def create_fields_displacement_gradients(coordinates: Field,
reference_coordinates: Field,
mesh: Mesh):
"""
:return: 1st and 2nd displacement gradients of (coordinates - referenceCoordinates) w.r.t. referenceCoordinates.
"""
assert (coordinates.getNumberOfComponents()
== 3) and (reference_coordinates.getNumberOfComponents() == 3)
fieldmodule = mesh.getFieldmodule()
dimension = mesh.getDimension()
with ChangeManager(fieldmodule):
if dimension == 3:
u = coordinates - reference_coordinates
displacement_gradient = fieldmodule.createFieldGradient(
u, reference_coordinates)
displacement_gradient2 = fieldmodule.createFieldGradient(
displacement_gradient, reference_coordinates)
elif dimension == 2:
# Note this needs improvement as missing cross terms
# assume xi directions are approximately normal;
# effect is to penalise elements where this is not so, which is also desired
dX_dxi1 = fieldmodule.createFieldDerivative(
reference_coordinates, 1)
dX_dxi2 = fieldmodule.createFieldDerivative(
reference_coordinates, 2)
dx_dxi1 = fieldmodule.createFieldDerivative(coordinates, 1)
dx_dxi2 = fieldmodule.createFieldDerivative(coordinates, 2)
dS1_dxi1 = fieldmodule.createFieldMagnitude(dX_dxi1)
dS2_dxi2 = fieldmodule.createFieldMagnitude(dX_dxi2)
du_dS1 = (dx_dxi1 - dX_dxi1) / dS1_dxi1
du_dS2 = (dx_dxi2 - dX_dxi2) / dS2_dxi2
displacement_gradient = fieldmodule.createFieldConcatenate(
[du_dS1, du_dS2])
# curvature:
d2u_dSdxi1 = fieldmodule.createFieldDerivative(
displacement_gradient, 1)
d2u_dSdxi2 = fieldmodule.createFieldDerivative(
displacement_gradient, 2)
displacement_gradient2 = fieldmodule.createFieldConcatenate(
[d2u_dSdxi1 / dS1_dxi1, d2u_dSdxi2 / dS2_dxi2])
else: # dimension == 1
dX_dxi1 = fieldmodule.createFieldDerivative(
reference_coordinates, 1)
dx_dxi1 = fieldmodule.createFieldDerivative(coordinates, 1)
dS1_dxi1 = fieldmodule.createFieldMagnitude(dX_dxi1)
displacement_gradient = (dx_dxi1 - dX_dxi1) / dS1_dxi1
# curvature:
displacement_gradient2 = fieldmodule.createFieldDerivative(
displacement_gradient, 1) / dS1_dxi1
return displacement_gradient, displacement_gradient2
def evaluate_field_mesh_integral(field: Field, coordinates: Field, mesh: Mesh, number_of_points=4):
"""
Integrate value of a field over mesh using Gaussian Quadrature.
:param field: Field to integrate over mesh.
:param coordinates: Field giving spatial coordinates to integrate over.
:param mesh: The mesh or mesh group to integrate over.
:param number_of_points: Number of integration points in each dimension.
:return: Integral value.
"""
fieldmodule = mesh.getFieldmodule()
components_count = field.getNumberOfComponents()
with ChangeManager(fieldmodule):
integral = fieldmodule.createFieldMeshIntegral(field, coordinates, mesh)
integral.setNumbersOfPoints(number_of_points)
fieldcache = fieldmodule.createFieldcache()
result, value = integral.evaluateReal(fieldcache, components_count)
del integral
del fieldcache
assert result == RESULT_OK
return value