shape_function#

sectionproperties.analysis.fea.shape_function(coords: ndarray, gauss_point: tuple[float, float, float, float]) → tuple[ndarray, ndarray, float, float, float][source]#

Calculates shape functions, derivates and the Jacobian determinant.

Computes the shape functions, shape function derivatives and the determinant of the Jacobian matrix for a Tri6 element at a given Gauss point.

Parameters:

  • coords (ndarray) – Global coordinates of the quadratic triangle vertices, of size [2 x 6]

  • gauss_point (tuple[float, float, float, 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 6]), the derivative of the shape functions in the j-th global direction B(i,j) ([2 x 6]), the determinant of the Jacobian matrix j, the global cooridnates of the Gauss point (x, y)

Return type:

tuple[ndarray, ndarray, float, float, float]