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老师说这个是拓扑优化的入门程序,要看明白的,个人感觉不错,
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- %%%% 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(-dc./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) = -1;
- fixeddofs = union([1:2:2*(nely+1)],[2*(nelx+1)*(nely+1)]);
- alldofs = [1:2*(nely+1)*(nelx+1)];
- freedofs = setdiff(alldofs,fixeddofs);
- % SOLVING
- U(freedofs,:) = K(freedofs,freedofs) \ F(freedofs,:);
- U(fixeddofs,:)= 0;
- %%%%%%%%%% ELEMENT STIFFNESS MATRIX %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
- function [KE]=lk
- E = 1.;
- nu = 0.3;
- k=[ 1/2-nu/6 1/8+nu/8 -1/4-nu/12 -1/8+3*nu/8 ...
- -1/4+nu/12 -1/8-nu/8 nu/6 1/8-3*nu/8];
- KE = E/(1-nu^2)*[ k(1) k(2) k(3) k(4) k(5) k(6) k(7) k(8)
- k(2) k(1) k(8) k(7) k(6) k(5) k(4) k(3)
- k(3) k(8) k(1) k(6) k(7) k(4) k(5) k(2)
- k(4) k(7) k(6) k(1) k(8) k(3) k(2) k(5)
- k(5) k(6) k(7) k(8) k(1) k(2) k(3) k(4)
- k(6) k(5) k(4) k(3) k(2) k(1) k(8) k(7)
- k(7) k(4) k(5) k(2) k(3) k(8) k(1) k(6)
- k(8) k(3) k(2) k(5) k(4) k(7) k(6) k(1)];
- %
- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
- % This Matlab code was written by Ole Sigmund, Department of Solid %
- % Mechanics, Technical University of Denmark, DK-2800 Lyngby, Denmark. %
- % Please sent your comments to the author: [email]sigmund@fam.dtu.dk[/email]%
- % %
- % The code is intended for educational purposes and theoretical details %
- % are discussed in the paper %
- % "A 99 line topology optimization code written in Matlab" %
- % by Ole Sigmund (2001), Structural and Multidisciplinary Optimization, %
- % Vol 21, pp. 120--127. %
- % %
- % The code as well as a postscript version of the paper can be %
- % downloaded from the web-site: [url]http://www.topopt.dtu.dk[/url] %
- % %
- % Disclaimer: %
- % The author reserves all rights but does not guaranty that the code is %
- % free from errors. Furthermore, he shall not be liable in any event %
- % caused by the use of the program. %
- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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[ 本帖最后由 ChaChing 于 2010-1-30 23:35 编辑 ] |
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