2 changed files with 141 additions and 0 deletions
@ -0,0 +1,51 @@ |
|||
function f = TPMS() |
|||
f1 = @(x1,y1,z1) cos(x1) + cos(y1) + cos(z1) + 0.2 ; % P-element |
|||
f2 = @(x2,y2,z2) cos(x2).*cos(y2).*cos(z2) - sin(x2).*sin(y2).*sin(z2) + 0.2; % D-element |
|||
f3 = @(x3,y3,z3) sin(x3).*cos(y3) + sin(y3).*cos(z3) + sin(z3).*cos(x3); % G-element |
|||
f4 = @(x4,y4,z4) 2.*(cos(x4).*cos(y4) + cos(y4).*cos(z4) + cos(z4).*cos(x4)) ... |
|||
- (cos(2.*x4) + cos(2.*y4) + cos(2.*z4)); % I-WP-element |
|||
f5 = @(x5,y5,z5) -2.*(cos(2.*x5).*cos(2.*y5) + cos(2.*y5).*cos(2.*z5) + cos(2.*z5).*cos(2.*x5))... |
|||
+ 8.*cos(x5).*cos(y5).*cos(z5); % F-RD-element |
|||
f6 = @(x6,y6,z6) cos(2.*pi.*x6 - pi) + cos(2.*pi.*y6 - pi) + cos(2.*pi.*z6 - pi); % P-element(diff domain) |
|||
f7 = @(x7,y7,z7) 0.8 -(f1(x7,y7,z7) + 0.2); % P-element-opposite |
|||
f8 = @(x8,y8,z8) sin(x8 + y8)./sqrt(x8.^2 + y8.^2 + z8.^2 + 1); % Phi(x,y,z,c) = A(x,y,z) * RBF(x,y,z,c) |
|||
f9 = @(x9,y9,z9) f1(x9,y9,z9) - f8(x9,y9,z9); % P-element(x,y,z,c) - Phi(x,y,z,c) |
|||
f10 = @(x10,y10,z10) f7(x10,y10,z10) + f8(x10,y10,z10); % P-element-oppsite(x,y,z,c) + Phi(x,y,z,c) |
|||
Ralpha = 0; |
|||
f11 = @(x11,y11,z11) 1/(1+Ralpha).*(f9(x11,y11,z11) + f10(x11,y11,z11)... |
|||
- power(power(f9(x11,y11,z11),2) + power(f10(x11,y11,z11),2)... |
|||
- 2.* Ralpha.* f9(x11,y11,z11).* f10(x11,y11,z11),1/2)); % P-shell(with RBF) |
|||
|
|||
[x,y,z] = meshgrid(-3.2:.1:3.2,-3.2:.1:3.2,-3.2:.1:3.2); |
|||
%[x,y,z] = meshgrid(-1.58:.1:4.72,-1.58:.1:4.72,-1.58:.1:4.72); |
|||
%[x,y,z] = meshgrid(0:.1:6.3,0:.1:6.3,0:.1:6.3); |
|||
%[x,y,z] = meshgrid(-5:.1:5,-5:.1:5,-5:.1:5); |
|||
%[x,y,z] = meshgrid(-10:.1:10,-10:.1:10,-10:.1:10); |
|||
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|||
% v = f8(x,y,z); |
|||
% h1 = patch(isosurface(x,y,z,v,0)); |
|||
% %h2 = patch(isocaps(x,y,z,v,0)); |
|||
% set(h1,'FaceColor','[0.5 0.5 0.5]','EdgeColor','none'); |
|||
% %set(h2,'FaceColor','green','EdgeColor','none'); |
|||
% xlabel('x');ylabel('y');zlabel('z'); |
|||
% alpha(1); grid on; view([1,1,1]); axis equal; camlight; lighting gouraud |
|||
|
|||
% hold on |
|||
% v = f7(x,y,z); |
|||
% h1 = patch(isosurface(x,y,z,v,0)); |
|||
% %h2 = patch(isocaps(x,y,z,-v,0)); |
|||
% set(h1,'FaceColor','red','EdgeColor','none'); |
|||
% %set(h2,'FaceColor','blue','EdgeColor','none'); |
|||
% xlabel('x');ylabel('y');zlabel('z'); |
|||
