def shapeopt(RBF, Kinit, Vinit, iel, LSFip):
# Variables
nelx = variables.nelx
nely = variables.nely
f = variables.f
si_max = variables.si_max
kappa = variables.kappa
rhomin = variables.rhomin
edof = variables.edof
# Discard/free DOFs
ndof = np.max(edof) + 1
dofs = np.arange(ndof)
disc = np.setdiff1d(edof[iel == 0, :], edof[iel != 0, :])
free = np.setdiff1d(dofs, np.append(variables.fix, disc))
dofs[np.append(variables.fix, disc)] = -1
# Optimizer initialization (MMA)
mma = optimizers.MMA(variables.nele,
dmax=si_max,
dmin=-si_max,
movelimit=0.2,
asy=(0.5, 1.2, 0.65),
scaling=True)
x = RBF[:, :, 2].T.reshape(-1).copy()
iter = 1
while iter < 10.5:
# Stiffness matrix
phi = LSFip.dot(x[:])
rho = rhomin + (1 - rhomin) * (1 / (1 + np.exp(-kappa * phi)))
K = FCM.K(Kinit, iel, rho)
# Reverse Cuthill-McKee ordering
ind = sp.csgraph.reverse_cuthill_mckee(K, symmetric_mode=True)
free = dofs[ind][dofs[ind] != -1]
# Solve (reduced) system
u = np.zeros((np.size(K, 0), ))
u[free] = solver(K[free, :][:, free], f[free])
# Compliance objective and its sensitivity
[C, dC] = obj(Kinit, iel, LSFip, u, phi, rho, f, free)
# Volume fraction constraint and its sensitivity
[g, dg] = constr(Vinit, iel, LSFip, phi, rho)
# Shape optimization
dx = mma.solve(x, C, dC, g, dg, iter)
x = x + dx
# Update log
print(['%.3f' % i for i in [iter, C, g]])
iter += 1
RBF[:, :, 2] = x.reshape(nely, nelx).T
return RBF
