Coupling functions
Function to compute the coupling matrix. Most of the code is a port (with some modifications) of the Matlab code from VKGong
Integrals for building the mass and stifness matrices
assemble_K_and_M
assemble_K_and_M (Npsi, Lx, Ly)
build_I4
build_I4 (N, L)
Returns the N x N matrix whose (m,p) entry = int4(m,p,L).
build_I2
build_I2 (N, L)
Returns the N x N matrix whose (m,p) entry = int2(m,p,L).
build_I1
build_I1 (N, L)
Returns the N x N matrix whose (m,p) entry = int1(m,p,L).
int2_mat
int2_mat (N, L)
Builds the N x N matrix whose (m,p) entry is int2(m,p,L). Mirrors the logic of the original Matlab int2_mat function exactly, but we can do it more simply by calling int2 in a loop.
int2
int2 (m, p, L)
Function int2(m,p,L). Piecewise definition from the Matlab code.
int1
int1 (m, p, L)
| Type | Details | |
|---|---|---|
| m | int | First mode number |
| p | int | Second mode number |
| L | float | Length of the domain |
| Returns | float | Value of the integral |
int4
int4 (m:int, p:int, L:float)
Compute the integral of Xd(m,x)Xd(p,x) from 0 to L, where X is the clamped-plate function and d denotes derivative in x.
The integral is computed for different cases based on the mode numbers m and p.*
| Type | Details | |
|---|---|---|
| m | int | First mode number |
| p | int | Second mode number |
| L | float | Length of the domain |
| Returns | float | Value of the integral |
airy_stress_coefficients
airy_stress_coefficients (n_psi, vals, vecs)
Compute the Airy stress function coefficients from the eigenvalues and eigenvectors
Basis used to build the mass and stiffness matrices
basis
basis (m:int, n:int, x:float|numpy.ndarray, y:float|numpy.ndarray, Lx:float, Ly:float)
*Evaluate the full 2D basis function for indices (m, n) at point (x, y).
The basis function is defined as:
.. math:: _{mn}(x,y) = X_m(x)Y_n(y)
where X_m and Y_n are the 1D basis functions in x and y directions.*
| Type | Details | |
|---|---|---|
| m | int | Mode number in x direction |
| n | int | Mode number in y direction |
| x | float | numpy.ndarray | x coordinate(s) where to evaluate |
| y | float | numpy.ndarray | y coordinate(s) where to evaluate |
| Lx | float | Length in x direction |
| Ly | float | Length in y direction |
| Returns | float | numpy.ndarray | Value of the basis function at (x,y) |
Partial integrals to calculate the coupling matrix
i13_mat
i13_mat (Npsi, Nphi, L)
i12_mat
i12_mat (Npsi, Nphi, L)
i11_mat
i11_mat (Npsi, Nphi, L)
i10_mat
i10_mat (Npsi, Nphi, L)
i9_mat
i9_mat (Npsi, Nphi, L)
i5_mat
i5_mat (Npsi, Nphi, L)
i4_mat
i4_mat (Npsi, Nphi, L)
Auxiliary integral for the computation of the coupling coefficient H.
i3_mat
i3_mat (Npsi, Nphi, L)
Auxiliary integral for the computation of the coupling coefficient H.
i2_mat
i2_mat (Npsi, Nphi, L)
i1_mat
i1_mat (Npsi, Nphi, L)
functions to put together the coupling matrix
g6
g6 (Npsi, Nphi, S, ky, cache)
g5
g5 (Npsi, Nphi, S, kx, cache)
g4
g4 (Npsi, Nphi, S, ky, cache)
g3
g3 (Npsi, Nphi, S, ky, cache)
g2
g2 (Npsi, Nphi, S, kx, cache)
g1
g1 (Npsi, Nphi, S, kx, cache)
build_s_matrix
build_s_matrix (Npsi, Nphi, partials, idx_array, factor_mode)
Summation of partial integrals in a 3D array with a factor.
| Type | Details | |
|---|---|---|
| Npsi | ||
| Nphi | ||
| partials | ||
| idx_array | ||
| factor_mode | ||
| Returns | np.ndarray of shape (Npsi, Nphi, Nphi) | The 3D tensor after summation and factor application. |
compute_partial_integrals
compute_partial_integrals (Npsi, Nphi, Lx, Ly)
Precompute and store all partial-integral matrices needed. Returns them in a dictionary or a custom object.
H_tensor_rectangular
H_tensor_rectangular (coeff0, coeff1, coeff2, Nphi, Npsi, Lx, Ly, kx, ky)
Compute the H tensor for rectangular plates.
compute_coupling_matrix
compute_coupling_matrix (n_psi, n_phi, lx, ly, kx_indices, ky_indices)