99 lines
2.5 KiB
Mathematica
99 lines
2.5 KiB
Mathematica
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function [] = FESolveSimp()
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% MATLAB based 1-D XFEM Solver
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% J. Grogan (2012)
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clear all
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% Define Geometry
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len=10.;
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% Define Section Properties
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rho=1.;
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% Generate Mesh
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numElem=10;
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charlen=len/numElem;
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ndCoords=linspace(0,len,numElem+1);
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numNodes=size(ndCoords,2);
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indx=1:numElem;
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elemNodes(:,1)=indx;
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elemNodes(:,2)=indx+1;
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% dofs per node
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ndof=1;
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% Initial temperatures
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Tnew=zeros(numNodes,1);
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Bound=zeros(numNodes,1);
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Tnew(1)=1.;
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Bound(1)=1.;
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% Define Time Step
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dtime=0.01;
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tsteps=10;
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time=0.;
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% Loop through time steps
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for ts=1:tsteps
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K=zeros(numNodes,numNodes);
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M=zeros(numNodes,numNodes);
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% Loop Through Elements
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for e=1:numElem
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Ke=zeros(2*ndof);
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Me=zeros(2*ndof);
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crdn1=ndCoords(elemNodes(e,1));
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crdn2=ndCoords(elemNodes(e,2));
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elen=abs(crdn2-crdn1);
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ajacob=elen/2.;
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gpx(1)=-1/sqrt(3.);
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gpx(2)=1/sqrt(3.);
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w(1)=1.;
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w(2)=1.;
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% Loop Through Int Points
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for i=1:2;
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c=gpx(i);
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phi(1)=(1.-c)/2.;
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phi(2)=(1.+c)/2.;
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cond=1.;
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spec=1.;
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phic(1)=-0.5;
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phic(2)=0.5;
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phix(1)=phic(1)/ajacob;
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phix(2)=phic(2)/ajacob;
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we=ajacob*w(i);
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Ke=Ke+we*cond*phix'*phix;
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Me=Me+(we*rho*spec*phi'*phi)/dtime;
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end
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% Assemble Global Matrices
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gnum=elemNodes(e,1);
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for i=1:2;
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for j=1:2;
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K(gnum+j-1,gnum+i-1)=K(gnum+j-1,gnum+i-1)+Ke(j,i);
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M(gnum+j-1,gnum+i-1)=M(gnum+j-1,gnum+i-1)+Me(j,i);
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end
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end
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end
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%Remove NON-ENHANCED DOFs(Reduce Matrices)
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iindex=0.;
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A=K+M;
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Sub=A*Bound;
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RHS=M*Tnew-Sub;
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% Apply Boundary Conditions
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for i=1:numNodes;
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if Bound(i)==0.;
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iindex=iindex+1;
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RHSR(iindex)=RHS(i);
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jindex=0;
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for j=1:numNodes;
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if Bound(j)==0.;
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jindex=jindex+1;
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AR(iindex,jindex)=A(i,j);
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end
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end
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end
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end
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%Solve
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Tnewr=(AR^-1)*RHSR';
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% Restore Matrices
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iindex=0;
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for i=1:numNodes;
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if Bound(i)==0.;
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iindex=iindex+1;
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Tnew(i)=Tnewr(iindex);
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end
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end
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Tnew
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end
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