%%%% A 99 LINE TOPOLOGY OPTIMIZATION CODE BY OLE SIGMUND, JANUARY 2000 %%%
%%%% CODE MODIFIED FOR INCREASED SPEED, September 2002, BY OLE SIGMUND %%%
function toph(nelx,nely,volfrac,penal,rmin, kappa1, kappa2)
% 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,kappa1, kappa2);         
% 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([n1;n2;n2+1;n1+1],1);
      c = c + (kappa2+(kappa1-kappa2)*x(ely,elx)^penal)*Ue'*KE*Ue;
      dc(ely,elx) = -(kappa1-kappa2)*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,kappa1,kappa2)
[KE] = lk; 
K = sparse((nelx+1)*(nely+1), (nelx+1)*(nely+1));
F = sparse((nely+1)*(nelx+1),1); U = sparse((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 = [n1; n2; n2+1; n1+1];
    K(edof,edof) = K(edof,edof) + (kappa2 + (kappa1-kappa2)*x(ely,elx)^penal)*KE;
  end
end
% DEFINE LOADS AND SUPPORTS (SQUARE PLATE WITH HEAT SINK)
F(:,1) = 0.01;
fixeddofs   = [nely/2+1-(nely/20):2:nely/2+1+(nely/20)];
alldofs     = [1:(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
KE = [2/3 -1/6 -1/3 -1/6
      -1/6 2/3 -1/6 -1/3
      -1/3 -1/6 2/3 -1/6
      -1/6 -1/3 -1/6 2/3];
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 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: sigmund@fam.dtu.dk              %
%                                                                          %
% 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: 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.                                        %
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%