使用scipy.solve_ivp错误解决偏转曲线：&#39；所需步长小于数字之间的间距'

当我使用大长度的梁（管道）时，我在使用scipy.solve_ivp解决偏转曲线时遇到了失败。以下是我的脚本。

# -*- coding: utf-8 -*-

#
# Calculate deflection curve under gravity
#

import numpy as np
from scipy.integrate import solve_ivp
import matplotlib.pyplot as plt


# round pipe's sectional area
def area_round(D,t):
    d = D - 2 * t
    return np.pi*(D*D-d*d)/4.0

# area moment of inertia section properties of round pipe
def moi_round(D,t):
    d = D - 2 * t
    return np.pi/64.0*(D**4-d**4)

# gravity force per unit length for round pipe
def G_round(dens,D,t):
    g = 9.8  # gravity coef, N/kg
    A = area_round(D,t)
    return A*dens*g

# Calculate 2D plane(xy) bending of a beam undering self-gravity
# minus y is the gravity direction
# - Young's modules E
# - area moment of inertia: Iz

# x: coordinate position along x-axis
# u=[y,dydx]: deflection at y direction , first order derivative on x
def deflection(x,u,E,Iz,G,LG):
    y,dy_dx = u
    MG = np.select([x<=LG,x>LG],[G*(0.5*LG**2+0.5*x**2-LG*x),0])   # distributed force    
    ddy_ddx = np.power(1.0+dy_dx*dy_dx,3.0/2.0)*MG/E/Iz
    return [dy_dx,ddy_ddx]

# solve initial value problem using numerical method
# Given x list, calcuate y and y'
def solve_deflection(E,Iz,Gy,Lg,x_list):
    # initial value
    y0 = 0.0
    dy_dx_x0 = 0.0
    sol = solve_ivp(deflection,t_span=[0.0,Lg],y0=[y0,dy_dx_x0],method='RK45',t_eval=x_list,vectorized=True,args=(E,Iz,Gy,Lg),rtol=1.0e-3,atol=1.0e-4)
    print("sol:",sol)
    return sol.y[0,:],sol.y[1,:]

    
# test of solving deflection equation
# unit sytem: length mm force:N pressure:N/mm^2/MPa
def test():
    dens = 7880.0e-9  # Kg/mm^3
    E = 210e3    # elastic modulus, N/mm^2
    
    # round pipe
    Dp = 60.0  # mm, outer diameter
    tp = 3.0  # mm ,thickness
    print("Dp:",Dp,' tp:',tp)
    
    Iz= moi_round(Dp,tp)      # section const
    Gy = -G_round(dens,Dp,tp)     # gravity force per unit 
    print(" Iz:",Iz,' Gy:',Gy)

    # Lg = 10000.0 # mm,  this length is OK
    Lg = 20000.0  # mm, this length leads to failure
    
    print("Lg=",Lg)


    xlist = np.linspace(0.0,Lg,num=100,endpoint=True)    
    
    res = solve_deflection(E, Iz, Gy=Gy, Lg=Lg, x_list=xlist)
    plt.plot(xlist,res[0])
    plt.show()
    
    

