element_definitions

This module defines elements by the dictionaries:

• R_at_nodes_of_element

• exponents_of_shape_functions_of_element

• R_at_integration_points_of_element

• weights_of_integration_points_of_element

• face_count_of_element

The integration points and weights are computed using Abaqus. The other dictionaries are defined manually.

See also

The module conforce_gen.expressions describes how to use the nodes, exponents, etc.

Access dictionaries

To acces the nodes, exponents, etc. for a specific element, the element type can be looked up in the dictionaries. For example,

>>> element_type = CPE4R

is a four-noded 2 D element with one integration point.

>>> ref_nodes = R_at_nodes_of_element[element_type]
>>> ref_nodes.shape
(4, 2)
>>> shape_exponents = exponents_of_shape_functions_of_element[element_type]
>>> shape_exponents.shape
(4, 2)
>>> int_points = R_at_integration_points_of_element[element_type]
>>> int_points.shape
(1, 2)
>>> int_weights = weights_of_integration_points_of_element[element_type]
>>> int_weights.shape
(1,)
>>> face_count = face_count_of_element[element_type]
>>> face_count
4

Attributes

R_at_nodes_of_element	Coordinates of the element nodes in the reference coordinate system
exponents_of_shape_functions_of_element	Exponents of powers used by the shape functions defined in the reference space
R_at_integration_points_of_element	Coordinates of integration points in the reference coordinates system
weights_of_integration_points_of_element	Weights corresponding to the integration points
face_count_of_element	number of faces an element has.
C3D20	3D 20-node quadratic brick
C3D20R	3D 20-node quadratic brick, reduced integration
CPE8	2D 8-node bilinear quadrilateral
CPE8R	2D 8-node bilinear quadrilateral, reduced integration
C3D8	3D 8-node quadratic brick
C3D8R	3D 8-node quadratic brick, reduced integration
CPE4	2D 4-node bilinear quadrilateral
CPE4R	2D 4-node bilinear quadrilateral, reduced integration
C3D10	3D 10-node quadratic tetrahedron
C3D4	3D 4-node linear tetrahedron
C3D15	3D 15-node quadratic triangular prism
CPE6	2D 6-node quadratic triangle
C3D6	3D 6-node quadratic triangular prism
CPE3	2D 3-node linear triangle