Finite Element

finite_element.assemble_stiffness_matrix(element_dof_ids: ndarray[Any, dtype[uint64]], element_densities: ndarray[Any, dtype[float]], element_stiffness_matrix: ndarray[Any, dtype[float]]) → csc_matrix

Assemble the stiffness matrix from the element stiffness matrices and densities

Parameters:

• element_dof_ids – NDArray[np.uint] - The global DOF indices for each element (8 x num_elements) Numbering is clockwise from the bottom left corner

• element_densities – NDArray[float] - The density of each element

• element_stiffness_matrix – NDArray[float] - The stiffness matrix for a single element

finite_element.element_stiffness_matrix(youngs_modulus: float, poissons_ratio: float, element_size: tuple[float, float], element_thickness: float) → ndarray[Any, dtype[_ScalarType_co]]

Create the stiffness matrix for a single element

Parameters:

• youngs_modulus – float - Young’s modulus

• poissons_ratio – float - Poisson’s ratio

• element_size – tuple[float, float] - The size of the element

• element_thickness – float - The thickness of the element

Returns:

NDArray - The stiffness matrix for a single element