def calculate_internal_force_array_old(self, test=False):
"""Computes the 2D internal nodal force array for the element for the current configuration using Gauss
quadrature. Runs for each deformed configuration in the analysis.
OLD: uses the inverse jacobian and the first Piola-Kirchhoff stress, and is in 2D.
:param bool test: whether to perform numerical differentiation check on the result
"""
# Initialize force array to be computed using Gauss quadrature
force_array = numpy.zeros((self.degrees_of_freedom, self.node_quantity))
# Sum over quadrature points
for quadrature_point in self.quadrature_points:
# Initialize integrand to be computed for this quadrature point
integrand = numpy.zeros((self.degrees_of_freedom, self.node_quantity))
for dof_1 in range(self.degrees_of_freedom):
for node_index in range(self.node_quantity):
# Sum over repeated indices
for dof_2 in range(self.degrees_of_freedom):
for coordinate_index in range(self.dimension):
integrand[dof_1][node_index] += (
quadrature_point.first_piola_kirchhoff_stress[dof_1][dof_2]
* self.shape_function_derivatives(
node_index=node_index, position=quadrature_point.position,
coordinate_index=coordinate_index)
* self.jacobian_matrix_inverse[coordinate_index][dof_2])
# Weight the integrand
integrand *= quadrature_point.weight
# Add the integrand to the internal_force_array
force_array += integrand
# Scale the force array for isoparametric triangle and multiply by the thickness (assumed to be constant)
force_array *= .5 * self.thickness
if test:
tests.numerical_differentiation_force_array(element=self, force_array=force_array)
return force_array
def calculate_internal_force_array(self, test=False):
"""Computes the 3D internal nodal force array for the element for the current configuration using Gauss
quadrature. Runs for each deformed configuration in the analysis.
Uses the residual force, Kirchhoff stress, and curvilinear coordinate system.
:param bool test: whether to perform numerical differentiation check on the result
"""
# Initialize force array
dimensions = (self.degrees_of_freedom, self.node_quantity)
internal_force_array = numpy.zeros(dimensions)
# Sum over quadrature points
for quadrature_point in self.quadrature_points:
# Initialize integrand to be computed for this quadrature point
integrand = numpy.zeros((self.degrees_of_freedom, self.node_quantity))
for dof_1 in range(self.degrees_of_freedom):
for node_index in range(self.node_quantity):
# Sum over repeated indices
for dof_2 in range(self.degrees_of_freedom):
for coordinate_index in range(self.dimension):
integrand[dof_1][node_index] += (
quadrature_point.kirchhoff_stress[coordinate_index][dof_2]
* quadrature_point.current_configuration.basis[dof_2][dof_1]
* self.shape_function_derivatives(node_index=node_index,
position=quadrature_point.position,
coordinate_index=coordinate_index))
# Weight the integrand
integrand *= quadrature_point.weight
# Add the integrand to the internal_force_array
internal_force_array += integrand
# Scale the force array for isoparametric triangle and multiply by the thickness and differential area
internal_force_array *= .5 * self.thickness * self.reference_configuration.differential_area
if test:
tests.numerical_differentiation_force_array(element=self, force_array=internal_force_array)
return internal_force_array