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200 lines
7.6 KiB
200 lines
7.6 KiB
3 years ago
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%--------------------------
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% @Author: Jingqiao Hu
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% @Date: 2022-01-18 00:12:35
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% @LastEditTime: 2022-01-18 00:41:09
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%--------------------------
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% AN 169 LINE 3D TOPOLOGY OPITMIZATION CODE BY LIU AND TOVAR (JUL 2013)
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function x = top3d(nelx,nely,nelz,volfrac, vF,optDesign)
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% USER-DEFINED LOOP PARAMETERS
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maxloop = 100; % Maximum number of iterations
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tolx = 0.001; % Terminarion criterion
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displayflag = 0; % Display structure flag
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% USER-DEFINED MATERIAL PROPERTIES
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E0 = 1; % Young's modulus of solid material
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Emin = 1e-9; % Young's modulus of void-like material
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nu = 0.3; % Poisson's ratio
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penal = 1;
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rmin = 2;
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% USER-DEFINED LOAD DOFs
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switch optDesign
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case 'cantilever'
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il = nelx; jl = 0; kl = 0:nelz; % Coordinates
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loadnid = kl*(nelx+1)*(nely+1)+il*(nely+1)+(nely+1-jl); % Node IDs
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loaddof = 3*loadnid(:) - 1; % DOFs
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% USER-DEFINED SUPPORT FIXED DOFs
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[jf,kf] = meshgrid(1:nely+1,1:nelz+1); % Coordinates
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fixednid = (kf-1)*(nely+1)*(nelx+1)+jf; % Node IDs
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fixeddof = [3*fixednid(:); 3*fixednid(:)-1; 3*fixednid(:)-2]; % DOFs
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case 'Lshape'
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fixednid = [];
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for i = 1:nely/2+1
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idx = (i-1) * (nely+1) * (nelx+1) + 1;
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fixednid = [fixednid; idx : nely+1 : (nelx/2)*(nely+1)+idx];
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end
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fixeddof = [3*fixednid(:); 3*fixednid(:)-1; 3*fixednid(:)-2]; % DOFs
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loadnid = (nely+1) * (nelx+1) * (nelz/2) - nely/4;
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loaddof = 3*loadnid(:) - 1; % DOFs
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end
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% PREPARE FINITE ELEMENT ANALYSIS
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nele = nelx*nely*nelz;
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ndof = 3*(nelx+1)*(nely+1)*(nelz+1);
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F = sparse(loaddof,1,-vF,ndof,1);
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U = zeros(ndof,1);
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freedofs = setdiff(1:ndof,fixeddof);
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KE = lk_H8(nu);
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nodegrd = reshape(1:(nely+1)*(nelx+1),nely+1,nelx+1);
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nodeids = reshape(nodegrd(1:end-1,1:end-1),nely*nelx,1);
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nodeidz = 0:(nely+1)*(nelx+1):(nelz-1)*(nely+1)*(nelx+1);
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nodeids = repmat(nodeids,size(nodeidz))+repmat(nodeidz,size(nodeids));
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edofVec = 3*nodeids(:)+1;
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edofMat = repmat(edofVec,1,24)+ ...
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repmat([0 1 2 3*nely + [3 4 5 0 1 2] -3 -2 -1 ...
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3*(nely+1)*(nelx+1)+[0 1 2 3*nely + [3 4 5 0 1 2] -3 -2 -1]],nele,1);
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iK = reshape(kron(edofMat,ones(24,1))',24*24*nele,1);
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jK = reshape(kron(edofMat,ones(1,24))',24*24*nele,1);
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% PREPARE FILTER
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iH = ones(nele*(2*(ceil(rmin)-1)+1)^2,1);
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jH = ones(size(iH));
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sH = zeros(size(iH));
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k = 0;
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for k1 = 1:nelz
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for i1 = 1:nelx
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for j1 = 1:nely
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e1 = (k1-1)*nelx*nely + (i1-1)*nely+j1;
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for k2 = max(k1-(ceil(rmin)-1),1):min(k1+(ceil(rmin)-1),nelz)
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for i2 = max(i1-(ceil(rmin)-1),1):min(i1+(ceil(rmin)-1),nelx)
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for j2 = max(j1-(ceil(rmin)-1),1):min(j1+(ceil(rmin)-1),nely)
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e2 = (k2-1)*nelx*nely + (i2-1)*nely+j2;
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k = k+1;
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iH(k) = e1;
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jH(k) = e2;
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sH(k) = max(0,rmin-sqrt((i1-i2)^2+(j1-j2)^2+(k1-k2)^2));
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end
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end
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end
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end
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end
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end
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H = sparse(iH,jH,sH);
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Hs = sum(H,2);
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% INITIALIZE ITERATION
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x = repmat(volfrac,[nely,nelx,nelz]);
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xPhys = x;
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loop = 0;
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change = 1;
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% START ITERATION
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while change > tolx && loop < maxloop
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loop = loop+1;
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% FE-ANALYSIS
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sK = reshape(KE(:)*(Emin+xPhys(:)'.^penal*(E0-Emin)),24*24*nele,1);
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K = sparse(iK,jK,sK); K = (K+K')/2;
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U(freedofs,:) = K(freedofs,freedofs)\F(freedofs,:);
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% OBJECTIVE FUNCTION AND SENSITIVITY ANALYSIS
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ce = reshape(sum((U(edofMat)*KE).*U(edofMat),2),[nely,nelx,nelz]);
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c = sum(sum(sum((Emin+xPhys.^penal*(E0-Emin)).*ce)));
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dc = -penal*(E0-Emin)*xPhys.^(penal-1).*ce;
