unbanlanced_tension/exp.py

import sympy
import math

# h 悬点高差
# l_i 悬点档距
# alpha 导线膨胀系数  1/°C
# elastic 弹性系数 N/mm2
# t_e 架线时考虑初伸长的降温，取正值。单位°C
# lambda_i 计算不平衡张力时导线比载 N/(m.mm)
# sigma_i 计算不平衡张力时最低点水平应力 单位N/mm2
# t_i 计算不平衡张力时导线温度 单位°C
# lambda_m 导线架线时时导线比载 N/(m.mm)
# sigma_m 导线架线时时最低点水平应力 单位N/mm2
# t_m 导线架线时时导线温度 单位°C


def delta_li():
    (
        delta_l_i,
        l_i,
        lambda_i,
        alpha,
        E,
        t_e,
        t_i,
        lambda_m,
        t_m,
        sigma_m,
        sigma_i,
        beta_i,
    ) = sympy.symbols(
        """ 
        delta_l_i,
        l_i,
        lambda_i,
        alpha,
        E,
        t_e,
        t_i,
        lambda_m,
        t_m,
        sigma_m,
        sigma_i,
        beta_i,"""
    )
    _delta_li = delta_l_i - (
        l_i
        / ((sympy.cos(beta_i) ** 2) * (1 + (lambda_i * l_i / sigma_i) ** 2 / 8))
        * (
            (l_i * sympy.cos(beta_i)) ** 2
            / 24
            * ((lambda_m / sigma_m) ** 2 - (lambda_i / sigma_i) ** 2)
            + ((sigma_i - sigma_m) / E / sympy.cos(beta_i))
            + alpha * (t_i + t_e - t_m)
        )
    )
    return _delta_li


# area 导线截面 单位mm2
# sigma_i 第i档内水平应力 单位N/mm2
# b_i 悬垂串沿线路方向水平偏移距离，沿大号方向为正，反之为负。 单位m
# stringlen_i 第i基直线塔串长 单位m
# G_i 第i基直线塔串重 单位N
# h_i 悬垂串处千中垂位置时，,第 i 基对第 i-1 杆塔上导线悬挂点间的高差大号比小号杆塔悬挂点高者h本身为正值，反之为负值。
# lambda_i 第i档导线比载 N/(m.mm)
# h_i1 悬垂串处千中垂位置时，第 i+1 基对第 i 杆塔上导线悬挂点间的高差大号比小号杆塔悬挂点高者h本身为正值，反之为负值。
# lambda_i1
def fun_sigma_i1(delta_Li):
    (
        G_i,
        A,
        lambda_i,
        lambda_i1,
        sigma_i,
        h_i,
        h_i1,
        l_i,
        l_i1,
        stringlen_i,
        sigma_i1,
        beta_i,
        beta_i1,
    ) = sympy.symbols(
        """
        G_i,
        A,
        lambda_i,
        lambda_i1,
        sigma_i,
        h_i,
        h_i1,
        l_i,
        l_i1,
        stringlen_i,
        sigma_i1,
        beta_i,
        beta_i1
        """
    )

    def b_i():
        _t = sympy.Float(0)
        for f in delta_Li:
            _t += f
        return _t

    _sigma_i1 = sigma_i1 - (
        (
            G_i / 2 / A  # G_i传入时已考虑导线分裂数
            + lambda_i * l_i / 2 / sympy.cos(beta_i)
            + lambda_i1 * l_i1 / 2 / sympy.cos(beta_i1)
            + sigma_i * h_i / l_i
        )
        + sigma_i / b_i() * sympy.sqrt(stringlen_i ** 2 - b_i() ** 2)
    ) / (sympy.sqrt(stringlen_i ** 2 - b_i() ** 2) / b_i() + h_i1 / l_i1)
    return _sigma_i1


