topsparse.m

连续体结构柔度最小

%% A SPARSITY REVISION OF A 99 LINE TOPOLOGY OPTIMIZATION CODE %%
%%%%  BY OLE SIGMUND. THE REVISION IS MADE BY ANDREAS RIETZ  %%%%
function TopSparse(nelx,nely,volfrac,penal,rmin);
% Insert for TopGUI by Kang Zhao. 2003-11-21 
% More info : http://www.geocities.com/chinakkong/research/topgui/
global fixeddofs F
[fixeddofs F]=topgui(nelx,nely);

% INITIALIZE
x(1:nely,1:nelx) = volfrac; 
change = 1.; loop = 0; 
% INITIALIZING THE NODE VECTOR
for ely=1:nely
for elx=1:nelx
    iter=elx+(ely-1)*nelx;
    n1 = (nely+1)*(elx-1)+ely; 
    n2 = (nely+1)* elx   +ely;
    edofvect(1,8*iter-7:8*iter)= ...
	[2*n1-1 2*n1 2*n2-1 2*n2 2*n2+1 2*n2+2 2*n1+1 2*n1+2];
end
end
% START ITERATION
while change > 0.01  
  loop = loop + 1;    xold = x;
% FE-ANALYSIS
  [U]=FE(nelx,nely,x,penal,edofvect);         
% OBJECTIVE FUNCTION AND SENSITIVITY ANALYSIS
  [KE] = lk; c = 0.;
  for ely = 1:nely;
    for elx = 1:nelx
      iter=elx+(ely-1)*nelx;
      Ue = U(edofvect(1,8*iter-7:8*iter)',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-round(rmin),1):min(i+round(rmin),nelx)
      for l = max(j-round(rmin),1):min(j+round(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,edofvect)
% Insert for TopGUI by Kang Zhao. 2003-11-21 
global fixeddofs F

U = sparse(2*(nely+1)*(nelx+1),1);
[KE]=reshape(lk,1,64); xrad=reshape(x',1,nelx*nely);
columnindex= reshape(kron(reshape(edofvect,8,nelx*nely), ...
		ones(1,8)), 1,64*nelx*nely);
rowindex=kron(edofvect,ones(1,8));
K=sparse(rowindex,columnindex,kron(xrad.^penal,KE));
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)];
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% The origin of 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: [e-mail]              %
%                                                                          %
% 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 (To appear in Structural Optimization).                   %
%                                                                          %
% The first code as well as a postscript version of the paper can be       %
% downloaded from the web-site: http://www.topopt.dtu.dk                   %
%                                                                          %
% 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.                                        %
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%