if __name__ == '__main__':
    test()
    pass

当长度为10000mm时，可以给出正确的结果，如下图所示

但当我将其更改为20000mm时，它失败并输出以下消息：，

sol:   message: 'Required step size is less than spacing between numbers.'
     nfev: 944
     njev: 0
      nlu: 0
      sol: None
   status: -1
  success: False
        t: array([   0.        ,  202.02020202,  404.04040404,  606.06060606,
        808.08080808, 1010.1010101 , 1212.12121212, 1414.14141414,
       1616.16161616, 1818.18181818, 2020.2020202 , 2222.22222222,
       2424.24242424, 2626.26262626, 2828.28282828, 3030.3030303 ,
       3232.32323232, 3434.34343434, 3636.36363636, 3838.38383838,
       4040.4040404 , 4242.42424242, 4444.44444444, 4646.46464646,
       4848.48484848, 5050.50505051, 5252.52525253, 5454.54545455,
       5656.56565657, 5858.58585859, 6060.60606061, 6262.62626263,
       6464.64646465, 6666.66666667, 6868.68686869, 7070.70707071,
       7272.72727273, 7474.74747475, 7676.76767677, 7878.78787879,
       8080.80808081, 8282.82828283, 8484.84848485, 8686.86868687,
       8888.88888889])
 t_events: None
        y: array([[ 0.00000000e+00, -3.66155907e+00, -1.45618988e+01,
        -3.25951385e+01, -5.76794150e+01, -8.97565181e+01,
        -1.28794030e+02, -1.74786625e+02, -2.27730361e+02,
        -2.87640987e+02, -3.54556806e+02, -4.28538678e+02,
        -5.09670018e+02, -5.98056798e+02, -6.93827544e+02,
        -7.97133338e+02, -9.08147821e+02, -1.02706718e+03,
        -1.15411018e+03, -1.28951811e+03, -1.43356488e+03,
        -1.58659673e+03, -1.74895654e+03, -1.92104924e+03,
        -2.10335332e+03, -2.29642078e+03, -2.50087718e+03,
        -2.71742163e+03, -2.94684282e+03, -3.19021861e+03,
        -3.44843893e+03, -3.72265946e+03, -4.01447603e+03,
        -4.32592470e+03, -4.65948174e+03, -5.01806360e+03,
        -5.40502733e+03, -5.82494500e+03, -6.28452879e+03,
        -6.79299154e+03, -7.36408180e+03, -8.02047137e+03,
        -8.80421033e+03, -9.81478548e+03, -1.15113253e+04],
       [ 0.00000000e+00, -3.61399978e-02, -7.16869806e-02,
        -1.06770973e-01, -1.41512819e-01, -1.76024795e-01,
        -2.10415154e-01, -2.44799321e-01, -2.79258778e-01,
        -3.13875788e-01, -3.48738932e-01, -3.83943102e-01,
        -4.19589504e-01, -4.55785660e-01, -4.92645404e-01,
        -5.30288885e-01, -5.68842566e-01, -6.08439223e-01,
        -6.49217947e-01, -6.91324142e-01, -7.34921284e-01,
        -7.80235186e-01, -8.27461362e-01, -8.76842769e-01,
        -9.28683414e-01, -9.83348358e-01, -1.04126372e+00,
        -1.10291665e+00, -1.16888799e+00, -1.24022057e+00,
        -1.31734604e+00, -1.40101902e+00, -1.49267854e+00,
        -1.59444811e+00, -1.70913565e+00, -1.84023352e+00,
        -1.99191927e+00, -2.17052401e+00, -2.38680965e+00,
        -2.65797898e+00, -3.01398821e+00, -3.51651158e+00,
        -4.31409773e+00, -5.92506745e+00, -1.41760305e+01]])
 y_events: None
Traceback (most recent call last):

  File "mwe.py", line 82, in <module>
    test()

  File "mwe.py", line 76, in test
    plt.plot(xlist,res[0])

  File "\lib\site-packages\matplotlib\pyplot.py", line 3019, in plot
    return gca().plot(

  File "\lib\site-packages\matplotlib\axes\_axes.py", line 1605, in plot
    lines = [*self._get_lines(*args, data=data, **kwargs)]

  File "\lib\site-packages\matplotlib\axes\_base.py", line 315, in __call__
    yield from self._plot_args(this, kwargs)

  File "\lib\site-packages\matplotlib\axes\_base.py", line 501, in _plot_args
    raise ValueError(f"x and y must have same first dimension, but "

ValueError: x and y must have same first dimension, but have shapes (100,) and (45,)

我读过关于solve_ivp错误的类似问题：“所需步长小于数字之间的间距。”但我不能理解。

我也尝试了不同的环礁价值，但无法解决这个问题。我为此奋斗了好几天。

有人能帮我吗？非常感谢。