pysdic.get_triangle_3_gauss_points#

get_triangle_3_gauss_points(return_weights=False)[source]#

Get the natural coordinates \((\xi, \eta)\) and weights of Gauss quadrature points for a 3-node triangle element.

Parameters:

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 returned array has shape (1, 2).

  • weights (numpy.ndarray, optional) – If return_weights is True, the function also returns an array of weights with shape (1,) associated with each Gauss point.

Return type:

ndarray | Tuple[ndarray, ndarray]

Notes

A 3-node triangle element uses the following Gauss points and weights for numerical integration:

Point No.

\((\xi, \eta)\)

Weight \(w\)

1

\((\frac{1}{3}, \frac{1}{3})\)

\(\frac{1}{2}\)
Gauss quadrature points for 3-node triangle element

See also

pysdic.compute_triangle_3_shape_functions

Shape functions for 3-node triangle 2D-elements.

Examples

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

1import numpy
2from pysdic import get_triangle_3_gauss_points
3
4gauss_points = get_triangle_3_gauss_points()
5print("Gauss points:")
6print(gauss_points)

Gauss points:
[[0.33333333 0.33333333]]