傲世皇朝资讯
%%%% A 99 LINE TOPOLOGY OPTIMIZATION CODE BY OLE SIGMUND, JANUARY 2000 %%%
%%%% CODE MODIFIED FOR INCREASED SPEED, September 2002, BY OLE SIGMUND %%%
%%%% 一个由 OLE SIGMUND编写的99行拓扑优化代码，2000年1月 %%%
%%%% 为加速而修改的代码，2002年9月,由OLE SIGMUND编写 %%%
function top(nelx,nely,volfrac,penal,rmin);
% INITIALIZE
x(1:nely,1:nelx)=volfrac;
loop=0;
change=1.;
% START ITERATION
while change > 0.01
loop=loop + 1;
xold=x;
% FE-ANALYSIS
[U]=FE(nelx,nely,x,penal);
% OBJECTIVE FUNCTION AND SENSITIVITY ANALYSIS
[KE]=lk;
c=0.;
for ely=1:nely
for elx=1:nelx
n1=(nely+1)*(elx-1)+ely;
n2=(nely+1)* elx +ely;
Ue=U([2*n1-1;2*n1; 2*n2-1;2*n2; 2*n2+1;2*n2+2; 2*n1+1;2*n1+2],1);
c=c + x(ely,elx)^penal*Ue'*KE*Ue;
dc(ely,elx)=-penal*x(ely,elx)^(penal-1)*Ue'*KE*Ue;
end
end
% FILTERING OF SENSITIVITIES
[dc]=check(nelx,nely,rmin,x,dc);
% DESIGN UPDATE BY THE OPTIMALITY CRITERIA METHOD
[x]=OC(nelx,nely,x,volfrac,dc);
% PRINT RESULTS
change=max(max(abs(x-xold)));
disp([' It.: ' sprintf('%4i',loop) ' Obj.: ' sprintf('%10.4f',c) ...
' Vol.: ' sprintf('%6.3f',sum(sum(x))/(nelx*nely)) ...
' ch.: ' sprintf('%6.3f',change )])
% PLOT DENSITIES
colormap(gray); imagesc(-x); axis equal; axis tight; axis off;pause(1e-6);
end
%%%%%%%%%% OPTIMALITY CRITERIA UPDATE %%%%%%%%%%%%%%%%%%%%%%%%%%%%
function [xnew]=OC(nelx,nely,x,volfrac,dc)
l1=0; l2=100000; move=0.2;
while (l2-l1 > 1e-4)
lmid=0.5*(l2+l1);
xnew=max(0.001,max(x-move,min(1.,min(x+move,x.*sqrt(-dchttps://wenku.baidu.com/view/lmid)))));
if sum(sum(xnew)) - volfrac*nelx*nely > 0;
l1=lmid;
else
l2=lmid;
end
end
%%%%%%%%%% MESH-INDEPENDENCY FILTER %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
function [dcn]=check(nelx,nely,rmin,x,dc)
dcn=zeros(nely,nelx);
for i=1:nelx
for j=1:nely
sum=0.0;
for k=max(i-floor(rmin),1):min(i+floor(rmin),nelx)
for l=max(j-floor(rmin),1):min(j+floor(rmin),nely)
fac=rmin-sqrt((i-k)^2+(j-l)^2);
sum=sum+max(0,fac);
dcn(j,i)=dcn(j,i) + max(0,fac)*x(l,k)*dc(l,k);
end
end
dcn(j,i)=dcn(j,i)/(x(j,i)*sum);
end
end
%%%%%%%%%% FE-ANALYSIS %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
function [U]=FE(nelx,nely,x,penal)
[KE]=lk;
K=sparse(2*(nelx+1)*(nely+1), 2*(nelx+1)*(nely+1));
F=sparse(2*(nely+1)*(nelx+1),1); U=zeros(2*(nely+1)*(nelx+1),1);
for elx=1:nelx
for ely=1:nely
n1=(nely+1)*(elx-1)+ely;
n2=(nely+1)* elx +ely;
edof=[2*n1-1; 2*n1; 2*n2-1; 2*n2; 2*n2+1; 2*n2+2; 2*n1+1; 2*n1+2];
K(edof,edof)=K(edof,edof) + x(ely,elx)^penal*KE;
end
end
% DEFINE LOADS AND SUPPORTS (HALF MBB-BEAM)
F(2,1)=-
