Dear members,
I'm strugling with implementing the MMA code (Svanberg) in the 88 line code with Heaviside projection method.
The sensitivity and density filter both work correctly, but when ft == 3 (Heaviside) my volfrac goes to 1 (when it's supposed to be 0.5 or something else)
Can somebody help me with this?
I just paste the code here (without the MMA part, mmasub & subsolv, because its too long and I have not changed anything different than the original of Svanberg)
function top110MMA(nelx,nely,volfrac,penal,rmin,ft)
%% MATERIAL PROPERTIES
E0 = 1;
Emin = 1e-9;
nu = 0.3;
%% PREPARE FINITE ELEMENT ANALYSIS//blijft
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]);
nodenrs = reshape(1:(1+nelx)*(1+nely),1+nely,1+nelx);
edofVec = reshape(2*nodenrs(1:end-1,1:end-1)+1,nelx*nely,1);
edofMat = repmat(edofVec,1,8)+repmat([0 1 2*nely+[2 3 0 1] -2 -1],nelx*nely,1);
iK = reshape(kron(edofMat,ones(8,1))',64*nelx*nely,1);
jK = reshape(kron(edofMat,ones(1,8))',64*nelx*nely,1);
% DEFINE LOADS AND SUPPORTS (HALF MBB-BEAM)//blijft
F = sparse(2,1,-1,2*(nely+1)*(nelx+1),1);
U = zeros(2*(nely+1)*(nelx+1),1);
fixeddofs = union([1:2:2*(nely+1)],[2*(nelx+1)*(nely+1)]);
alldofs = [1:2*(nely+1)*(nelx+1)];
freedofs = setdiff(alldofs,fixeddofs);
%% PREPARE FILTER ///blijft
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);
%% INITIALIZE ITERATION
x = repmat(volfrac,nely,nelx);
beta = 1;
if ft == 1 || ft == 2
xPhys = x;
elseif ft == 3
xTilde = x;
xPhys = 1-exp(-beta*xTilde)+xTilde*exp(-beta);
end
loopbeta = 0;
loop = 0;
change = 1;
m = 1; % number of general constraints
n = nely*nelx; % Number of design variables
nelm = nely*nelx;
xmin = 1e-9*ones(nelm,1); % Minimum value of each DV
xmax = ones(nelm,1); % Maximum value of each DV
xval = reshape(x,nelm,1); % Initial value of each DV
xold1 = xval; % Previous value of each DV
xold2 = xval; % Previous previous value of each DV
u = xval; % Extra vector used to determine xold1 and xold2
a0 = 1; % Vector of constants (set to 1 fronm exercise description)
ai = 0;
ci = 1000; % Vector of constants >= 0
di = 0; % Vector of constants >= 0
low = ones(nelm,1);
upp = ones(nelm,1);
%% START ITERATION
while change > 0.01
loopbeta = loopbeta+1;
loop = loop+1;
iter = loop;
%% FE-ANALYSIS
sK = reshape(KE(:)*(Emin+xPhys(:)'.^penal*(E0-Emin)),64*nelx*nely,1);
K = sparse(iK,jK,sK); K = (K+K')/2;
U(freedofs) = K(freedofs,freedofs)\F(freedofs);
%% OBJECTIVE FUNCTION AND SENSITIVITY ANALYSIS
ce = reshape(sum((U(edofMat)*KE).*U(edofMat),2),nely,nelx);
c = sum(sum((Emin+xPhys.^penal*(E0-Emin)).*ce));
dc = -penal*(E0-Emin)*xPhys.^(penal-1).*ce;
dv = ones(nely,nelx);
fscale = c/10;
c = fscale;
%% FILTERING/MODIFICATION OF SENSITIVITIES
if ft == 1
dc(:) = H*(x(:).*dc(:))./Hs./max(1e-3,x(:));
elseif ft == 2
dc(:) = H*(dc(:)./Hs);
dv(:) = H*(dv(:)./Hs);
elseif ft == 3
dx = beta*exp(-beta*xTilde)+exp(-beta);
dc(:) = H*(dc(:).*dx(:)./Hs);
dv(:) = H*(dv(:).*dx(:)./Hs);
end
%% MMA Update
xval = reshape(x,nelm,1);
fval = sum(sum(x(:)))/(volfrac*nely*nelx)-1;
dfdx = ones(1,nelm)*1/(volfrac*nely*nelx);
f0val = c;
df0dx = reshape(dc,nelm,1);
df0dx2 = 0*df0dx;
dfdx2 = 0*dfdx;
[xmma,~,~,~,~,~,~,~,~,low,upp] = ...
mmasub(m,n,iter,xval,xmin,xmax,xold1,xold2, ...
f0val,df0dx,df0dx2,fval,dfdx,dfdx2,low,upp,a0,ai,ci,di);
xnew = reshape(xmma,nely,nelx);
if ft == 1
xPhys = xnew;
elseif ft == 2
xPhys(:) = (H*xnew(:))./Hs;
elseif ft == 3
xTilde(:) = (H*xnew(:))./Hs;
xPhys = 1-exp(-beta*xTilde)+xTilde*exp(-beta);
end
xold2 = xold1(:);
xold1 = x(:);
change = max(abs(xnew(:)-x(:)));
x = xnew;
%% PRINT RESULTS
fprintf(' It.:%5i Obj.:%11.4f Vol.:%7.3f ch.:%7.3f\n',loop,c, ...
sum(xPhys(:))/(nelx*nely),change);
%% PLOT DENSITIES
colormap(gray); imagesc(1-xPhys); caxis([0 1]); axis equal; axis off; drawnow;
%% UPDATE HEAVISIDE REGULARIZATION PARAMETER
if ft == 3 && beta < 512 && (loopbeta >= 50 || change <= 0.01)
beta = 2*beta;
loopbeta = 0;
change = 1;
fprintf('Parameter beta increased to %g.\n',beta);
end
end