"""Euler-Bernoulli beam solvers with exact closed-form solutions.

Six configurations covering common support and loading combinations:
- Simply supported + point load / UDL
- Cantilever + point load / UDL
- Fixed-fixed + point load / UDL

Assumptions (Euler-Bernoulli theory):
- Plane sections remain plane after deformation
- Small deflections (linear elasticity)
- Homogeneous, isotropic material
- Rectangular cross-section

Reference: Timoshenko, S.P. & Gere, J.M., "Mechanics of Materials"
"""

from typing import Any

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


class SimplySupported_PointLoad(AnalyticalSolver):
    """Simply supported beam with central point load P.

    delta_max = PL^3 / (48EI)  at midspan
    sigma_max = PL / (4S)      at midspan (max bending moment M = PL/4)
    """

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

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

    def solve(self, params: dict[str, Any]) -> SolutionResult:
        L = params["length"]
        b = params["width"]
        h = params["height"]
        E = params["elastic_modulus"]
        sigma_y = params["yield_strength"]
        P = params["point_load"]

        I = b * h**3 / 12.0  # noqa: E741
        S = b * h**2 / 6.0

        max_deflection = P * L**3 / (48.0 * E * I)
        max_stress = P * L / (4.0 * S)

        return SolutionResult.from_stress(max_stress, max_deflection, sigma_y)


class SimplySupported_UDL(AnalyticalSolver):
    """Simply supported beam with uniform distributed load w.

    delta_max = 5wL^4 / (384EI)  at midspan
    sigma_max = wL^2 / (8S)      at midspan (max bending moment M = wL^2/8)
    """

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

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

    def solve(self, params: dict[str, Any]) -> SolutionResult:
        L = params["length"]
        b = params["width"]
        h = params["height"]
        E = params["elastic_modulus"]
        sigma_y = params["yield_strength"]
        w = params["distributed_load"]

        I = b * h**3 / 12.0  # noqa: E741
        S = b * h**2 / 6.0

        max_deflection = 5.0 * w * L**4 / (384.0 * E * I)
        max_stress = w * L**2 / (8.0 * S)

        return SolutionResult.from_stress(max_stress, max_deflection, sigma_y)


class Cantilever_PointLoad(AnalyticalSolver):
    """Cantilever beam with tip point load P.

    delta_max = PL^3 / (3EI)   at free end
    sigma_max = PL / S         at fixed end (max bending moment M = PL)
    """

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

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

    def solve(self, params: dict[str, Any]) -> SolutionResult:
        L = params["length"]
        b = params["width"]
        h = params["height"]
        E = params["elastic_modulus"]
        sigma_y = params["yield_strength"]
        P = params["point_load"]

        I = b * h**3 / 12.0  # noqa: E741
        S = b * h**2 / 6.0

        max_deflection = P * L**3 / (3.0 * E * I)
        max_stress = P * L / S

        return SolutionResult.from_stress(max_stress, max_deflection, sigma_y)


class Cantilever_UDL(AnalyticalSolver):
    """Cantilever beam with uniform distributed load w.

    delta_max = wL^4 / (8EI)   at free end
    sigma_max = wL^2 / (2S)    at fixed end (max bending moment M = wL^2/2)
    """

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

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

    def solve(self, params: dict[str, Any]) -> SolutionResult:
        L = params["length"]
        b = params["width"]
        h = params["height"]
        E = params["elastic_modulus"]
        sigma_y = params["yield_strength"]
        w = params["distributed_load"]

        I = b * h**3 / 12.0  # noqa: E741
        S = b * h**2 / 6.0

        max_deflection = w * L**4 / (8.0 * E * I)
        max_stress = w * L**2 / (2.0 * S)

        return SolutionResult.from_stress(max_stress, max_deflection, sigma_y)


class FixedFixed_PointLoad(AnalyticalSolver):
    """Fixed-fixed beam with central point load P.

    delta_max = PL^3 / (192EI)  at midspan
    sigma_max = PL / (8S)       at fixed ends (max bending moment M = PL/8)
    """

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

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

    def solve(self, params: dict[str, Any]) -> SolutionResult:
        L = params["length"]
        b = params["width"]
        h = params["height"]
        E = params["elastic_modulus"]
        sigma_y = params["yield_strength"]
        P = params["point_load"]

        I = b * h**3 / 12.0  # noqa: E741
        S = b * h**2 / 6.0

        max_deflection = P * L**3 / (192.0 * E * I)
        max_stress = P * L / (8.0 * S)

        return SolutionResult.from_stress(max_stress, max_deflection, sigma_y)


class FixedFixed_UDL(AnalyticalSolver):
    """Fixed-fixed beam with uniform distributed load w.

    delta_max = wL^4 / (384EI)  at midspan
    sigma_max = wL^2 / (12S)    at fixed ends (max bending moment M = wL^2/12)
    """

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

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

    def solve(self, params: dict[str, Any]) -> SolutionResult:
        L = params["length"]
        b = params["width"]
        h = params["height"]
        E = params["elastic_modulus"]
        sigma_y = params["yield_strength"]
        w = params["distributed_load"]

        I = b * h**3 / 12.0  # noqa: E741
        S = b * h**2 / 6.0

        max_deflection = w * L**4 / (384.0 * E * I)
        max_stress = w * L**2 / (12.0 * S)

        return SolutionResult.from_stress(max_stress, max_deflection, sigma_y)


# Registry of all beam solvers
BEAM_SOLVERS: dict[str, type[AnalyticalSolver]] = {
    "beam_ss_point": SimplySupported_PointLoad,
    "beam_ss_udl": SimplySupported_UDL,
    "beam_cantilever_point": Cantilever_PointLoad,
    "beam_cantilever_udl": Cantilever_UDL,
    "beam_fixed_point": FixedFixed_PointLoad,
    "beam_fixed_udl": FixedFixed_UDL,
}