% alpha(1); grid on; view([1,1,1]); axis equal; camlight; lighting gouraud |
|||
|
|||
% P-Shell |
|||
v = f11(x,y,z); |
|||
h1 = patch(isosurface(x,y,z,v,0)); |
|||
%h2 = patch(isocaps(x,y,z,v,0)); |
|||
set(h1,'FaceColor','red','EdgeColor','none'); |
|||
%set(h2,'FaceColor','blue','EdgeColor','none'); |
|||
xlabel('x');ylabel('y');zlabel('z'); |
|||
alpha(1); grid on; view([1,1,1]); axis equal; camlight; lighting gouraud |
|||
|
|||
f = f11; |
|||
@ -0,0 +1,90 @@ |
|||
%%%% An 88 LINE PARAMETERIZED LEVEL SET-BASED TOPOLOGY OPTIMIZATION CODE %%%% |
|||
%function topRBF(nelx,nely,volfrac) |
|||
nelx = 5; nely = 3; volfrac = 0.5; |
|||
%% LEVEL SET FUNCTION INITIALIZATION |
|||
r = nely*0.1; %RADIUS OF INITIAL HOLES |
|||
hX = nelx*[repmat([1/6,5/6],1,3),repmat([0,1/3,2/3,1],1,2),1/2]; |
|||
hY = nely*[kron([0,1/2,1],ones(1,2)),kron([1/4,3/4],ones(1,4)),1/2]; |
|||
[X,Y] = meshgrid(0:1:nelx,0:1:nely); |
|||
dX = bsxfun(@minus,repmat(X,[1,1,numel(hX)]),reshape(hX,1,1,numel(hX))); |
|||
dY = bsxfun(@minus,repmat(Y,[1,1,numel(hY)]),reshape(hY,1,1,numel(hY))); |
|||
Phi = max(-3,min(3,min(sqrt(dX.^2+dY.^2)-r,[],3))); |
|||
%% RADIAL BASIS FUNCTION INITIALIZATION |
|||
cRBF = 1e-4; %RBF PARAMETER |
|||
nNode = (nely+1)*(nelx+1); |
|||
Ax = bsxfun(@minus,X(:),X(:)'); |
|||
Ay = bsxfun(@minus,Y(:),Y(:)'); |
|||
A = sqrt(Ax.^2+Ay.^2+cRBF^2); |
|||
G = [A,ones(nNode,1),X(:),Y(:);[ones(1,nNode);X(:)';Y(:)'],zeros(3,3)]; |
|||
pGpX = [Ax./A,repmat([0,1,0],nNode,1);repmat([0;1;0],1,nNode),zeros(3,3)]; |
|||
pGpY = [Ay./A,repmat([0,0,1],nNode,1);repmat([0;0;1],1,nNode),zeros(3,3)]; |
|||
Alpha = G\[Phi(:);0;0;0]; |
|||
%% FINITE ELEMENT ANALYSIS PREPARATION |
|||
E0 = 1; Emin = 1e-9; nu = 0.3; %MATERIAL PROPERTIES |
|||
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]); |
|||
eleN1 = repmat((1:nely)',1,nelx)+kron(0:nelx-1,(nely+1)*ones(nely,1)); |
|||
eleNode = repmat(eleN1(:),1,4)+repmat([0,nely+[1,2],1],nelx*nely,1); |
|||
edofMat = kron(eleNode,[2,2])+repmat([-1,0],nelx*nely,4); |
|||
iK = reshape(kron(edofMat,ones(8,1))',64*nelx*nely,1); |
|||
jK = reshape(kron(edofMat,ones(1,8))',64*nelx*nely,1); |
|||
%% BOUNDARY CONDITION DEFINITION |
|||
% F = sparse(2*((nely+1)*nelx+ceil(nely/2)+1),1,-100,2*nNode,1); %NODAL LOADS |
|||
% fixeddofs = 1:1:2*(nely+1); %DISPLACEMENT CONSTRAINTS |
|||
F = sparse(2*((nely+1)*(ceil(nelx/2)+1)),1,-100,2*nNode,1); %NODAL LOADS |
|||
fixeddofs = [1,2,2*(nely+1)*nelx+2]; %DISPLACEMENT CONSTRAINTS |
|||
