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 numpy as np
import matplotlib.pyplot as plt

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)
../../_images/cantileverbeam_Test_test_cantilever_beam.png

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)