def manual_diff_delta_li_sigma_i(
    h_i, l_i, lambda_m, lambda_i, sigma_i, sigma_m, alpha, t_i, t_e, t_m, E
):
    beta_i = math.atan(h_i / l_i)
    A = (
        (l_i * math.cos(beta_i)) ** 2
        / 24
        * ((lambda_m / sigma_m) ** 2 - (lambda_i / sigma_i) ** 2)
        + (sigma_i - sigma_m) / E / math.cos(beta_i)
        + alpha * (t_i + t_e - t_m)
    )
    B = 1 + (lambda_i * l_i / sigma_i) ** 2 / 8
    dA_dsigma_i = ((l_i * math.cos(beta_i)) ** 2) / 24 * 2 * lambda_i ** 2 * (
        sigma_i ** (-3)
    ) + 1 / E / math.cos(beta_i)
    dB_dsigma_i = -2 * (lambda_i * l_i) ** 2 / 8 * (sigma_i ** (-3))
    _t = -l_i / (math.cos(beta_i) ** 2) * (dA_dsigma_i * B - A * dB_dsigma_i) / (B ** 2)
    return _t


def manual_diff_sigma_i1_d_l_i(
    h_i, l_i, h_i1, l_i1, Gi, A, lambda_i, lambda_i1, sigma_i, stringlen, b_i
):
    beta_i = math.atan(h_i / l_i)
    beta_i1 = math.atan(h_i1 / l_i1)
    A = (
        Gi / 2 / A
        + lambda_i * l_i / 2 / math.cos(beta_i)
        + lambda_i1 * l_i1 / 2 / math.cos(beta_i1)
        + sigma_i * h_i / l_i
        + sigma_i / b_i * ((stringlen ** 2 - b_i ** 2) ** 0.5)
    )
    B = ((stringlen ** 2 - b_i ** 2) ** 0.5) / b_i + h_i1 / l_i1
    dA_d_delta_L1 = (
        sigma_i
        * (
            -((stringlen ** 2 - b_i ** 2) ** -0.5) * (b_i ** 2)
            - (stringlen ** 2 - b_i ** 2) ** 0.5
        )
        / (b_i ** 2)
    )
    dB_d_delta_L1 = (
        1
        / (b_i ** 2)
        * (
            -((stringlen ** 2 - b_i ** 2) ** -0.5) * (b_i ** 2)
            - (stringlen ** 2 - b_i ** 2) ** 0.5
        )
    )
    _t = -(dA_d_delta_L1 * B - A * dB_d_delta_L1) / (B ** 2)
    return _t


def get_lambdify_d_delta_l_i_sigma_i(_d_delta_l_i_sigma_i):
    (
        delta_l_i,
        l_i,
        lambda_i,
        alpha,
        E,
        t_e,
        t_i,
        lambda_m,
        t_m,
        sigma_m,
        _sigma_i,
        beta_i,
    ) = sympy.symbols(
        """ 
        delta_l_i,
        l_i,
        lambda_i,
        alpha,
        E,
        t_e,
        t_i,
        lambda_m,
        t_m,
        sigma_m,
        sigma_i,
        beta_i
        """
    )
    return sympy.lambdify(
        [
            delta_l_i,
            l_i,
            lambda_i,
            alpha,
            E,
            t_e,
            t_i,
            lambda_m,
            t_m,
            sigma_m,
            _sigma_i,
            beta_i,
        ],
        _d_delta_l_i_sigma_i,
    )


def get_lambdify_d_sigma_i1_d_l_i(_d_sigma_i1_d_l_i, delta_Li):
    (
        G_i,
        A,
        lambda_i,
        lambda_i1,
        _sigma_i,
        h_i,
        h_i1,
        l_i,
        l_i1,
        stringlen_i,
        _sigma_i1,
        beta_i,
        beta_i1,
    ) = sympy.symbols(
        """
        G_i,
        A,
        lambda_i,
        lambda_i1,
        sigma_i,
        h_i,
        h_i1,
        l_i,
        l_i1,
        stringlen_i,
        sigma_i1,
        beta_i,
        beta_i1,
        """
    )

    return sympy.lambdify(
        [
            G_i,
            A,
            lambda_i,
            lambda_i1,
            _sigma_i,
            h_i,
            h_i1,
            l_i,
            l_i1,
            stringlen_i,
            _sigma_i1,
            beta_i,
            beta_i1,
            *delta_Li,
        ],
        _d_sigma_i1_d_l_i,
    )