/
test_53.py
151 lines (118 loc) · 4.96 KB
/
test_53.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
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
from dolfin import *
import numpy as np
import sys
# Optimization options for the form compiler
parameters["form_compiler"]["cpp_optimize"] = True
ffc_options = {"optimize": True, \
"eliminate_zeros": True, \
"precompute_basis_const": True, \
"precompute_ip_const": True}
discret=2
mesh = UnitCubeMesh(discret,discret,discret)
dolfin.plot(mesh, "3D mesh")
FS = FunctionSpace(mesh, "CG", 2)
W = MixedFunctionSpace([FS, FS, FS, FS, FS, FS, FS, FS, FS, FS,
FS, FS, FS, FS, FS, FS, FS, FS, FS, FS,
FS, FS, FS, FS, FS, FS, FS, FS, FS, FS])
(u0, u1, u2, v000, v001, v002, v010, v011, v012, v020, v021, v022, v100, v101, v102, v110, v111, v112, v120, v121, v122, v200, v201, v202, v210, v211, v212, v220, v221, v222) = TrialFunctions(W)
(du0, du1, du2, dv000, dv001, dv002, dv010, dv011, dv012, dv020, dv021, dv022, dv100, dv101, dv102, dv110, dv111, dv112, dv120, dv121, dv122, dv200, dv201, dv202, dv210, dv211, dv212, dv220, dv221, dv222) = TestFunctions(W)
# Lower face
def DB_0(x, on_boundary):
return x[2] < DOLFIN_EPS and on_boundary
# Point on upper face
TOL = 1e-3
class Pinpoint(SubDomain):
def __init__(self, coords):
self.coords = np.array(coords)
SubDomain.__init__(self)
def move(self, coords):
self.coords[:] = np.array(coords)
def inside(self, x, on_boundary):
return np.linalg.norm(x-self.coords) < TOL
pinpoint = Pinpoint([0.5, 0.5, 1.0])
# Neumann boundary: everything but the lower face
class Neumann(SubDomain):
def inside(self, x, on_boundary):
return x[0] < DOLFIN_EPS and on_boundary or \
x[0] > 1.0 - DOLFIN_EPS and on_boundary or \
x[1] < DOLFIN_EPS and on_boundary or \
x[1] > 1.0 - DOLFIN_EPS and on_boundary or \
x[2] > 1.0 - DOLFIN_EPS and on_boundary
subdomains = MeshFunction("double", mesh)
neumann = Neumann()
neumann.mark(subdomains, 1)
# Displacement boundary condition on Dirichlet boundary (lower face and pinpoint)
u0_0=Expression('0.0')
u1_0=Expression('0.0')
u2_0=Expression('0.0')
u0_1=Expression('0.0')
u1_1=Expression('0.0')
u2_1=Expression('-0.01')
bc = [
DirichletBC(W.sub(0), u0_0, DB_0),
DirichletBC(W.sub(1), u1_0, DB_0),
DirichletBC(W.sub(2), u2_0, DB_0),
DirichletBC(W.sub(0), u0_1, pinpoint, 'pointwise'),
DirichletBC(W.sub(1), u1_1, pinpoint, 'pointwise'),
DirichletBC(W.sub(2), u2_1, pinpoint, 'pointwise')]
# Isotropic stiffness tetradic and hexadic
delta=[[1,0,0],[0,1,0],[0,0,1]]
lambada=100.0
mu=100.0
c1=0.0
c2=0.0
c3=0.0
c4=10.0
c5=0.0
C4=[[[[
lambada*delta[i][j]*delta[k][l]+mu*(delta[i][k]*delta[j][l]+delta[i][l]*delta[j][k])
for i in range(3)]
for j in range(3)]
for k in range(3)]
for l in range(3)]
C6=[[[[[[
c1 * ( delta[i][j]*delta[k][l]*delta[m][n] + delta[i][j]*delta[k][m]*delta[l][n] + delta[i][k]*delta[j][n]*delta[l][m] + delta[i][n]*delta[k][j]*delta[l][m] ) +
c2 * ( delta[i][k]*delta[j][l]*delta[m][n] + delta[i][l]*delta[j][k]*delta[m][n] + delta[i][k]*delta[j][m]*delta[l][n] + delta[i][m]*delta[k][j]*delta[l][n] ) +
c3 * ( delta[i][l]*delta[j][n]*delta[k][m] + delta[i][n]*delta[k][m]*delta[j][l] + delta[i][m]*delta[k][l]*delta[j][n] + delta[i][n]*delta[k][l]*delta[m][j] ) +
c4 * ( delta[i][m]*delta[k][n]*delta[j][l] + delta[i][l]*delta[j][m]*delta[k][n] ) +
c5 * delta[i][j]*delta[k][n]*delta[l][m]
for i in range(3)]
for j in range(3)]
for k in range(3)]
for l in range(3)]
for m in range(3)]
for n in range(3)]
# Generation of equation string
eq1 = "("
for i in range(3):
for j in range(3):
for k in range(3):
eq1 = eq1 + ("+v"+"%g%g%g" %(i,j,k) +"*dv"+"%g%g%g" %(i,j,k))
eq1 = eq1 + ("+u%g.dx(%g)" %(i,j) +"*dv%g%g%g.dx(%g)" %(i,j,k,k))
for l in range(3):
if(C4[i][j][k][l]!=0.0):
eq1 = eq1 + "+C4[%g][%g][%g][%g]*v%g%g%g*du%g" %(i,j,k,l,k,l,j,i)
for m in range(3):
for n in range(3):
if(C6[i][j][k][l][m][n]!=0.0):
eq1 = eq1 + "+C6[%g][%g][%g][%g][%g][%g]*v%g%g%g.dx(%g)*du%g.dx(%g)" %(i,j,k,l,m,n,l,m,n,j,i,k)
eq1 = eq1+")*dx"
n = FacetNormal(mesh)
eq2 = "("
for i in range(3):
for j in range(3):
for k in range(3):
eq2 = eq2 + "-u%g.dx(%g)*n[%g]*dv%g%g%g" %(i,j,k,i,j,k)
for l in range(3):
for m in range(3):
for o in range(3):
if(C6[i][j][k][l][m][o]!=0.0):
eq2 = eq2 + "-C6[%g][%g][%g][%g][%g][%g]*v%g%g%g.dx(%g)*n[%g]*du%g" %(i,j,k,l,m,o,l,m,o,j,k,i)
eq2 = eq2 + ")*ds(1)"
print 'Booom!'
a=eval(eq1+"+"+eq2)
z = Constant(0.0)
L = z*(du0+du1+du2+dv000+dv001+dv002+dv010+dv011+dv012+dv020+dv021+dv022+dv100+dv101+dv102+dv110+dv111+dv112+dv120+dv121+dv122+dv200+dv201+dv202+dv210+dv211+dv212+dv220+dv221+dv222)*dx
w = Function(W)
A, b = assemble_system(a, L, bc)
#solve(a == L, w, bc)