From 17f93a9f8fe780bdcdf8ddfa28fd1c9a4e0144a2 Mon Sep 17 00:00:00 2001 From: Wxwei <12221108@zju.edu.cn> Date: Mon, 18 Sep 2023 10:13:19 +0000 Subject: [PATCH] =?UTF-8?q?=E4=B8=8A=E4=BC=A0=E6=96=87=E4=BB=B6=E8=87=B3?= =?UTF-8?q?=20'Top99Code'?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit top99：a 99 line topology optimization code by Ole Sigmund,October 1999 top88：AN 88 LINE TOPOLOGY OPTIMIZATION CODE Nov, 2010 --- Top99Code/top88.m | 114 ++++++++++++++++++++++++++++++++++++++++++++ Top99Code/top99.m | 117 ++++++++++++++++++++++++++++++++++++++++++++++ 2 files changed, 231 insertions(+) create mode 100644 Top99Code/top88.m create mode 100644 Top99Code/top99.m diff --git a/Top99Code/top88.m b/Top99Code/top88.m new file mode 100644 index 0000000..7290eb4 --- /dev/null +++ b/Top99Code/top88.m @@ -0,0 +1,114 @@ +%%%% AN 88 LINE TOPOLOGY OPTIMIZATION CODE Nov, 2010 %%%% +function top88(nelx,nely,volfrac,penal,rmin,ft) +%% MATERIAL PROPERTIES +E0 = 1; +Emin = 1e-9; +nu = 0.3; +%% PREPARE FINITE ELEMENT ANALYSIS +A11 = [12 3 -6 -3; 3 12 3 0; -6 3 12 -3; -3 0 -3 12]; +A12 = [-6 -3 0 3; -3 -6 -3 -6; 0 -3 -6 3; 3 -6 3 -6]; +B11 = [-4 3 -2 9; 3 -4 -9 4; -2 -9 -4 -3; 9 4 -3 -4]; +B12 = [ 2 -3 4 -9; -3 2 9 -2; 4 9 2 3; -9 -2 3 2]; +KE = 1/(1-nu^2)/24*([A11 A12;A12' A11]+nu*[B11 B12;B12' B11]); +nodenrs = reshape(1:(1+nelx)*(1+nely),1+nely,1+nelx); +edofVec = reshape(2*nodenrs(1:end-1,1:end-1)+1,nelx*nely,1); +edofMat = repmat(edofVec,1,8)+repmat([0 1 2*nely+[2 3 0 1] -2 -1],nelx*nely,1); +iK = reshape(kron(edofMat,ones(8,1))',64*nelx*nely,1); +jK = reshape(kron(edofMat,ones(1,8))',64*nelx*nely,1); +% DEFINE LOADS AND SUPPORTS (HALF MBB-BEAM) +F = sparse(2,1,-1,2*(nely+1)*(nelx+1),1); +U = zeros(2*(nely+1)*(nelx+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); +%% PREPARE FILTER +iH = ones(nelx*nely*(2*(ceil(rmin)-1)+1)^2,1); +jH = ones(size(iH)); +sH = zeros(size(iH)); +k = 0; +for i1 = 1:nelx + for j1 = 1:nely + e1 = (i1-1)*nely+j1; + for i2 = max(i1-(ceil(rmin)-1),1):min(i1+(ceil(rmin)-1),nelx) + for j2 = max(j1-(ceil(rmin)-1),1):min(j1+(ceil(rmin)-1),nely) + e2 = (i2-1)*nely+j2; + k = k+1; + iH(k) = e1; + jH(k) = e2; + sH(k) = max(0,rmin-sqrt((i1-i2)^2+(j1-j2)^2)); + end + end + end +end +H = sparse(iH,jH,sH); +Hs = sum(H,2); +%% INITIALIZE ITERATION +x = repmat(volfrac,nely,nelx); +xPhys = x; +loop = 0; +change = 1; +%% START ITERATION +while change > 0.01 + loop = loop + 1; + %% FE-ANALYSIS + sK = reshape(KE(:)*(Emin+xPhys(:)'.^penal*(E0-Emin)),64*nelx*nely,1); + K = sparse(iK,jK,sK); K = (K+K')/2; + U(freedofs) = K(freedofs,freedofs)\F(freedofs); + %% OBJECTIVE FUNCTION AND SENSITIVITY ANALYSIS + ce = reshape(sum((U(edofMat)*KE).*U(edofMat),2),nely,nelx); + c = sum(sum((Emin+xPhys.^penal*(E0-Emin)).*ce)); + dc = -penal*(E0-Emin)*xPhys.^(penal-1).