initial

gripyth.solving.assembly.initial

Initial values of the system's stiffness matrix.

FUNCTION	DESCRIPTION
initial	Compute initial values.

initial

initial(
    mesh: Mesh,
    dofs: Dofs,
    t: float,
    materials: list[Material],
    quadrature: Quadrature,
    p_field: NDArray[float64],
    elasticity_tensor: Callable[
        [float, float], NDArray[float64]
    ],
) -> tuple[
    NDArray[float64],
    NDArray[int32],
    NDArray[int32],
    NDArray[float64],
    NDArray[int32],
    NDArray[int32],
    NDArray[float64],
    NDArray[int32],
    NDArray[int32],
    NDArray[float64],
    NDArray[int32],
    NDArray[int32],
]

Compute initial values.

Initial calculation of the non-zero entries of the tangent stiffness matrix K, the L2 interpolation matrix M (smoothing matrix), and the strains'/stresses' right-hand-side vectors required for L2 interpolation.

Input:

• mesh: mesh-related parameters
• dofs: parameters regarding the degrees of freedom
• t: out-of-plane specimen thickness
• materials: list of materials used in the mesh
• quadrature: quadrature parameters
• elasticity_tensor: function creating an elasticity tensor for given values of E and ν in Voigt notation
• p_field: damage field at the nodes

Output:

• K_vector: non-zero entries of the tangent stiffness matrix K
• i_row: row indices of of non-zero entries in K
• j_col: column indices of the non-zero entries in K
• M_vector: non-zero entries of the L2 interpolation matrix M
• i_row_sig: row indices of the non-zero entries in M
• j_col_sig: column indices of the non-zero entries in M
• eps_vector: non-zeros entries of the strains calculated at the Gauss points, used with M to interpolate the strains to the nodes
• i_row_eps: row indices of the non-zero entries of eps_vector
• j_col_eps column indices of the non-zero entries of eps_vector
• sig0_vector: non-zeros entries of the stresses calculated at the Gauss points, used with M to interpolate the stresses to the nodes
• i_row_pf: row indices of the non-zero entries of sig0_vector
• j_col_pf: column indices of the non-zero entries of sig0_vector