99_BESO matalb

%固定两边中间的点，在最上方中点施加压力 function top(nelx,nely,volfrac,penal,rmin); nelx=80; nely=50; volfrac=0.5; penal=3; rmin=3; % 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]=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 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 = 0.2; 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 %%%%%%%%%% 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]=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 = zeros(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 (HALF MBB-BEAM) %固定两边中间的点，在最上方中点施加压力 F(2*(nelx/2+1)*(nely+1)-2*nely,1) = 1; fixeddofs = [2*(nely/2+1),2*nelx*(nely+1)+2*(nely/2+1)]; alldofs = [1:2*(nely+1)*(nelx+1)]; freedofs = setdiff(alldofs,fixeddofs); U(freedofs,:) = K(freedofs,freedofs) \ F(freedofs,:); U(fixeddofs,:)= 0; % SOLVING %%U(freedofs, :)= K(freedofs,freedofs) \ F(freedofs,:??; %U(fixeddofs,:??= 0; % ???????????ó??????????×?·?????????????·????ú??QQ±í % ?é?????????????? %%%%%%%%%% 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)]; %