pyserep.models

pyserep.models — built-in synthetic FE model generators for testing.

pyserep.models.euler_beam(n_elements: int = 50, length: float = 1.0, EI: float = 10000.0, rho_A: float = 1.0, fixed_left: bool = True, fixed_right: bool = False) → Tuple[csc_matrix, csc_matrix][source]

1D Euler-Bernoulli beam (consistent mass matrix).

DOFs per node: transverse displacement w and rotation θ. Total DOFs: 2 × (n_elements + 1). Fixed BCs applied by row/column zeroing with large diagonal penalty.

Parameters:

  • n_elements (int)

  • length (float) – Total beam length (m).

  • EI (float) – Bending stiffness (N·m²).

  • rho_A (float) – Mass per unit length (kg/m).

  • fixed_left (bool) – Clamped boundary conditions at the respective ends.

  • fixed_right (bool) – Clamped boundary conditions at the respective ends.

Returns:

K, M

Return type:

scipy.sparse.csc_matrix, shape (2*(n_elements+1), …)

pyserep.models.model_info(K: spmatrix, M: spmatrix, label: str = '') → str[source]

Return a one-line description of a (K, M) pair.

pyserep.models.plate_2d(nx: int = 10, ny: int = 10, lx: float = 1.0, ly: float = 1.0, D: float = 1000.0, rho_h: float = 1.0) → Tuple[csc_matrix, csc_matrix][source]

2D rectangular Kirchhoff plate using finite differences.

Simply supported on all four edges. DOFs: transverse displacement w at interior grid points only. Total DOFs: (nx-1) × (ny-1).

Parameters:

  • nx (int) – Number of intervals in x and y (interior nodes = nx-1, ny-1).

  • ny (int) – Number of intervals in x and y (interior nodes = nx-1, ny-1).

  • lx (float) – Plate dimensions (m).

  • ly (float) – Plate dimensions (m).

  • D (float) – Flexural rigidity D = E h³ / (12(1-ν²)) (N·m).

  • rho_h (float) – Mass per unit area ρ·h (kg/m²).

Returns:

K, M

Return type:

scipy.sparse.csc_matrix

Notes

Uses the 13-point biharmonic finite difference stencil for ∇⁴w.

pyserep.models.random_symmetric_pd(n: int = 50, kappa_K: float = 10000.0, seed: int = 42) → Tuple[csc_matrix, csc_matrix][source]

Random symmetric positive-definite (K, M) pair.

Useful for unit testing and algorithm benchmarks where the structural interpretation is irrelevant.

Parameters:

  • n (int) – Matrix size.

  • kappa_K (float) – Target condition number for K.

  • seed (int) – Random seed.

Returns:

K, M

Return type:

scipy.sparse.csc_matrix (dense matrices wrapped in sparse)

pyserep.models.spring_chain(n: int = 300, k: float = 100000.0, m: float = 1.0, fixed_left: bool = True, fixed_right: bool = False) → Tuple[csc_matrix, csc_matrix][source]

1D spring-mass chain.

Physical model: o–k–o–k–o … –k–o

m m m m

Parameters:

  • n (int) – Number of mass nodes (= DOFs).

  • k (float) – Spring stiffness (N/m).

  • m (float) – Mass of each node (kg).

  • fixed_left (bool) – If True, node 0 is fixed (Kₐ[0,0] = k, not 2k).

  • fixed_right (bool) – If True, node n-1 is also fixed.

Returns:

K, M

Return type:

scipy.sparse.csc_matrix

Examples

>>> K, M = spring_chain(n=500, k=2e5)
>>> K.shape
(500, 500)