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101 lines
3.5 KiB
101 lines
3.5 KiB
function compliance_after_threshold()
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load top3d_case2_p1.mat
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xx = xPhys>=0.33;
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xx = max(xx,1e-3);
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xPhys = xx;
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nelx=60;
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nely=20;
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nelz=1;
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E0 = 1; % Young's modulus of solid material
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Emin = 1e-3; % Young's modulus of void-like material
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nu = 0.33; % Poisson's ratio
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% USER-DEFINED LOAD DOFs
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[il,jl,kl] = meshgrid(nelx, 0, 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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[iif,jf,kf] = meshgrid(0,0:nely,0:nelz); % Coordinates
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fixednid = kf*(nelx+1)*(nely+1)+iif*(nely+1)+(nely+1-jf); % Node IDs
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fixeddof = [3*fixednid(:); 3*fixednid(:)-1; 3*fixednid(:)-2]; % DOFs
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ndof = 3*(nelx+1)*(nely+1)*(nelz+1);
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F = sparse(loaddof,1,-1,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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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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compliance = (Emin+xPhys.^penal*(E0-Emin)).*ce;
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set(gcf,'position',[100 650 300 300])
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cc = squeeze(compliance(:,:,1));
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colormap(1-gray);
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imagesc(cc);
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axis equal; axis tight; axis off;
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disp(sum(sum(compliance)))
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end
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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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