pysdic.get_quadrangle_4_gauss_points

get_quadrangle_4_gauss_points(return_weights=False)

Get the natural coordinates \((\xi, \eta)\) and weights of Gauss quadrature points for a 4-node quadrangle 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 (4, 2).

• weights (numpy.ndarray, optional) – If return_weights is True, the function also returns an array of weights with shape (4,) associated with each Gauss point.

Return type:

ndarray | Tuple[ndarray, ndarray]

Notes

A 4-node quadrangle element uses the following Gauss points and weights for numerical integration:

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

See also

pysdic.compute_quadrangle_4_shape_functions

Shape functions for 4-node quadrangle 2D-elements.

Examples

Get the Gauss points for a 4-node quadrangle element:

import numpy
from pysdic import get_quadrangle_4_gauss_points

gauss_points = get_quadrangle_4_gauss_points()
print("Gauss points:")
print(gauss_points)

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