def get_fields(shape, delta_x):
"""Get the fields for the displacement and test function
Args:
shape: the shape of the domain
delta_x: the mesh spacing
Returns:
tuple of field variables
"""
return pipe(
np.array(shape),
lambda x: gen_block_mesh(
x * delta_x, x + 1, np.zeros_like(shape), verbose=False
),
lambda x: Domain("domain", x),
lambda x: x.create_region("region_all", "all"),
lambda x: Field.from_args("fu", np.float64, "vector", x, approx_order=2),
lambda x: (
FieldVariable("u", "unknown", x),
FieldVariable("v", "test", x, primary_var_name="u"),
),
)
def _solve(self, property_array):
"""
Solve the Sfepy problem for one sample.
Args:
property_array: array of shape (n_x, n_y, 2) where the last
index is for Lame's parameter and shear modulus,
respectively.
Returns:
the strain field of shape (n_x, n_y, 2) where the last
index represents the x and y displacements
"""
shape = property_array.shape[:-1]
mesh = self._get_mesh(shape)
domain = Domain('domain', mesh)
region_all = domain.create_region('region_all', 'all')
field = Field.from_args('fu', np.float64, 'vector', region_all, # pylint: disable=no-member
approx_order=2)
u = FieldVariable('u', 'unknown', field)
v = FieldVariable('v', 'test', field, primary_var_name='u')
m = self._get_material(property_array, domain)
integral = Integral('i', order=4)
t1 = Term.new('dw_lin_elastic_iso(m.lam, m.mu, v, u)',
integral, region_all, m=m, v=v, u=u)
eq = Equation('balance_of_forces', t1)
eqs = Equations([eq])
epbcs, functions = self._get_periodicBCs(domain)
ebcs = self._get_displacementBCs(domain)
lcbcs = self._get_linear_combinationBCs(domain)
ls = ScipyDirect({})
pb = Problem('elasticity', equations=eqs, auto_solvers=None)
pb.time_update(
ebcs=ebcs, epbcs=epbcs, lcbcs=lcbcs, functions=functions)
ev = pb.get_evaluator()
nls = Newton({}, lin_solver=ls,
fun=ev.eval_residual, fun_grad=ev.eval_tangent_matrix)
try:
pb.set_solvers_instances(ls, nls)
except AttributeError:
pb.set_solver(nls)
vec = pb.solve()
u = vec.create_output_dict()['u'].data
u_reshape = np.reshape(u, (tuple(x + 1 for x in shape) + u.shape[-1:]))
dims = domain.get_mesh_bounding_box().shape[1]
strain = np.squeeze(
pb.evaluate(
'ev_cauchy_strain.{dim}.region_all(u)'.format(
dim=dims),
mode='el_avg',
copy_materials=False))
strain_reshape = np.reshape(strain, (shape + strain.shape[-1:]))
stress = np.squeeze(
pb.evaluate(
'ev_cauchy_stress.{dim}.region_all(m.D, u)'.format(
dim=dims),
mode='el_avg',
copy_materials=False))
stress_reshape = np.reshape(stress, (shape + stress.shape[-1:]))
return strain_reshape, u_reshape, stress_reshape
