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rbto_den_L.m
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rbto_den_L.m
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%%% rbto_den_L(60,60,3,1.5,dismax)
function rbto_den_L(nelx,nely,penal,rmin,dismax,reli,lwE,fn,title)
%%% Initial values
nKL = 2;
init_val = 0.5;
x(1:nely,1:nelx) = init_val;
xphy(1:nely,1:nelx) = init_val;
passive=zeros(nely,nelx);
for i=1:nelx
for j=1:nely
if (i > nelx/2) && (j <= nely/2)
passive(j,i)=1;
end
end
end
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 = 1/(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)];
%%% MMA
m = 1;
n = nelx*nely;
xmin(1:n,1) = 0.001;
xmax(1:n,1) = 1;
low = xmin;
upp = xmax;
a0 = 1;
a(1:m,1) = 0;
ci(1:m,1) = 1000;
d(1:m,1) = 0;
xold1 = x;
xold2 = x;
[eigV,eigF] = KL(nelx,nely,nKL);
dof = 2*(nelx)*(nely+1)+2*(nely*3/4+1);
upE = 1;
roots = [sqrt(3 + sqrt(6))...
-sqrt(3 + sqrt(6))...
sqrt(3 - sqrt(6))...
-sqrt(3 - sqrt(6))];
colPoints = [ 0 0;...
roots(1) 0;...
0 roots(1);...
roots(2) 0;...
0 roots(2);...
roots(3) 0;...
0 roots(3);...
roots(4) 0;...
0 roots(4);...
roots(3) roots(3);...
roots(4) roots(4);...
roots(3) roots(4);...
roots(4) roots(3);...
roots(1) roots(3);...
roots(1) roots(4);...
roots(3) roots(1);...
roots(4) roots(1);...
roots(2) roots(3);...
roots(3) roots(2);...
roots(2) roots(4);...
roots(4) roots(2);...
roots(1) roots(2);...
roots(2) roots(1)];
%%% Prepare filter
iH = ones(nelx*nely*(2*(ceil(rmin)-1)+1)^2,1);
jH = ones(size(iH));
sH = zeros(size(iH));
k = 0;
for i1 = 1:nelx
for j1 = 1:nely
e1 = (i1-1)*nely+j1;
for i2 = max(i1-(ceil(rmin)-1),1):min(i1+(ceil(rmin)-1),nelx)
for j2 = max(j1-(ceil(rmin)-1),1):min(j1+(ceil(rmin)-1),nely)
e2 = (i2-1)*nely+j2;
k = k+1;
iH(k) = e1;
jH(k) = e2;
sH(k) = max(0,rmin-sqrt((i1-i2)^2+(j1-j2)^2));
end
end
end
end
H = sparse(iH,jH,sH);
Hs = sum(H,2);
mpp = [0 0];
mpptol = 1.;
fval(1,1) = 1;
main_loop = 0;
while mpptol > 0.001 && main_loop < 20
mppold = mpp;
loop = 0;
main_loop = main_loop + 1;
change = 1.;
x(1:nely,1:nelx) = init_val;
x(passive == 1) = 0.001;
xphy = x;
E = update_E(eigV, eigF, mpp, nKL, upE, lwE, nelx, nely);
while change > 0.001
loop = loop + 1;
[U] = FEL(nelx,nely,xphy,penal,KE,E,dof);
dcf(1:nely,1:nelx) = 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);
dcf(ely,elx) = -Ue'*penal*xphy(ely,elx)^(penal-1)*E(ely,elx)*KE*Ue;
end
end
c = sum(xphy(:));
dc(1:nely,1:nelx) = 1;
dc(:) = H*(dc(:)./Hs);
f0val = c;
df0dx = dc(:);
fval(1,1) = U(dof)/dismax -1;
dcf(:) = H*(dcf(:)./Hs);
dfdx(1,1:n) = dcf(:)/dismax;
%%% The MMA subproblem is solved at the point xval:
outeriter = loop;
[xmma,~,~,~,~,~,~,~,~,low,upp] = ...
mmasub(m,n,outeriter,x(:),xmin,xmax,xold1(:),xold2(:), ...
f0val,df0dx,fval,dfdx,low,upp,a0,a,ci,d);
%%% Update
xold2 = xold1;
xold1 = x;
xnew = reshape(xmma,nely,nelx);
xphy(:) = (H*xnew(:))./Hs;
change = max(abs(xnew(:)-x(:)));
x = xnew;
xphy(passive == 1) = 0.001;
% Results
disp([' It.: ' sprintf('%4i',loop) ' Obj.: ' sprintf('%6.4f',c) ...
