pysdic.get_gauss_points

get_gauss_points(element_type, return_weights=False)

Get the natural coordinates and weights of Gauss quadrature points for a specified element type.

Parameters:

• element_type (str) –

  The type of element for which to retrieve Gauss points. Supported types are:

  • 'segment_2': 2-node segment element

  • 'segment_3': 3-node segment element

  • 'triangle_3': 3-node triangle element

  • 'triangle_6': 6-node triangle element

  • 'quadrangle_4': 4-node quadrangle element

  • 'quadrangle_8': 8-node quadrangle element

• return_weights (bool, optional) – If True, the function will also return the weights associated with each Gauss point. Default is False.

Returns:

• gauss_points (numpy.ndarray) – Natural coordinates of the Gauss points. The shape of the returned array is \((N_{gp}, K)\), where \(N_{gp}\) is the number of Gauss points for the specified element type and \(K\) is the topological dimension of the element.

• weights (numpy.ndarray, optional) – If return_weights is True, the function also returns an array of weights with shape \((N_{gp},)\) associated with each Gauss point.

Return type:

ndarray | Tuple[ndarray, ndarray]

See also

pysdic.get_segment_2_gauss_points

Gauss points for 2-node segment elements.

pysdic.get_segment_3_gauss_points

Gauss points for 3-node segment elements.

pysdic.get_triangle_3_gauss_points

Gauss points for 3-node triangle elements.

pysdic.get_triangle_6_gauss_points

Gauss points for 6-node triangle elements.

pysdic.get_quadrangle_4_gauss_points

Gauss points for 4-node quadrangle elements.

pysdic.get_quadrangle_8_gauss_points

Gauss points for 8-node quadrangle elements.

Examples

Get the Gauss points for a 3-node triangle element:

import numpy
from pysdic import get_gauss_points

gauss_points_array = get_gauss_points("triangle_3")
print("Gauss points for triangle_3:")
print(gauss_points_array)

Gauss points for triangle_3:
[[0.33333333 0.33333333]]