Cantilever beam function

\[\frac{50}{600}\sum\limits_{i=1}^{17}\left[\frac{12}{b_ih_i^3}\left(\left(\sum\limits_{j=i}^{17}l_j\right)^3-\left(\sum\limits_{j=i+1}^{17}l_j\right)^3\right)\right],\]

\(b_i\in [0.01,0.05], \quad h_i\in[0.3,0.65], \quad l_i\in[0.5,1].\)

Usage

import matplotlib.pyplot as plt
import numpy as np

from smt.problems import CantileverBeam

ndim = 3
problem = CantileverBeam(ndim=ndim)

num = 100
x = np.ones((num, ndim))
x[:, 0] = np.linspace(0.01, 0.05, num)
x[:, 1] = 0.5
x[:, 2] = 0.5
y = problem(x)

yd = np.empty((num, ndim))
for i in range(ndim):
    yd[:, i] = problem(x, kx=i).flatten()

print(y.shape)
print(yd.shape)

plt.plot(x[:, 0], y[:, 0])
plt.xlabel("x")
plt.ylabel("y")
plt.show()

(100, 1)
(100, 3)

Options

List of options

Option	Default	Acceptable values	Acceptable types	Description
ndim	3	None	[‘int’]
return_complex	False	None	[‘bool’]
name	CantileverBeam	None	[‘str’]
P	50000.0	None	[‘int’, ‘float’]	Tip load (50 kN)
E	200000000000.0	None	[‘int’, ‘float’]	Modulus of elast. (200 GPa)