' Vol Frac.: ' sprintf('%6.4f',sum(sum(xphy))/(3/4*nelx*nely)) ...
' ch.: ' sprintf('%6.3f',change )])
% PLOT DENSITIES
% colormap(gray);
% imagesc(1-xphy);
% axis equal;
% axis tight;
% axis off;
% pause(1e-6);
end
mpp = find_mpp(colPoints, eigV, eigF, nKL, nelx, nely, xphy, penal,...
KE, dof, upE, lwE, dismax,reli);
mpptol = max(abs(mpp(:)-mppold(:)));
end
figure
colormap(gray);
imagesc(1-xphy);
axis equal;
axis tight;
axis off;
savefig(fn);
close all;
fileID = fopen('data.txt','a+');
fprintf(fileID,'%s',title);
fprintf(fileID,'\nVol Frac.: %6.4f',sum(sum(xphy))/(3/4*nelx*nely));
fprintf(fileID,'\nmain_loop: %4i',main_loop);
fclose(fileID);
%%%
disp('END OPTIMIZATION');
rbto_mc_L(nelx, nely, penal, xphy, dismax, dof, upE, lwE);
end
function newE = update_E(eigV, eigF, mpp, nKL, c, d, nelx, nely)
Z = sqrt(eigV).* mpp';
E(1:nely,1:nelx) = 0;
for j = 1:nKL
E = E + Z(j)*squeeze(eigF(j,:,:));
end
newE = c + (d-c)*normcdf(E);
end
function mpp = find_mpp(colPoints, eigV, eigF, nKL, nelx, nely, x, penal,...
KE, dof, c, d, dismax,reli)
s = length(colPoints);
v(1:s) = 0;
for i = 1:s
Z = sqrt(eigV).*colPoints(i,:)';
E(1:nely,1:nelx) = 0;
for j = 1:nKL
E = E + Z(j)*squeeze(eigF(j,:,:));
end
E = c + (d-c)*normcdf(E);
[U] = FEL(nelx,nely,x,penal,KE,E,dof);
v(i) = U(dof);
end
numVar = 10;
N(1:s,1:numVar) = 0;
for i = 1:s
N(i,1) = 1;
N(i,2) = colPoints(i, 1);
N(i,3) = colPoints(i, 2);
N(i,4) = colPoints(i, 1)^2 - 1;
N(i,5) = colPoints(i,2)^2 - 1;
N(i,6) = colPoints(i,1)*colPoints(i,2);
N(i,7) = colPoints(i,1)^3 - 3*colPoints(i,1);
N(i,8) = colPoints(i,2)^3 - 3*colPoints(i,2);
N(i,9) = colPoints(i,1)*colPoints(i,2)^2 - colPoints(i,1);
N(i,10) = colPoints(i,2)*colPoints(i,1)^2 - colPoints(i,2);
end
a = N'*N \ N'*v';
h = @(x) a(1) + a(2)*x(:,1) + a(3)*x(:,2) +...
a(4)*(x(:,1)^2 - 1) + a(5)*(x(:,2)^2 - 1) +...
a(6)*x(:,1)*x(:,2) +...
a(7)*(x(:,1)^3 - 3*x(:,1)) + a(8)*(x(:,2)^3 - 3*x(:,2)) +...
a(9)*(x(:,1)*(x(:,2)^2) - x(:,1)) + a(10)*((x(:,1)^2)*x(:,2) - x(:,2));
%g = @(x) h(x)/dismax - 1;
g = @(x) dismax/h(x) - 1;
%T = @(x) x;
Tinv = @(u) u;
res = CODES.reliability.iform(g,2,reli,'solver','hmv','Tinv',Tinv);
disp(res)
mpp = res.MPTP;
end