diff --git a/auto_differentiation.py b/auto_differentiation.py index 20ea613..16effb6 100644 --- a/auto_differentiation.py +++ b/auto_differentiation.py @@ -1,9 +1,12 @@ # 利用自动微分计算 +from typing import List + import sympy import data import exp import math import main +import numpy as np sympy.init_printing() # h_i 悬点高差 @@ -26,7 +29,6 @@ delta_Li = ( *delta_Li__1, sympy.symbols("delta_Li_i"), ) -# sigma_i = sympy.symbols("sigma_i:{span_count}".format(span_count=data.span_count)) loop_end = data.loop_end # 最大循环次数 @@ -44,19 +46,13 @@ sigma_m_data = data.sigma_m # 架线时，初伸长未释放前的最低点水 span_count = data.span_count # 几个档距 # n个档距,n-1个直线塔 h_array = data.h_array -hi_matrix = sympy.Matrix(h_array) # sympy.pprint(hi_matrix) l_array = data.l_array -l_matrix = sympy.Matrix(l_array) t_data = data.t conductor_n = data.conductor_n # ti_matrix = sympy.Matrix(t_array) lambda_i_array = data.lambda_i_array # TODO: 暂时没考虑荷载变化 -lambda_m_matrix = sympy.Matrix(lambda_i_array) -lambda_i_matrix = sympy.Matrix(lambda_i_array) - - symbol_delta_l_i = exp.delta_li() sigma_i = sympy.symbols("sigma_i") d_delta_l_i_sigma_i = sympy.diff(symbol_delta_l_i, sigma_i) @@ -113,11 +109,7 @@ def get_lambdify_d_delta_l_i_sigma_i(_d_delta_l_i_sigma_i): fx_d_delta_l_i_sigma_i = get_lambdify_d_delta_l_i_sigma_i(d_delta_l_i_sigma_i) - symbol_sigma_i1 = exp.fun_sigma_i1(delta_Li) -# d_sigma_i1_sigma_i = sympy.diff(symbol_sigma_i1, sigma_i) -# sigma_i1 = sympy.symbols("sigma_i1") -# d_sigma_i1_sigma_i1 = sympy.diff(symbol_sigma_i1, sigma_i) delta_Li_i = sympy.symbols("delta_Li_i") d_sigma_i1_d_l_i = sympy.diff(symbol_sigma_i1, delta_Li_i) @@ -315,7 +307,7 @@ def evaluate_d_sigma_i1_d_delta_sigma_i(val_delta_li): def solve(): # 初始化 - val_delta_li = [1 for _ in range(span_count)] + val_delta_li = [0.1 for _ in range(span_count)] # val_delta_li = [0.15931589580330385, -0.19294219226439696, 0.035236744603670586, -0.03124795962518869, 0.034422847061933395, 0.1639551737321582, -0.18876605469917845, 0.03862307099222713, -0.01858088432390902] # val_sigma_i = [175.44277576372207, 176.07105062365383, 175.94897602628689, 175.95574563415994, 175.83116207025824, 175.84778616876434, 176.5132398968081, 176.4405408454816, 176.51871673188586] @@ -346,7 +338,6 @@ def solve(): A = sympy.Matrix([[M_A, M_B], [M_C, M_D], [M_E]]) fx_delta_Li = [] fx_sigma_i1 = [] - b_i = 0 for i in range(span_count): fx_delta_Li.append( val_delta_li[i] @@ -381,35 +372,24 @@ def solve(): lambda_i_array[i + 1], ) ) - - # lambda_i1 = lambda_i_array[i + 1] - # h_i1 = h_array[i + 1] - # l_i1 = l_array[i + 1] - # h_i = h_array[i] - # l_i = l_array[i] - # beta_i = math.atan(h_i / l_i) - # beta_i1 = math.atan(h_i1 / l_i1) - # w_i = ( - # lambda_i_array[i] * l_array[i] / 2 / math.cos(beta_i) - # + val_sigma_i[i] * h_i / l_i - # + (lambda_i1 * l_i1 / 2 / math.cos(beta_i1) - val_sigma_i[i+1] * h_i1 / l_i1) - # ) - # b_i += val_delta_li[i] - # # 新版大手册p329 (5-61) 最上方公式 - # right_equ = val_sigma_i[i] + b_i / math.sqrt(string_length ** 2 - b_i ** 2) * ( - # string_g/conductor_n / 2 / area + w_i # string_g已在传入时考虑了导线分裂数 - # ) - fx_sum_Li = [math.fsum(val_delta_li)] b_list = [] b_list.extend(fx_delta_Li) b_list.extend(fx_sigma_i1) b_list.extend(fx_sum_Li) - b = sympy.Matrix(b_list) - # sympy.pprint(b) - x = sympy.linsolve((-A, b)) - x_list = [float(_x) for _x in list(x)[0]] - abs_min = [math.fabs(_x) for _x in x_list] + # b = sympy.Matrix(b_list) + # x = sympy.linsolve((-A, b)) + # x_list = [float(_x) for _x in list(x)[0]] + # numpy + # print(A.tolist()) + AA = np.array(A.tolist(), np.float64) + # AA=np.array([[1, 0, 0, -0.0104519104486432, 0, 0], [0, 1, 0, 0, -0.00782784930594165, 0], [0, 0, 1, 0, 0, -0.00640057303461462], [-3.78731866382623, 0, 0, -1.00000000000000, 1, 0], [-3.47643075688507, -3.47643075688507, 0, 0, -1.00000000000000, 1], [1, 1, 1, 0, 0, 0]]) + # print(b.transpose().tolist()[0]) + b = np.array(b_list, dtype=np.float64) + # BB=[-0.159573673689794, 0.140383878899664, 0.00728144380483030, -0.378687120179166, -0.694957566239367, 0.300000000000000] + x = np.linalg.solve(-AA, b) + x_list = x + abs_min: List[float] = [math.fabs(_x) for _x in x_list] abs_min.sort() if abs_min[-1] < 1e-5: break @@ -421,7 +401,7 @@ def solve(): if loop >= loop_end: print("不收敛") else: - print("经过{loop}次迭代收敛,最大偏差{bias}".format(loop=loop,bias=abs_min[-1])) + print("经过{loop}次迭代收敛,最大偏差{bias}".format(loop=loop, bias=abs_min[-1])) # print(val_delta_li) # print(val_sigma_i) verify(val_delta_li, val_sigma_i) diff --git a/data.py b/data.py index 414ec8b..87e0171 100644 --- a/data.py +++ b/data.py @@ -12,15 +12,20 @@ area = 154.48 # 导线面积 mm2 lambda_m = 14.8129 / area # 导线比载 N/(m.mm) lambda_i_array = [ lambda_m * 0.9, - lambda_m * 1.3, + lambda_m * 1.2, + lambda_m, + lambda_m, + lambda_m, + lambda_m * 0.9, + lambda_m * 1.1, + lambda_m, + lambda_m, + lambda_m, lambda_m, lambda_m, lambda_m, lambda_m * 0.9, lambda_m * 1.3, - lambda_m, - lambda_m, - lambda_m, ] # 取400m代表档距下 sigma_m = 28517 / area # 架线时，初伸长未释放前的最低点水平应力。单位N/mm2 @@ -37,8 +42,29 @@ h_array = [ 0, 0, 0, + 0, + 0, + 0, + 0, + 0, +] +l_array = [ + 400, + 300, + 300, + 500, + 300, + 400, + 300, + 300, + 500, + 300, + 300, + 500, + 300, + 400, + 300, ] -l_array = [400, 300, 300, 500, 300, 400, 300, 300, 500, 300] t = 15 epsilon = 1e-4 # 收敛判据 conductor_n = 6 # 导线分裂数 diff --git a/main.py b/main.py index c4c3632..13e0d06 100644 --- a/main.py +++ b/main.py @@ -69,15 +69,18 @@ def fun_sigma_i1( ) -> float: beta_i = math.atan(h_i / l_i) beta_i1 = math.atan(h_i1 / l_i1) - _sigma_i1 = ( - ( - g_i / 2 / area # g_i传入时已考虑导线分裂数 - + 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 * math.sqrt(length_i ** 2 - b_i ** 2) - ) / (math.sqrt(length_i ** 2 - b_i ** 2) / b_i + h_i1 / l_i1) + try: + _sigma_i1 = ( + ( + g_i / 2 / area # g_i传入时已考虑导线分裂数 + + 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 * math.sqrt(length_i ** 2 - b_i ** 2) + ) / (math.sqrt(length_i ** 2 - b_i ** 2) / b_i + h_i1 / l_i1) + except: + a=12 return _sigma_i1