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dv = ones(nely,nelx,nelz);
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% FILTERING AND MODIFICATION OF SENSITIVITIES
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dc(:) = H*(dc(:)./Hs);
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dv(:) = H*(dv(:)./Hs);
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% OPTIMALITY CRITERIA UPDATE
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l1 = 0; l2 = 1e9; move = 0.2;
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while (l2-l1)/(l1+l2) > 1e-3
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lmid = 0.5*(l2+l1);
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xnew = max(0,max(x-move,min(1,min(x+move,x.*sqrt(-dc./dv/lmid)))));
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xPhys(:) = (H*xnew(:))./Hs;
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if sum(xPhys(:)) > volfrac*nele, l1 = lmid; else l2 = lmid; end
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end
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change = max(abs(xnew(:)-x(:)));
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x = xnew;
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% PRINT RESULTS
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fprintf(' It.:%5i Obj.:%11.4f Vol.:%7.3f ch.:%7.3f\n',loop,c,mean(xPhys(:)),change);
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% PLOT DENSITIES
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% if displayflag, clf; display_3D(xPhys); end %#ok<UNRCH>
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if strcmp(optDesign, 'Lshape')
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xPhys(1:nely/2, nelx/2+1:nelx, :) = 0;
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end
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xPhys(nely/4:(nely/4*3),(nelx/8*3):(nelx/8*5), :) = 0;
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clf; display_3D(xPhys);
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end
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% clf; display_3D(xPhys);
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end
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% === GENERATE ELEMENT STIFFNESS MATRIX ===
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function [KE] = lk_H8(nu)
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A = [32 6 -8 6 -6 4 3 -6 -10 3 -3 -3 -4 -8;
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-48 0 0 -24 24 0 0 0 12 -12 0 12 12 12];
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k = 1/144*A'*[1; nu];
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K1 = [k(1) k(2) k(2) k(3) k(5) k(5);
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k(2) k(1) k(2) k(4) k(6) k(7);
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k(2) k(2) k(1) k(4) k(7) k(6);
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k(3) k(4) k(4) k(1) k(8) k(8);
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k(5) k(6) k(7) k(8) k(1) k(2);
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k(5) k(7) k(6) k(8) k(2) k(1)];
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K2 = [k(9) k(8) k(12) k(6) k(4) k(7);
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k(8) k(9) k(12) k(5) k(3) k(5);
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k(10) k(10) k(13) k(7) k(4) k(6);
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k(6) k(5) k(11) k(9) k(2) k(10);
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k(4) k(3) k(5) k(2) k(9) k(12)
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k(11) k(4) k(6) k(12) k(10) k(13)];
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K3 = [k(6) k(7) k(4) k(9) k(12) k(8);
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k(7) k(6) k(4) k(10) k(13) k(10);
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k(5) k(5) k(3) k(8) k(12) k(9);
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k(9) k(10) k(2) k(6) k(11) k(5);
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k(12) k(13) k(10) k(11) k(6) k(4);
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k(2) k(12) k(9) k(4) k(5) k(3)];
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K4 = [k(14) k(11) k(11) k(13) k(10) k(10);
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k(11) k(14) k(11) k(12) k(9) k(8);
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k(11) k(11) k(14) k(12) k(8) k(9);
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k(13) k(12) k(12) k(14) k(7) k(7);
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k(10) k(9) k(8) k(7) k(14) k(11);
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k(10) k(8) k(9) k(7) k(11) k(14)];
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K5 = [k(1) k(2) k(8) k(3) k(5) k(4);
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k(2) k(1) k(8) k(4) k(6) k(11);
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k(8) k(8) k(1) k(5) k(11) k(6);
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k(3) k(4) k(5) k(1) k(8) k(2);
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k(5) k(6) k(11) k(8) k(1) k(8);
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k(4) k(11) k(6) k(2) k(8) k(1)];
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K6 = [k(14) k(11) k(7) k(13) k(10) k(12);
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k(11) k(14) k(7) k(12) k(9) k(2);
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k(7) k(7) k(14) k(10) k(2) k(9);
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k(13) k(12) k(10) k(14) k(7) k(11);
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k(10) k(9) k(2) k(7) k(14) k(7);
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k(12) k(2) k(9) k(11) k(7) k(14)];
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KE = 1/((nu+1)*(1-2*nu))*...
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[ K1 K2 K3 K4;
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K2' K5 K6 K3';
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K3' K6 K5' K2';
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K4 K3 K2 K1'];
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end
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% === DISPLAY 3D TOPOLOGY (ISO-VIEW) ===
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function display_3D(rho)
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[nely,nelx,nelz] = size(rho);
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hx = 1; hy = 1; hz = 1; % User-defined unit element size
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face = [1 2 3 4; 2 6 7 3; 4 3 7 8; 1 5 8 4; 1 2 6 5; 5 6 7 8];
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set(gcf,'Name','ISO display','NumberTitle','off');
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for k = 1:nelz
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z = (k-1)*hz;
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for i = 1:nelx
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x = (i-1)*hx;
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for j = 1:nely
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y = nely*hy - (j-1)*hy;
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if (rho(j,i,k) > 0.1) % User-defined display density threshold
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vert = [x y z; x y-hx z; x+hx y-hx z; x+hx y z; x y z+hx;x y-hx z+hx; x+hx y-hx z+hx;x+hx y z+hx];
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vert(:,[2 3]) = vert(:,[3 2]); vert(:,2,:) = -vert(:,2,:);
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patch('Faces',face,'Vertices',vert,'FaceColor',[0.2+0.8*(1-rho(j,i,k)),0.2+0.8*(1-rho(j,i,k)),0.2+0.8*(1-rho(j,i,k))]);
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hold on;
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end
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end
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end
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end
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axis equal; axis tight; axis off; box on; view([30,30]); pause(1e-6);
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end
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