.
|
||||
iindex=iindex+1;
|
||||
F(i)=Fred(iindex);
|
||||
end
|
||||
end
|
||||
% Update level set
|
||||
mMat=zeros(numNodes);
|
||||
mMatGLS=zeros(numNodes);
|
||||
f1=zeros(numNodes,1);
|
||||
f2=zeros(numNodes,1);
|
||||
f3=zeros(numNodes,1);
|
||||
h2=0.00001;
|
||||
visc=0.0005;
|
||||
for i=1:NBindex
|
||||
mMatL=zeros(3);
|
||||
mMatGLSL=zeros(3);
|
||||
f1L=zeros(3,1);
|
||||
f2L=zeros(3,1);
|
||||
f3L=zeros(3,1);
|
||||
gx(1)=2./3.;
|
||||
gx(2)=1./6.;
|
||||
gx(3)=1./6.;
|
||||
hx(1)=1./6.;
|
||||
hx(2)=1./6.;
|
||||
hx(3)=2./3.;
|
||||
x1=Node(NBelem(i,1),1);
|
||||
y1=Node(NBelem(i,1),2);
|
||||
x2=Node(NBelem(i,2),1);
|
||||
y2=Node(NBelem(i,2),2);
|
||||
x3=Node(NBelem(i,3),1);
|
||||
y3=Node(NBelem(i,3),2);
|
||||
for j=1:3
|
||||
g=gx(j);
|
||||
h=hx(j);
|
||||
phi(1)=1.-g-h;
|
||||
phi(2)=g;
|
||||
phi(3)=h;
|
||||
phig(1)=-1.;
|
||||
phig(2)=1.;
|
||||
phig(3)=0.;
|
||||
phih(1)=-1.;
|
||||
phih(2)=0.;
|
||||
phih(3)=1.;
|
||||
djac=abs(x1*(y2-y3)+x2*(y3-y1)+x3*(y1-y2));
|
||||
for k=1:3
|
||||
phix(k)=(1./djac)*((-y1+y3)*phig(k)+(y1-y2)*phih(k));
|
||||
phiy(k)=(1./djac)*((x1-x3)*phig(k)+(-x1+x2)*phih(k));
|
||||
end
|
||||
delphi=[phix;phiy];
|
||||
nodalLset=[lSet(NBelem(i,1));lSet(NBelem(i,2));lSet(NBelem(i,3))];
|
||||
nodalF=[F(NBelem(i,1));F(NBelem(i,2));F(NBelem(i,3))];
|
||||
delset=delphi*nodalLset;
|
||||
Floc=phi*nodalF;
|
||||
mMatL=mMatL+(phi'*phi)/3.;
|
||||
mMatGLSL=mMatGLSL+((delphi'*(delset/norm(delset)))*Floc*(h2/abs(Floc)))*phi/3.;
|
||||
f1L=f1L+phi'*Floc*norm(delset)/3.;
|
||||
f2L=f2L+(delphi'*(delset/norm(delset))*Floc)*(h2/abs(Floc))*Floc*norm(delset)/3.;
|
||||
vs=h2*((abs(visc+Floc*norm(delset)))/(norm(Floc*delset)+h2));
|
||||
f3L=f3L+vs*delphi'*delset/3.;
|
||||
end
|
||||
for k=1:3;
|
||||
for j=1:3;
|
||||
mMat(NBelem(i,j),NBelem(i,k))=mMat(NBelem(i,j),NBelem(i,k))+mMatL(j,k);
|
||||
mMatGLS(NBelem(i,j),NBelem(i,k))=mMatGLS(NBelem(i,j),NBelem(i,k))+mMatGLSL(j,k);
|
||||
end
|
||||
f1(NBelem(i,k))=f1(NBelem(i,k))+f1L(k);
|
||||
f2(NBelem(i,k))=f2(NBelem(i,k))+f2L(k);
|
||||
f3(NBelem(i,k))=f3(NBelem(i,k))+f3L(k);
|
||||
end
|
||||
end
|
||||
dt=0.01;
|
||||
lSet=lSet-((((mMat+mMatGLS)^-1)*dt)*(f1+f2+f3))';
|
||||
end
|
||||
lSet'
|
||||
%[X Y]=meshgrid(0:1.:8);
|
||||
%Z=zeros(9);
|
||||
%for i=1:81
|
||||
% Z(i)=lSet(i);
|
||||
%end
|
||||
%surf(X,Y,Z)
|
||||
|
||||
|
||||
|
||||
|
||||
2
Unpublished/XFEM2/1D_Solver/testGrid.asv
Normal file
2
Unpublished/XFEM2/1D_Solver/testGrid.asv
Normal file
|
|
@ -0,0 +1,2 @@
|
|||
function [] = testGrid()
|
||||
|
||||
4
Unpublished/XFEM2/1D_Solver/testGrid.m
Normal file
4
Unpublished/XFEM2/1D_Solver/testGrid.m
Normal file
|
|
@ -0,0 +1,4 @@
|
|||
function [] = testGrid()
|
||||
[X,Y]=meshgrid(1:1:10);
|
||||
Z=2*X+Y
|
||||
surf(X,Y,Z)
|
||||
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Add table
Add a link
Reference in a new issue