shape_function#

concreteproperties.utils.shape_function(coords: ndarray, gauss_point: list[float]) → tuple[ndarray, float][source]#

Returns the shape functions and Jacobian determinant.

Computes shape functions and the determinant of the Jacobian matrix for a linear triangular element at a given Gauss point.

Parameters:

  • coords (ndarray) – Global coordinates of the linear triangle vertices [2 x 3]

  • gauss_point (list[float]) – Gaussian weight and isoparametric location of the Gauss point

Returns:

The value of the shape functions N(i) at the given Gauss point [1 x 3] and the determinant of the Jacobian matrix j

Return type:

tuple[ndarray, float]