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117 lines
3.4 KiB
117 lines
3.4 KiB
3 years ago
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nelx = 4; nely = 4;
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microx = 50;
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cx = nelx * microx / 2;
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cy = nely * microx / 2;
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nelx = nelx * microx;
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nely = nely * microx;
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poly = [-cx, -cy;
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cx, -cy;
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cx, 0;
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0, 0;
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0, cy;
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-cx, cy];
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optDesign = 'Lshape';
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vF = 1;
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[~,fixeddofs,F,~] = designDomain(optDesign,nelx,nely, vF, microx, 1);
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volfrac = 0.4;
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E0 = 1; nu = 0.3; Emin = 1e-9;
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penal=1; %���ϲ�ֵ�ijͷ�����
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rmin=2; %���ȹ��˰뾶
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ft = 2;
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%% MATERIAL PROPERTIES
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% E0 = 1;
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Emin = 1e-9;
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% nu = 0.3;
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%% PREPARE FINITE ELEMENT ANALYSIS
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A11 = [12 3 -6 -3; 3 12 3 0; -6 3 12 -3; -3 0 -3 12];
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A12 = [-6 -3 0 3; -3 -6 -3 -6; 0 -3 -6 3; 3 -6 3 -6];
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B11 = [-4 3 -2 9; 3 -4 -9 4; -2 -9 -4 -3; 9 4 -3 -4];
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B12 = [ 2 -3 4 -9; -3 2 9 -2; 4 9 2 3; -9 -2 3 2];
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KE = 1/(1-nu^2)/24*([A11 A12;A12' A11]+nu*[B11 B12;B12' B11]);
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nodenrs = reshape(1:(1+nelx)*(1+nely),1+nely,1+nelx);
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edofVec = reshape(2*nodenrs(1:end-1,1:end-1)+1,nelx*nely,1);
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edofMat = repmat(edofVec,1,8)+repmat([0 1 2*nely+[2 3 0 1] -2 -1],nelx*nely,1);
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iK = reshape(kron(edofMat,ones(8,1))',64*nelx*nely,1);
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jK = reshape(kron(edofMat,ones(1,8))',64*nelx*nely,1);
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% DEFINE LOADS AND SUPPORTS (HALF MBB-BEAM)
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% F = sparse(2,1,-1,2*(nely+1)*(nelx+1),1);
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U = zeros(2*(nely+1)*(nelx+1),1);
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% fixeddofs = union([1:2:2*(nely+1)],[2*(nelx+1)*(nely+1)]);
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alldofs = [1:2*(nely+1)*(nelx+1)];
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freedofs = setdiff(alldofs,fixeddofs);
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%% PREPARE FILTER
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iH = ones(nelx*nely*(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 i1 = 1:nelx
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for j1 = 1:nely
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e1 = (i1-1)*nely+j1;
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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 = (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));
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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);
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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 > 0.01 && loop < 100
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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)),64*nelx*nely,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);
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c = 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);
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%% FILTERING/MODIFICATION OF SENSITIVITIES
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if ft == 1
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dc(:) = H*(x(:).*dc(:))./Hs./max(1e-3,x(:));
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elseif ft == 2
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dc(:) = H*(dc(:)./Hs);
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dv(:) = H*(dv(:)./Hs);
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end
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%% OPTIMALITY CRITERIA UPDATE OF DESIGN VARIABLES AND PHYSICAL DENSITIES
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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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if ft == 1
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xPhys = xnew;
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elseif ft == 2
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xPhys(:) = (H*xnew(:))./Hs;
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end
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if sum(xPhys(:)) > volfrac*nelx*nely, 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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if loop==1
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scale = 10.0/c;
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end
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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*scale, ...
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mean(xPhys(:)),change);
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xPhys(1:nely/2, nelx/2+1:nelx) = 0;
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%% PLOT DENSITIES
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figure(4); clf; colormap(gray); imagesc(1-xPhys); caxis([0 1]); axis equal; axis off; drawnow;
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end
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