freedofs = setdiff(1:2*nNode,fixeddofs); |
|||
U = zeros(2*nNode,1); |
|||
%% ITERATION OPTIMIZATION |
|||
nLoop = 100; nRelax = 30; |
|||
dt = 0.5; delta = 10; mu = 20; gamma = 0.05; |
|||
comp = zeros(nLoop,1); vol = zeros(nLoop,1); |
|||
for iT = 1:nLoop |
|||
%% FINITE ELEMENT ANALYSIS |
|||
[s,t] = meshgrid(-1:0.1:1,-1:0.1:1); |
|||
tmpPhi = (1-s(:)).*(1-t(:))/4*Phi(eleNode(:,1))'+(1+s(:)).*(1-t(:))/4*... |
|||
Phi(eleNode(:,2))'+(1+s(:)).*(1+t(:))/4*Phi(eleNode(:,3))'+... |
|||
(1-s(:)).*(1+t(:))/4*Phi(eleNode(:,4))'; |
|||
eleVol = sum(tmpPhi>=0,1)'/numel(s); |
|||
vol(iT) = sum(eleVol)/(nelx*nely); |
|||
sK = reshape(KE(:)*(Emin+eleVol'*(E0-Emin)),64*nelx*nely,1); |
|||
K = sparse(iK,jK,sK); K = (K+K')/2; |
|||
U(freedofs,1) = K(freedofs,freedofs)\F(freedofs,1); |
|||
eleComp = sum((U(edofMat)*KE).*U(edofMat),2).*(Emin+eleVol*(E0-Emin)); |
|||
comp(iT) = sum(eleComp); |
|||
%% DISPLAY RESULTS |
|||
% fprintf('No.%i, Obj:%f, Vol:%f\n',[iT,comp(iT),vol(iT)]); |
|||
% figure(1); contourf(Phi,[0,0]); |
|||
% colormap([0,0,0]); set(gcf,'color','w'); axis equal; axis off; |
|||
% figure(2); surf(Phi); caxis([-12,12]); |
|||
% axis equal; axis([0,nelx,0,nely,-12,12]); view(3); |
|||
% figure(3); subplot(2,1,1); plot(comp(1:iT),'-'); title('Compliance'); |
|||
% subplot(2,1,2); plot(vol(1:iT),'-'); title('Volume fraction'); |
|||
%% CONVERGENCE CHECK |
|||
if iT>nRelax && abs(vol(iT)-volfrac)/volfrac<1e-3 && all(abs(comp(iT)-comp(iT-9:iT-1))/comp(iT)<1e-3) |
|||
break; |
|||
end |
|||
%% LAGRANGE MULTIPLIER |
|||
if iT<=nRelax |
|||
lag = mu*(vol(iT)-vol(1)+(vol(1)-volfrac)*iT/nRelax); |
|||
else |
|||
lag = lag+gamma*(vol(iT)-volfrac); |
|||
gamma = min(gamma+0.05,5); |
|||
end |
|||
%% LEVEL SET FUNCTION EVOLUTION |
|||
gradPhi = sqrt((pGpX*Alpha).^2+(pGpY*Alpha).^2); |
|||
indexDelta = (abs(Phi(:))<=delta); |
|||
DeltaPhi = zeros(size(Phi)); |
|||
DeltaPhi(indexDelta) = 0.75/delta*(1-Phi(indexDelta).^2/delta^2); |
|||
eleComp = reshape(eleComp,nely,nelx); |
|||
eleCompLR = [eleComp(:,1),eleComp]+[eleComp,eleComp(:,end)]; |
|||
nodeComp = ([eleCompLR;eleCompLR(end,:)]+[eleCompLR(1,:);eleCompLR])/4; |
|||
B = (nodeComp(:)/median(nodeComp(:))-lag).*DeltaPhi(:)*delta/0.75; |
|||
Alpha = Alpha+dt*(G\[B;0;0;0]); |
|||
Alpha = Alpha/mean(gradPhi(unique(eleNode((eleVol<1 & eleVol>0),:)))); |
|||
Phi = reshape(G(1:end-3,:)*Alpha,nely+1,nelx+1); |
|||
end |
|||
%end |
|||
Loading…
Reference in new issue