src/data/solvers/plate.py

"""Kirchhoff-Love rectangular plate solvers with Navier series solutions.

Two configurations:
- Simply supported on all edges + uniform pressure
- Clamped on all edges + uniform pressure

The simply supported case uses the exact Navier double Fourier series.
The clamped case uses tabulated coefficients from Timoshenko & Woinowsky-Krieger.

Assumptions (Kirchhoff-Love theory):
- Thin plate (t << a, b)
- Small deflections (w << t)
- Linear elasticity
- Homogeneous, isotropic material

Reference: Timoshenko, S.P. & Woinowsky-Krieger, S.,
           "Theory of Plates and Shells", 2nd Ed.
"""

import math
from typing import Any

import numpy as np

from src.data.schema import SolutionResult
from src.data.solvers.base import AnalyticalSolver


class SimplySupported_UniformPressure(AnalyticalSolver):
    """Simply supported rectangular plate under uniform pressure q.

    Uses Navier's double Fourier series solution (exact):
        w(x,y) = sum_m sum_n [a_mn * sin(m*pi*x/a) * sin(n*pi*y/b)]

    where a_mn = 16*q / (pi^6 * D * m*n * (m^2/a^2 + n^2/b^2)^2)
    for odd m, n only.

    Max deflection at center (a/2, b/2):
        w_max = sum of a_mn * sin(m*pi/2) * sin(n*pi/2)

    Max bending stress from max moment:
        M_x_max at center, sigma = 6*M_x / t^2
    """

    N_TERMS = 50  # Fourier series terms (converges well by ~20)

    @property
    def config_id(self) -> str:
        return "plate_ss_uniform"

    @property
    def problem_family(self) -> str:
        return "plate"

    def solve(self, params: dict[str, Any]) -> SolutionResult:
        a = params["length_a"]
        b = params["length_b"]
        t = params["thickness"]
        E = params["elastic_modulus"]
        nu = params["poisson_ratio"]
        sigma_y = params["yield_strength"]
        q = params["pressure"]

        D = E * t**3 / (12.0 * (1.0 - nu**2))

        w_max = 0.0
        Mx_max = 0.0
        My_max = 0.0

        for m in range(1, self.N_TERMS + 1, 2):  # odd m only
            for n in range(1, self.N_TERMS + 1, 2):  # odd n only
                denom = (m**2 / a**2 + n**2 / b**2) ** 2

                # Fourier coefficient
                a_mn = 16.0 * q / (math.pi**6 * D * m * n * denom)

                # Deflection at center: sin(m*pi/2) * sin(n*pi/2)
                sign_w = math.sin(m * math.pi / 2) * math.sin(n * math.pi / 2)
                w_max += a_mn * sign_w

                # Bending moments at center
                # M_x = -D * (d2w/dx2 + nu * d2w/dy2)
                factor_x = (m * math.pi / a) ** 2 + nu * (n * math.pi / b) ** 2
                factor_y = nu * (m * math.pi / a) ** 2 + (n * math.pi / b) ** 2

                Mx_max += a_mn * factor_x * sign_w
                My_max += a_mn * factor_y * sign_w

        # Convert moment to stress: sigma = 6*M / t^2 (plate bending formula)
        Mx_max *= D  # a_mn already divided by D, so Mx = D * sum(a_mn * factor * sign)
        My_max *= D

        sigma_x = 6.0 * abs(Mx_max) / t**2
        sigma_y_stress = 6.0 * abs(My_max) / t**2
        max_stress = max(sigma_x, sigma_y_stress)

        return SolutionResult.from_stress(max_stress, abs(w_max), sigma_y)


class Clamped_UniformPressure(AnalyticalSolver):
    """Clamped rectangular plate under uniform pressure q.

    No exact Fourier series exists for clamped edges. Uses interpolated
    coefficients from Timoshenko Table 35 (pp. 202):

        w_max = alpha * q * a^4 / D
        M_max = beta * q * a^2

    where alpha and beta depend on the aspect ratio b/a.
    For b/a >= 1 (a is the shorter side), standard tabulated values apply.

    Reference values (b/a -> alpha, beta_center, beta_edge):
        1.0 -> 0.00126, 0.0231, 0.0513
        1.2 -> 0.00172, 0.0299, 0.0639
        1.4 -> 0.00207, 0.0349, 0.0726
        1.6 -> 0.00230, 0.0381, 0.0780
        1.8 -> 0.00245, 0.0401, 0.0812
        2.0 -> 0.00254, 0.0412, 0.0829
        inf -> 0.00260, 0.0417, 0.0833
    """

    # Tabulated coefficients: (b/a, alpha, beta_edge)
    # beta_edge gives max stress at mid-edge (clamped), which exceeds center stress
    _TABLE = np.array([
        [1.0, 0.00126, 0.0513],
        [1.2, 0.00172, 0.0639],
        [1.4, 0.00207, 0.0726],
        [1.6, 0.00230, 0.0780],
        [1.8, 0.00245, 0.0812],
        [2.0, 0.00254, 0.0829],
        [3.0, 0.00260, 0.0833],  # approaches infinite strip
        [5.0, 0.00260, 0.0833],
    ])

    @property
    def config_id(self) -> str:
        return "plate_fixed_uniform"

    @property
    def problem_family(self) -> str:
        return "plate"

    def solve(self, params: dict[str, Any]) -> SolutionResult:
        a_dim = params["length_a"]
        b_dim = params["length_b"]
        t = params["thickness"]
        E = params["elastic_modulus"]
        nu = params["poisson_ratio"]
        sigma_y = params["yield_strength"]
        q = params["pressure"]

        # Ensure a <= b (a is the shorter side for table lookup)
        if a_dim > b_dim:
            a, b = b_dim, a_dim
        else:
            a, b = a_dim, b_dim

        D = E * t**3 / (12.0 * (1.0 - nu**2))
        ratio = b / a

        # Interpolate coefficients from table
        alpha = float(np.interp(ratio, self._TABLE[:, 0], self._TABLE[:, 1]))
        beta = float(np.interp(ratio, self._TABLE[:, 0], self._TABLE[:, 2]))

        max_deflection = alpha * q * a**4 / D
        # beta is the moment coefficient: M_max = beta * q * a^2
        # Bending stress: sigma = 6*M / t^2
        max_stress = 6.0 * beta * q * a**2 / t**2

        return SolutionResult.from_stress(max_stress, abs(max_deflection), sigma_y)


PLATE_SOLVERS: dict[str, type[AnalyticalSolver]] = {
    "plate_ss_uniform": SimplySupported_UniformPressure,
    "plate_fixed_uniform": Clamped_UniformPressure,
}