Я хочу решить проблему механики сплошных сред, благодаря FEniCS. Я прикладываю давление и учитываю вес. Но когда я добавляю компонент термоупругости, он больше не работает.
Вот мой код:
from dolfin import *
from fenics import *
from ufl import nabla_div
from ufl import as_tensor
import matplotlib.pyplot as plt
import numpy as np
E = Constant(100*10**9)
nu = Constant(0.3)
Lg = 0.01; W = 0.2
mu = E/(2+2*nu)
rho = Constant(2200)
delta = W/Lg
gamma = 0.4*delta**2
beta = 8
lambda_ = (E*nu)/((1+nu)*(1-2*nu))
alpha = 1.2*(10**(-8))
deltaT = Constant(50)
Kt = E*alph*deltaT/(1-2*nu)
g = 9.81
tol = 1E-14
# Create mesh and define function space
mesh = RectangleMesh(Point(-2., 0.),Point(2., 10.), 80, 200)
V = VectorFunctionSpace(mesh, "P", 1)
# Define boundary condition
def clamped_boundary(x, on_boundary):
return on_boundary and x[1] < tol
class UpFace(SubDomain):
def inside(self, x, on_boundary):
return on_boundary and (x[1] > 10 - tol)
ueN = UpFace()
boundaries = MeshFunction("size_t", mesh, mesh.topology().dim()-1, 0)
ueN.mark(boundaries, 1)
ds = Measure("ds", domain=mesh, subdomain_data=boundaries)
bc = DirichletBC(V, Constant((0, 0)), clamped_boundary)
def epsilon(u):
return 0.5*(nabla_grad(u) + nabla_grad(u).T)
def sigma(u):
return (lambda_*nabla_div(u) - Kt)*Identity(d) + (2*mu)*epsilon(u)
# Define variational problem
u = TrialFunction(V)
d = u.geometric_dimension() # space dimension
v = TestFunction(V)
f = Constant((0,-rho*g))
T = Constant((0, 0))
Pr = Constant((0, -2*10**9))
a = inner(sigma(u), epsilon(v))*dx
L = dot(f, v)*dx + dot(T, v)*ds + dot(Pr,v)*ds(1)
# Compute solution
u = Function(V)
solve(a == L, u, bc)
# Plot solution
plot(u, mode="displacement", color= "red")
plt.colorbar(plot(u))
Я получаю это сообщение об ошибке:
---------------------------------------------------------------------------
ArityMismatch Traceback (most recent call last)
<ipython-input-54-805d7c5b704f> in <module>
17 # Compute solution
18 u = Function(V)
---> 19 solve(a == L, u, bc)
20
21 # Plot solution
/usr/lib/python3/dist-packages/dolfin/fem/solving.py in solve(*args, **kwargs)
218 # tolerance)
219 elif isinstance(args[0], ufl.classes.Equation):
--> 220 _solve_varproblem(*args, **kwargs)
221
222 # Default case, just call the wrapped C++ solve function
/usr/lib/python3/dist-packages/dolfin/fem/solving.py in _solve_varproblem(*args, **kwargs)
240 # Create problem
241 problem = LinearVariationalProblem(eq.lhs, eq.rhs, u, bcs,
--> 242 form_compiler_parameters=form_compiler_parameters)
243
244 # Create solver and call solve
/usr/lib/python3/dist-packages/dolfin/fem/problem.py in __init__(self, a, L, u, bcs, form_compiler_parameters)
54 else:
55 L = Form(L, form_compiler_parameters=form_compiler_parameters)
---> 56 a = Form(a, form_compiler_parameters=form_compiler_parameters)
57
58 # Initialize C++ base class
/usr/lib/python3/dist-packages/dolfin/fem/form.py in __init__(self, form, **kwargs)
42
43 ufc_form = ffc_jit(form, form_compiler_parameters=form_compiler_parameters,
---> 44 mpi_comm=mesh.mpi_comm())
45 ufc_form = cpp.fem.make_ufc_form(ufc_form[0])
46
/usr/lib/python3/dist-packages/dolfin/jit/jit.py in mpi_jit(*args, **kwargs)
45 # Just call JIT compiler when running in serial
46 if MPI.size(mpi_comm) == 1:
---> 47 return local_jit(*args, **kwargs)
48
49 # Default status (0 == ok, 1 == fail)
/usr/lib/python3/dist-packages/dolfin/jit/jit.py in ffc_jit(ufl_form, form_compiler_parameters)
95 p.update(dict(parameters["form_compiler"]))
96 p.update(form_compiler_parameters or {})
---> 97 return ffc.jit(ufl_form, parameters=p)
98
99
/usr/lib/python3/dist-packages/ffc/jitcompiler.py in jit(ufl_object, parameters, indirect)
215
216 # Inspect cache and generate+build if necessary
--> 217 module = jit_build(ufl_object, module_name, parameters)
218
219 # Raise exception on failure to build or import module
/usr/lib/python3/dist-packages/ffc/jitcompiler.py in jit_build(ufl_object, module_name, parameters)
131 name=module_name,
132 params=params,
--> 133 generate=jit_generate)
134 return module
135
/usr/lib/python3/dist-packages/dijitso/jit.py in jit(jitable, name, params, generate, send, receive, wait)
163 elif generate:
164 # 1) Generate source code
--> 165 header, source, dependencies = generate(jitable, name, signature, params["generator"])
166 # Ensure we got unicode from generate
167 header = as_unicode(header)
/usr/lib/python3/dist-packages/ffc/jitcompiler.py in jit_generate(ufl_object, module_name, signature, parameters)
64
65 code_h, code_c, dependent_ufl_objects = compile_object(ufl_object,
---> 66 prefix=module_name, parameters=parameters, jit=True)
67
68 # Jit compile dependent objects separately,
/usr/lib/python3/dist-packages/ffc/compiler.py in compile_form(forms, object_names, prefix, parameters, jit)
141 """This function generates UFC code for a given UFL form or list of UFL forms."""
