topmm.m

连续体动力学机构拓扑优化设计的程序代码

%%%% A 99 LINE COMPLAINT MECHANSIM CODE BY OLE SIGMUND, MAY 2002 %%%%%%% CODE MODIFIED FOR INCREASED SPEED, September 2002, BY OLE SIGMUND %%%
function mtop(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,c]=FE(nelx,nely,x,penal);         
% OBJECTIVE FUNCTION AND SENSITIVITY ANALYSIS
  [KE] = lk;
  for ely = 1:nely
    for elx = 1:nelx
      n1 = (nely+1)*(elx-1)+ely; 
      n2 = (nely+1)* elx   +ely;
      Ue1 = U([2*n1-1;2*n1; 2*n2-1;2*n2; 2*n2+1;2*n2+2; 2*n1+1;2*n1+2],1);
      Ue2 = U([2*n1-1;2*n1; 2*n2-1;2*n2; 2*n2+1;2*n2+2; 2*n1+1;2*n1+2],2);
      dc(ely,elx) = penal*x(ely,elx)^(penal-1)*Ue2'*KE*Ue1;
    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 = 0.1;
while (l2-l1)/(12+11) > 1e-4 & 12 > 1e-40
  lmid = 0.5*(l2+l1);
  xnew = max(0.001,max(x-move,min(1.,min(x+move,x.*(max(1e-10,-dc./lmid)).^0.3))));
  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,Uout]=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),2); U = sparse(2*(nely+1)*(nelx+1),2);
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 FORCE INVERTER)
din = 1;
dout = 2*nelx*(nely+1)+1;
F(din,1) = 1;
F(dout,2) = -1;
K(din,din) = K(din,din)+0.1;
K(dout,dout) = K(dout,dout)+0.1;
fixeddofs = union([2:2*(nely+1):2*(nely+1)*(nelx+1)],[2*(nely+1):-1:2*(nely+1)-3]);
alldofs     = [1:2*(nely+1)*(nelx+1)];
freedofs    = setdiff(alldofs,fixeddofs);
% SOLVING
U(freedofs,:) = K(freedofs,freedofs) \ F(freedofs,:);      
U(fixeddofs,:)= 0;
Uout = U(din,1);
%%%%%%%%%% 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: [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 (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.                                        %
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%