*ce; + dv = ones(nely,nelx); + %% FILTERING/MODIFICATION OF SENSITIVITIES + if ft == 1 + dc(:) = H*(x(:).*dc(:))./Hs./max(1e-3,x(:)); + elseif ft == 2 + dc(:) = H*(dc(:)./Hs); + dv(:) = H*(dv(:)./Hs); + end + %% OPTIMALITY CRITERIA UPDATE OF DESIGN VARIABLES AND PHYSICAL DENSITIES + l1 = 0; l2 = 1e9; move = 0.2; + while (l2-l1)/(l1+l2) > 1e-3 + lmid = 0.5*(l2+l1); + xnew = max(0,max(x-move,min(1,min(x+move,x.*sqrt(-dc./dv/lmid))))); + if ft == 1 + xPhys = xnew; + elseif ft == 2 + xPhys(:) = (H*xnew(:))./Hs; + end + if sum(xPhys(:)) > volfrac*nelx*nely, l1 = lmid; else l2 = lmid; end + end + change = max(abs(xnew(:)-x(:))); + x = xnew; + %% PRINT RESULTS + fprintf(' It.:%5i Obj.:%11.4f Vol.:%7.3f ch.:%7.3f\n',loop,c, ... + mean(xPhys(:)),change); + %% PLOT DENSITIES + colormap(gray); imagesc(1-xPhys); caxis([0 1]); axis equal; axis off; drawnow; +end +% +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +% This Matlab code was written by E. Andreassen, A. Clausen, M. Schevenels,% +% B. S. Lazarov and O. Sigmund, Department of Solid Mechanics, % +% Technical University of Denmark, % +% DK-2800 Lyngby, Denmark. % +% Please sent your comments to: sigmund@fam.dtu.dk % +% % +% The code is intended for educational purposes and theoretical details % +% are discussed in the paper % +% "Efficient topology optimization in MATLAB using 88 lines of code, % +% E. Andreassen, A. Clausen, M. Schevenels, % +% B. S. Lazarov and O. Sigmund, Struct Multidisc Optim, 2010 % +% This version is based on earlier 99-line code % +% 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 authors reserves all rights but do not guaranty that the code is % +% free from errors. Furthermore, we shall not be liable in any event % +% caused by the use of the program. % +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + diff --git a/Top99Code/top99.m b/Top99Code/top99.m new file mode 100644 index 0000000..d875bb3 --- /dev/null +++ b/Top99Code/top99.m @@ -0,0 +1,117 @@ +% a 99 line topology optimization code by Ole Sigmund,October 1999 +clear +nelx=60; +nely=40; +volfrac=0.5; +penal=3.; +rmin=1.5; +% initialize +x(1:nely,1:nelx)=volfrac; +loop=0; +change=1; +% start ineration +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 result + change=max(max(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 + +% 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=sparse(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 + ip=(nelx+1)*(nely+1); + F(2*ip,1)=-1; + +fixeddofs =[1:2*(nely+1)]; +alldofs =[1:2*(nely+1)*(nelx+1)]; +freedofs =setdiff(alldofs,fixeddofs); +% solving +U(freedofs,:)=K(freedofs,freedofs)\F(freedofs,:); +U(fixeddofs,:)=0; +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 +end + +% 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)]; +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 +end