pysdic.get_segment_3_gauss_points#

get_segment_3_gauss_points(return_weights=False)[source]#

Get the natural coordinates \(\xi\) and weights of Gauss quadrature points for a 3-node segment 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 (2, 1).
weights (numpy.ndarray, optional) – If return_weights is True, the function also returns an array of weights with shape (2,) associated with each Gauss point.

Return type:

ndarray | Tuple[ndarray, ndarray]

Notes

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

Point No.	\((\xi)\)	Weight \(w\)
1	\(-\frac{1}{\sqrt{3}}\)	\(1\)
2	\(\frac{1}{\sqrt{3}}\)	\(1\)

See also

pysdic.compute_segment_3_shape_functions: Shape functions for 3-node segment 1D-elements.

Examples

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

import numpy
from pysdic import get_segment_3_gauss_points

gauss_points = get_segment_3_gauss_points()
print("Gauss points:")
print(gauss_points)

Gauss points:
[[-0.57735027]
 [ 0.57735027]]