-
Notifications
You must be signed in to change notification settings - Fork 1
/
microTopOpt.py
135 lines (102 loc) · 4.23 KB
/
microTopOpt.py
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
from fenics import *
from fenics_adjoint import *
import matplotlib.pyplot as plt
class Periodic2DBoundary(SubDomain):
def inside(self, x, on_boundary):
return bool(near(x[0], 0) or near(x[1], 0)) and \
not (bool(near(x[0], 1)) and near(x[1], 0)) and \
not (bool(near(x[0], 0)) and near(x[1], 1)) and \
not (bool(near(x[0], 1)) and near(x[1], 1)) and \
on_boundary
def map(self, x, y):
if near(x[0], 1):
y[0] = x[0] - 1
else:
y[0] = x[0]
if near(x[1], 1):
y[1] = x[1] - 1
else:
y[1] = x[1]
def eps(v):
return sym(grad(v))
def sigma(v, Eps, phi):
E0, E1, nu = 0.91, 0.0001, 0.3 # E0 is material, E1 void
mu0 = E0/(2*(1+nu))
mu1 = E1/(2*(1+nu))
lmbda0 = E0*nu/((1+nu)*(1-2*nu))
lmbda1 = E1*nu/((1+nu)*(1-2*nu))
cmat0 = lmbda0 * tr(eps(v) + Eps) * Identity(2) + 2 * mu0 * (eps(v) + Eps)
cmat1 = lmbda1 * tr(eps(v) + Eps) * Identity(2) + 2 * mu1 * (eps(v) + Eps)
return phi**4*cmat0+(1-phi**4)*cmat1
def micro_elast(ii, phi):
Ve = VectorElement("CG", mesh.ufl_cell(), 2)
Re = VectorElement("R", mesh.ufl_cell(), 0)
W = FunctionSpace(mesh, MixedElement([Ve, Re]), constrained_domain=Periodic2DBoundary())
dv, dlamb = TrialFunctions(W)
v_, lamb_ = TestFunctions(W)
w = Function(W)
if(ii == 11):
Eij = E11
else:
Eij = E22
F = inner(sigma(dv, Eij, phi), eps(v_)) * dx
a, L = lhs(F), rhs(F)
a += dot(lamb_, dv) * dx + dot(dlamb, v_) * dx
solve(a == L, w)
(u, lamb) = split(w)
return u
def microTopOpt():
# Target values and weights
w1111, w1122, w2222 = 1, 30, 1
AT1111, AT1122, AT2222 = 0.2, -0.1, 0.2
# Parameters
m = 0.6
GL_gamma = 0.00001
GL_eps = 1
niter = 50
C = FunctionSpace(mesh, "Lagrange", 1, constrained_domain=Periodic2DBoundary())
initial_guess = Expression("(sin(2*pi*3*x[0]-0.5*pi)*sin(2*pi*3*x[1]-0.5*pi)+1)/2", degree=2)
phi = interpolate(initial_guess, C)
plt.figure(1)
c = plot(phi, mode='color', vmin=0, vmax=1, cmap="coolwarm")
plt.colorbar(c)
u11 = micro_elast(11, phi)
u22 = micro_elast(22, phi)
allctrls = File("homogenized/allcontrols.pvd")
rho_viz = Function(C)
def eval_cb(j, phi):
plt.figure(1)
plot(phi, mode='color', vmin=0, vmax=1,
cmap="coolwarm", title='Phasefield')
plt.pause(0.01)
rho_viz.assign(phi)
allctrls << rho_viz
J = 0.5*w1111*(assemble(inner(sigma(u11, E11, phi), eps(u11) + E11) * dx)-AT1111)**2 \
+ 0.5*w1122*(assemble(inner(sigma(u11, E11, phi), eps(u22) + E22) * dx)-AT1122)**2 \
+ 0.5*w2222*(assemble(inner(sigma(u22, E22, phi), eps(u22) + E22) * dx)-AT2222)**2 \
+ GL_gamma*assemble(GL_eps*dot(grad(phi), grad(phi)) * dx+0.25/GL_eps*(phi*phi-phi)**2*dx)
cntrl = Control(phi)
Jhat = ReducedFunctional(J, cntrl, eval_cb_post=eval_cb)
lb = 0.0
ub = 1.0
volume_constraint = UFLInequalityConstraint((Constant(m) - phi)*dx, cntrl)
problem = MinimizationProblem(Jhat, bounds=(lb, ub), constraints=volume_constraint)
parameters = {"acceptable_tol": 1.0e-16,"maximum_iterations": niter, "print_level": 6}
solver = IPOPTSolver(problem, parameters=parameters)
phi_opt = solver.solve()
u11_opt = micro_elast(11, phi_opt)
u22_opt = micro_elast(22, phi_opt)
A1111_opt = assemble(inner(sigma(u11_opt, E11, phi_opt), eps(u11_opt) + E11) * dx)
A1122_opt = assemble(inner(sigma(u11_opt, E11, phi_opt), eps(u22_opt) + E22) * dx)
A2222_opt = assemble(inner(sigma(u22_opt, E22, phi_opt), eps(u22_opt) + E22) * dx)
print(f"Target tensor value: {AT1111} Final value: {A1111_opt:.3f}")
print(f"Target tensor value: {AT1122} Final value: {A1122_opt:.3f}")
print(f"Target tensor value: {AT2222} Final value: {A2222_opt:.3f}")
print(f"First target poisson ratio: {AT1122/AT2222} Final value: {A1122_opt/A2222_opt:.3f}")
print(f"Second target poisson ratio: {AT1122/AT1111} Final value: {A1122_opt/A1111_opt:.3f}")
E11 = Constant(((1, 0), (0, 0)))
E22 = Constant(((0, 0), (0, 1)))
ndof = 50
mesh = UnitSquareMesh(ndof, ndof, "crossed")
microTopOpt()
# plt.show()