pysdic.get_triangle_6_gauss_points#

get_triangle_6_gauss_points(return_weights=False)[source]#

Get the natural coordinates \((\xi, \eta)\) and weights of Gauss quadrature points for a 6-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 (3, 2).

  • weights (numpy.ndarray, optional) – If return_weights is True, the function also returns an array of weights with shape (3,) associated with each Gauss point.

Return type:

ndarray | Tuple[ndarray, ndarray]

Notes

A 6-node triangle element uses the following Gauss points and weights for numerical integration:

Point No.

\((\xi, \eta)\)

Weight \(w\)

1

\((\frac{1}{6}, \frac{1}{6})\)

\(\frac{1}{6}\)

2

\((\frac{2}{3}, \frac{1}{6})\)

\(\frac{1}{6}\)

3

\((\frac{1}{6}, \frac{2}{3})\)

\(\frac{1}{6}\)
Gauss quadrature points for 6-node triangle element

See also

pysdic.compute_triangle_6_shape_functions

Shape functions for 6-node triangle 2D-elements.

Examples

Get the Gauss points for a 6-node triangle element:

1import numpy
2from pysdic import get_triangle_6_gauss_points
3
4gauss_points = get_triangle_6_gauss_points()
5print("Gauss points:")
6print(gauss_points)

Gauss points:
[[0.16666667 0.16666667]
 [0.66666667 0.16666667]
 [0.16666667 0.66666667]]