Welded beam function

\[\sqrt{\frac{\tau'^2+\tau''^2+l\tau'\tau''}{\sqrt{0.25\left(l^2+(h+t)^2\right)}}},\]

where \(\tau'=\frac{6000}{\sqrt{2}hl}, \quad\tau''=\frac{6000(14+0.5l)\sqrt{0.25\left(l^2+(h+t)^2\right)}}{2\left[0.707hl\left(\frac{l^2}{12}+0.25(h+t)^2\right)\right]},\quad \text{for}\quad h\in[0.125,1],\quad l,t\in[5,10].\)

Usage

import numpy as np
import matplotlib.pyplot as plt

from smt.problems import WeldedBeam

ndim = 3
problem = WeldedBeam(ndim=ndim)

num = 100
x = np.ones((num, ndim))
for i in range(ndim):
    x[:, i] = 0.5 * (problem.xlimits[i, 0] + problem.xlimits[i, 1])
x[:, 0] = np.linspace(5.0, 10.0, num)
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	1	None	[‘int’]
return_complex	False	None	[‘bool’]
name	WeldedBeam	None	[‘str’]
use_FD	False	None	[‘bool’]