FiniteElement#

class planestress.analysis.finite_element.FiniteElement(el_idx: int, el_tag: int, coords: npt.NDArray[np.float64], node_idxs: list[int], material: Material, num_nodes: int, int_points: int)[source]#

Bases: object

Abstract base class for a plane-stress finite element.

Methods

`b_matrix_jacobian`	Calculates the B matrix and jacobian at an isoparametric point.
`element_load_vector`	Assembles the load vector for the element.
`element_stiffness_matrix`	Assembles the stiffness matrix for the element.
`gauss_points`	Gaussian weights and locations for `n_point` Gaussian integration.
`get_element_results`	Calculates various results for the finite element given nodal displacements.
`get_triangulation`	Returns a list of triangle indices for the finite element.
`iso_to_global`	Converts a point in isoparametric coordinates to global coordinates.
`nodal_isoparametric_coordinates`	Returns the values of the isoparametric coordinates at the nodes.
`shape_functions`	Returns the shape functions at a point.
`shape_functions_derivatives`	Returns the derivatives of the shape functions at a point.

__init__(el_idx: int, el_tag: int, coords: npt.NDArray[np.float64], node_idxs: list[int], material: Material, num_nodes: int, int_points: int) → None[source]#

Inits the FiniteElement class.

Parameters:

el_idx (int) – Element index.
el_tag (int) – Element mesh tag.
coords (npt.NDArray[np.float64]) – A numpy.ndarray of coordinates defining the element, e.g. [[x1, x2, x3], [y1, y2, y3]].
node_idxs (list[int]) – List of node indexes defining the element, e.g. [idx1, idx2, idx3].
material (Material) – Material of the element.
num_nodes (int) – Number of nodes in the finite element.
int_points (int) – Number of integration points used for the finite element.

gauss_points(n_points: int) → ndarray[Any, dtype[float64]][source]#

Gaussian weights and locations for n_point Gaussian integration.

Parameters:: n_points (int) – Number of gauss points.
Raises:: NotImplementedError – If this method hasn’t been implemented for an element.
Return type:: ndarray[Any, dtype[float64]]

static shape_functions(iso_coords: tuple[float, float, float]) → ndarray[Any, dtype[float64]][source]#

Returns the shape functions at a point.

Parameters:: iso_coords (tuple[float, float, float]) – Location of the point in isoparametric coordinates.
Raises:: NotImplementedError – If this method hasn’t been implemented for an element.
Return type:: ndarray[Any, dtype[float64]]

static shape_functions_derivatives(iso_coords: tuple[float, float, float]) → ndarray[Any, dtype[float64]][source]#

Returns the derivatives of the shape functions at a point.

Parameters:: iso_coords (tuple[float, float, float]) – Location of the point in isoparametric coordinates.
Raises:: NotImplementedError – If this method hasn’t been implemented for an element.
Return type:: ndarray[Any, dtype[float64]]

iso_to_global(iso_coords: tuple[float, float, float]) → tuple[float, float][source]#

Converts a point in isoparametric coordinates to global coordinates.

Parameters:: iso_coords (tuple[float, float, float]) – Location of the point in isoparametric coordinates.
Returns:: Location of the point in global coordinates (x, y).
Return type:: tuple[float, float]

static nodal_isoparametric_coordinates() → ndarray[Any, dtype[float64]][source]#

Returns the values of the isoparametric coordinates at the nodes.

Raises:: NotImplementedError – If this method hasn’t been implemented for an element.
Return type:: ndarray[Any, dtype[float64]]

b_matrix_jacobian(iso_coords: tuple[float, float, float]) → tuple[ndarray[Any, dtype[float64]], float][source]#

Calculates the B matrix and jacobian at an isoparametric point.

Parameters:: iso_coords (tuple[float, float, float]) – Location of the point in isoparametric coordinates.
Raises:: NotImplementedError – If this method hasn’t been implemented for an element.
Return type:: tuple[ndarray[Any, dtype[float64]], float]

element_stiffness_matrix() → ndarray[Any, dtype[float64]][source]#

Assembles the stiffness matrix for the element.

Returns:: Element stiffness matrix.
Return type:: ndarray[Any, dtype[float64]]

element_load_vector() → ndarray[Any, dtype[float64]][source]#

Assembles the load vector for the element.

Returns:: Element load vector.
Return type:: ndarray[Any, dtype[float64]]

get_element_results(u: ndarray[Any, dtype[float64]]) → ElementResults[source]#

Calculates various results for the finite element given nodal displacements.

Calculates the following:

Stresses at nodes
TODO

Parameters:: u (ndarray[Any, dtype[float64]]) – Displacement vector for the element.
Returns:: ElementResults object.
Return type:: ElementResults

get_triangulation() → list[tuple[int, int, int]][source]#

Returns a list of triangle indices for the finite element.

Raises:: NotImplementedError – If this method hasn’t been implemented for an element.
Return type:: list[tuple[int, int, int]]