Я пытаюсь решить проблему механики сплошных сред с помощью FEniCS. Я хочу вычислить поле смещения u в определенном случае.
Вот мой код:
from dolfin import *
from fenics import *
import matplotlib.pyplot as plt
mesh = RectangleMesh(Point(-1., 0.0),Point(1., 10.), 10, 10)
plot(mesh, title="Rectangle")
P1 = FiniteElement('P', triangle,1)
element = P1*P1
V = FunctionSpace(mesh,element)
v_1, v_3 = TestFunction(V)
u = Function(V)
u_1, u_3 = split(u)
def boundaryDC(x):
return abs(x[1])<tol
u_D = as_vector((Expression('0.', degree = 0),Expression('0.', degree = 0)))
bc = DirichletBC(V,u_D,boundaryDC)
g11 = Expression('x[0]>(1.-pow(10,-14)) ? 1 : 0', degree = 0)
g12 = Expression('x[0]<(-1.+pow(10,-14)) ? 1 : 0', degree = 0)
g32 = Expression('x[1]>(10.-pow(10,-14)) ? 1 : 0', degree = 0)
a = -(dot(grad(u_1),grad(v_1))+dot(grad(u_3),grad(v_3))+(Dx(u_1,0)+Dx(u_3,0))*(Dx(v_1,0)+Dx(v_3,0)))*dx + ((-2)*Dx(u_1,0)*v_1-v_3*Dx(u_1,1))*(g11+g12)*ds + ((-2)*Dx(u_3,1)*v_3-v_1*Dx(u_3,0))*g32*ds
L = -(7.2*10**(-5))*(v_1*(g11-g12)+v_3*g32)*ds+(0.018)*v_3*g32*ds
solve(a==L, u, bc)
Когда я его запускаю, я получаю эту ошибку:
RuntimeError Traceback (most recent call last)
<ipython-input-50-766317262156> in <module>
28 L = -(7.2*10**(-5))*(v_1*(g11-g12)+v_3*g32)*ds+(0.018)*v_3*g32*ds
29
---> 30 solve(a==L, u, bc)
/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)
57
58 # Initialize C++ base class
---> 59 cpp.fem.LinearVariationalProblem.__init__(self, a, L, u._cpp_object, bcs)
60
61
RuntimeError:
*** -------------------------------------------------------------------------
*** DOLFIN encountered an error. If you are not able to resolve this issue
*** using the information listed below, you can ask for help at
***
*** fenics-support@googlegroups.com
***
*** Remember to include the error message listed below and, if possible,
*** include a *minimal* running example to reproduce the error.
***
*** -------------------------------------------------------------------------
*** Error: Unable to define linear variational problem a(u, v) == L(v) for all v.
*** Reason: Expecting the left-hand side to be a bilinear form (not rank 1).
*** Where: This error was encountered inside LinearVariationalProblem.cpp.
*** Process: 0
***
*** DOLFIN version: 2019.1.0
*** Git changeset: unknown
'
Ты знаешь как это исправить?