silex_lib_tet4_python

TET4 finite-element routines implemented in pure Python.

SILEXlight.silex_lib_tet4_python.det33_ligne_de_un(a)[source]

Compute the determinant of a 3x3 matrix with first row fixed to ones.

Parameters:

a (numpy.ndarray) – Array of shape (2, 3) corresponding to rows 2 and 3 of the matrix where row 1 is assumed to be [1, 1, 1].

Returns:

Determinant value.

Return type:

float

SILEXlight.silex_lib_tet4_python.det44_ligne_de_un(a)[source]

Compute the determinant of a 4x4 matrix with first row fixed to ones.

Parameters:

a (numpy.ndarray) – Array of shape (3, 4) corresponding to rows 2 to 4 of the matrix where row 1 is assumed to be [1, 1, 1, 1].

Returns:

Determinant value.

Return type:

float

SILEXlight.silex_lib_tet4_python.stiffnessmatrix(nodes, elements, material)[source]

Assemble TET4 stiffness coefficients in sparse triplet format.

Parameters:

  • nodes (numpy.ndarray) – Nodal coordinates with shape (n_nodes, 3).

  • elements (numpy.ndarray) – Element connectivity with shape (n_elem, 4) using 1-based node ids.

  • material (array-like) – Elastic material properties [Young, nu].

Returns:

(Ik, Jk, Vk) where each array has size 12*12*n_elem. Ik and Jk are dof indices and Vk contains stiffness values.

Return type:

tuple[numpy.ndarray, numpy.ndarray, numpy.ndarray]

Notes

The output is designed for sparse assembly, for example with scipy.sparse.coo_matrix((Vk, (Ik, Jk))).

SILEXlight.silex_lib_tet4_python.massmatrix(nodes, elements, rho)[source]

Assemble TET4 consistent mass coefficients in sparse triplet format.

Parameters:

  • nodes (numpy.ndarray) – Nodal coordinates with shape (n_nodes, 3).

  • elements (numpy.ndarray) – Element connectivity with shape (n_elem, 4) using 1-based node ids.

  • rho (float) – Material density.

Returns:

(Ik, Jk, Vk) where each array has size 12*12*n_elem.

Return type:

tuple[numpy.ndarray, numpy.ndarray, numpy.ndarray]

SILEXlight.silex_lib_tet4_python.forceonsurface(nodes, elements, press, direction)[source]

Assemble equivalent nodal forces on triangular surface elements.

Parameters:

  • nodes (numpy.ndarray) – Nodal coordinates with shape (n_nodes, 3).

  • elements (numpy.ndarray) – Surface triangular connectivity with shape (n_face, 3) using 1-based node ids.

  • press (float) – Pressure/traction magnitude.

  • direction (array-like) – Load direction vector. If its norm is near zero, local outward normal is used per face.

Returns:

Global force vector of size 3*n_nodes.

Return type:

numpy.ndarray

SILEXlight.silex_lib_tet4_python.compute_stress_strain_error(nodes, elements, material, QQ)[source]

Compute TET4 stress, strain and error estimators from displacements.

Parameters:

  • nodes (numpy.ndarray) – Nodal coordinates with shape (n_nodes, 3).

  • elements (numpy.ndarray) – Element connectivity with shape (n_elem, 4) using 1-based node ids.

  • material (array-like) – Elastic material properties [Young, nu].

  • QQ (numpy.ndarray) – Global displacement vector of size 3*n_nodes.

Returns:

(sigma, sig_smooth, EpsilonElem, EpsilonNodes, ErrElem, ErrGlob).

Return type:

tuple

Notes

sigma and sig_smooth store 7 components per row: [sxx, syy, szz, syz, sxz, sxy, von_mises].