142 return compile_ufl_objects(forms, "form", object_names,
--> 143 prefix, parameters, jit)
144
145
/usr/lib/python3/dist-packages/ffc/compiler.py in compile_ufl_objects(ufl_objects, kind, object_names, prefix, parameters, jit)
183 # Stage 1: analysis
184 cpu_time = time()
--> 185 analysis = analyze_ufl_objects(ufl_objects, kind, parameters)
186 _print_timing(1, time() - cpu_time)
187
/usr/lib/python3/dist-packages/ffc/analysis.py in analyze_ufl_objects(ufl_objects, kind, parameters)
88 # Analyze forms
89 form_datas = tuple(_analyze_form(form, parameters)
---> 90 for form in forms)
91
92 # Extract unique elements accross all forms
/usr/lib/python3/dist-packages/ffc/analysis.py in <genexpr>(.0)
88 # Analyze forms
89 form_datas = tuple(_analyze_form(form, parameters)
---> 90 for form in forms)
91
92 # Extract unique elements accross all forms
/usr/lib/python3/dist-packages/ffc/analysis.py in _analyze_form(form, parameters)
172 do_apply_geometry_lowering=True,
173 preserve_geometry_types=(Jacobian,),
--> 174 do_apply_restrictions=True)
175 elif r == "tsfc":
176 try:
/usr/lib/python3/dist-packages/ufl/algorithms/compute_form_data.py in compute_form_data(form, do_apply_function_pullbacks, do_apply_integral_scaling, do_apply_geometry_lowering, preserve_geometry_types, do_apply_default_restrictions, do_apply_restrictions, do_estimate_degrees, do_append_everywhere_integrals, complex_mode)
416 preprocessed_form = remove_complex_nodes(preprocessed_form)
417
--> 418 check_form_arity(preprocessed_form, self.original_form.arguments(), complex_mode) # Currently testing how fast this is
419
420 # TODO: This member is used by unit tests, change the tests to
/usr/lib/python3/dist-packages/ufl/algorithms/check_arities.py in check_form_arity(form, arguments, complex_mode)
175 def check_form_arity(form, arguments, complex_mode=False):
176 for itg in form.integrals():
--> 177 check_integrand_arity(itg.integrand(), arguments, complex_mode)
/usr/lib/python3/dist-packages/ufl/algorithms/check_arities.py in check_integrand_arity(expr, arguments, complex_mode)
157 key=lambda x: (x.number(), x.part())))
158 rules = ArityChecker(arguments)
--> 159 arg_tuples = map_expr_dag(rules, expr, compress=False)
160 args = tuple(a[0] for a in arg_tuples)
161 if args != arguments:
/usr/lib/python3/dist-packages/ufl/corealg/map_dag.py in map_expr_dag(function, expression, compress)
35 Return the result of the final function call.
36 """
---> 37 result, = map_expr_dags(function, [expression], compress=compress)
38 return result
39
/usr/lib/python3/dist-packages/ufl/corealg/map_dag.py in map_expr_dags(function, expressions, compress)
84 r = handlers[v._ufl_typecode_](v)
85 else:
---> 86 r = handlers[v._ufl_typecode_](v, *[vcache[u] for u in v.ufl_operands])
87
88 # Optionally check if r is in rcache, a memory optimization
/usr/lib/python3/dist-packages/ufl/algorithms/check_arities.py in sum(self, o, a, b)
46 def sum(self, o, a, b):
47 if a != b:
---> 48 raise ArityMismatch("Adding expressions with non-matching form arguments {0} vs {1}.".format(_afmt(a), _afmt(b)))
49 return a
50
ArityMismatch: Adding expressions with non-matching form arguments () vs ('v_1',).
Когда я пишу это (я удаляю Kt из sigma (u)):
def sigma(u):
return (lambda_*nabla_div(u))*Identity(d) + (2*mu)*epsilon(u)
Работает отлично. На этой странице (нажмите здесь ), они пытаются построить ту же самую проблему, и она работает на моем компьютере. Вы знаете, как это исправить?