222 lines
6.4 KiB
Mathematica
222 lines
6.4 KiB
Mathematica
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function [] = FESolveX()
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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=40;
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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=2;
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% initial interface position
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dpos=4.6;
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% Initial temperatures
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Tnew=zeros(numNodes*2,1);
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%storage
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stored(1)=dpos;
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for e=1:numElem
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crdn1=ndCoords(elemNodes(e,1));
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if crdn1<=dpos
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Tnew(2*elemNodes(e,1)-1)=1.;
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end
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end
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% Define Time Step
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dtime=0.1;
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tsteps=10;
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time=0.;
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% penalty term
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beta=200.;
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% Loop through time steps
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for ts=1:tsteps
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% Get interface velocity
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d(1)=dpos+charlen;
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d(2)=dpos+3*charlen/4;
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d(3)=dpos+charlen/4;
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d(4)=dpos;
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for e=1:numElem
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crdn1=ndCoords(elemNodes(e,1));
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crdn2=ndCoords(elemNodes(e,2));
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for j=1:4
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if d(j)>=crdn1 & d(j)<crdn2
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elen=abs(crdn2-crdn1);
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ajacob=elen/2.;
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point=(d(j)-crdn1)/ajacob-1.;
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theta(1)=abs(crdn1-dpos)*sign(crdn1-dpos);
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theta(2)=abs(crdn2-dpos)*sign(crdn2-dpos);
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tmp1a=Tnew(elemNodes(e,1)*2-1);
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tmp1b=Tnew(elemNodes(e,1)*2);
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tmp2a=Tnew(elemNodes(e,2)*2-1);
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tmp2b=Tnew(elemNodes(e,2)*2);
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xi=point;
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gm(1)=(1.-xi)/2.;
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gm(3)=(1.+xi)/2.;
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term=theta(1)*gm(1)+theta(2)*gm(3);
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gm(2)=gm(1)*(abs(term)-abs(theta(1)));
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gm(4)=gm(3)*(abs(term)-abs(theta(2)));
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t(j)=gm(1)*tmp1a+gm(2)*tmp1b+gm(3)*tmp2a+gm(4)*tmp2b;
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end
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end
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end
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vel=1.*(0.5/charlen)*(2*t(1)+t(2)-t(3)-2*t(4));
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vel=0.;
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% Update interface position
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dpos=dpos+vel*dtime;
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stored(ts+1)=dpos;
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K=zeros(numNodes*ndof,numNodes*ndof);
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M=zeros(numNodes*ndof,numNodes*ndof);
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pforce=zeros(numNodes*ndof,1);
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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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theta(1)=abs(crdn1-dpos)*sign(crdn1-dpos);
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theta(2)=abs(crdn2-dpos)*sign(crdn2-dpos);
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enr=2;
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elen=abs(crdn2-crdn1);
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ajacob=elen/2.;
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if sign(theta(1))~=sign(theta(2))
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% enriched element
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enr=4;
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% get interface position on element
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point=(dpos-crdn1)/ajacob-1.;
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% devide element for sub integration
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len1=abs(-point-1.);
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len2=abs(1.-point);
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mid1=-1+len1/2.;
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mid2=1-len2/2.;
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gpx(1)=-(len1/2.)/sqrt(3.)+mid1;
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gpx(2)=(len1/2.)/sqrt(3.)+mid1;
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gpx(3)=-(len2/2.)/sqrt(3.)+mid2;
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gpx(4)=(len2/2.)/sqrt(3.)+mid2;
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w(1)=(len1/2.);
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w(2)=(len1/2.);
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w(3)=(len2/2.);
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w(4)=(len2/2.);
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fdofs(1)=2*elemNodes(e,1);
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fdofs(2)=2*elemNodes(e,2);
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else
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% regular element - fix extra dofs
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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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end
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% Loop Through Int Points
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for i=1:enr;
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c=gpx(i);
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phi(1)=(1.-c)/2.;
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phi(3)=(1.+c)/2.;
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term=theta(1)*phi(1)+theta(2)*phi(3);
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if term<0
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cond=0.;
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spec=0.01;
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else
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cond=1.;
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spec=1.;
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end
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phi(2)=phi(1)*(abs(term)-abs(theta(1)));
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phi(4)=phi(3)*(abs(term)-abs(theta(2)));
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phic(1)=-0.5;
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phic(3)=0.5;
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dterm=sign(term)*(phic(1)*theta(1)+phic(3)*theta(2));
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phic(2)=phic(1)*(abs(term)-abs(theta(1)))+phi(1)*dterm;
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phic(4)=phic(3)*(abs(term)-abs(theta(2)))+phi(3)*dterm;
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phix(1)=phic(1)/ajacob;
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phix(2)=phic(2)/ajacob;
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phix(3)=phic(3)/ajacob;
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phix(4)=phic(4)/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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% Add penalty term and get temp gradient on interface
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if enr==4;
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xi=point;
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gm(1)=(1.-xi)/2.;
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gm(3)=(1.+xi)/2.;
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term=theta(1)*gm(1)+theta(2)*gm(3);
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gm(2)=gm(1)*(abs(term)-abs(theta(1)));
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gm(4)=gm(3)*(abs(term)-abs(theta(2)));
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tpos=gm(1)*Tnew(1)+gm(2)*Tnew(2)+gm(3)*Tnew(3)+gm(4)*Tnew(4);
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pen=beta*(gm'*gm);
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pfL=beta*1*gm';
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Ke=Ke+pen;
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else
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pen=zeros(4);
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pfL=zeros(4,1);
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end
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% Assemble Global Matrices
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gnum=2.*elemNodes(e,1)-1.;
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for i=1:4;
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for j=1:4;
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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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pforce(gnum+i-1)=pforce(gnum+i-1)+pfL(i);
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end
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end
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%Remove inactive DOFs(Reduce Matrices)
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T1=1;
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RHS=M*Tnew;
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iindex=0;
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for i=1:ndof*numNodes;
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check=1;
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if i==fdofs(1)|i==fdofs(2)
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check=0;
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elseif mod(i,2)~=0 & i~=1
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check=0;
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end
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if check==0
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jindex=0;
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iindex=iindex+1;
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for j=1:ndof*numNodes;
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check=1;
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if j==fdofs(1)|j==fdofs(2)
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check=0;
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elseif mod(j,2)~=0 & j~=1
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check=0;
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end
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if check==0
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jindex=jindex+1;
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Kred(iindex,jindex)=K(i,j);
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Mred(iindex,jindex)=M(i,j);
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end
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end
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Subr(iindex)=(K(i,1)+M(i,1))*T1;
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RHSr(iindex)=RHS(i);
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pforcer(iindex)=pforce(i);
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end
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end
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%Solve
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StiffI=(Mred+Kred)^-1;
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Tnewr=StiffI*(RHSr'-Subr'+pforcer');
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iindex=0.;
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for i=1:ndof*numNodes;
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check=1;
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if i==fdofs(1)|i==fdofs(2)
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check=0;
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elseif mod(i,2)~=0 & i~=1
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check=0;
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end
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if check==0
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iindex=iindex+1;
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Tnew(i)=Tnewr(iindex);
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else
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Tnew(i)=0.;
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end
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end
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Tnew(1)=1.;
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Tnew
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end
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stored'
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