steel: Steel Column Function
In gek: Gradient-Enhanced Kriging

View source: R/testfunctions.R

steel

R Documentation

Steel Column Function

Description

The steel column function is defined by

f_{\rm steel}(x) = F_S - P \left(\frac{1}{2BD} + \frac{F_0 E_b}{BDH(E_b - P)} \right),

with P = P_1 + P_2 + P_3, E_b = \frac{\pi^2 EBDH^2}{2L^2} and x = (F_S, P_1, P_2, P_3, B, D, H, F_0, E).

Usage

steel(x, L = 7500)
steelGrad(x, L = 7500)

Arguments

`x`	a numeric `vector` of length `9` or a numeric `matrix` with `n` rows and `9` columns.
`L`	length in `\rm mm` of the steel column. Default is `7500`.

Details

The steel column function describes the limite state function of a steel column with uncertain parameters.

Input	Distribution	Mean	Standard Deviation	Description
`F_S`	`\mathcal{LN}`	`400`	`35`	yield stress in `\rm MPa`
`P_1`	`\mathcal{N}`	`500000`	`50000`	dead weight load in `\rm N`
`P_2`	`\mathcal{G}`	`600000`	`90000`	variable load in `\rm N`
`P_3`	`\mathcal{G}`	`600000`	`90000`	variable load in `\rm N`
`B`	`\mathcal{LN}`	`b`	`3`	flange breadth in `\rm mm`
`D`	`\mathcal{LN}`	`t`	`2`	flange thickness in `\rm mm`
`H`	`\mathcal{LN}`	`h`	`5`	profile height in `\rm mm`
`F_0`	`\mathcal{N}`	`30`	`10`	initial deflection in `\rm mm`
`E`	`\mathcal{W}`	`210000`	`4200`	Young's modulus in `\rm MPa`

Here, \mathcal{N} is the normal distribution and \mathcal{LN} is the log-normal distribution. Further, \mathcal{G} represents the Gumbel distribution and \mathcal{W} denotes the Weibull distribution.

Value

steel returns the function value of steel column function at x.

steelGrad returns the gradient of steel column function at x.

Author(s)

Carmen van Meegen

References

Kuschel, N. and Rackwitz, R. (1997). Two Basic Problems in Reliability-Based Structural Optimization. Mathematical Methods of Operations Research, 46(3):309–333.

Surjanovic, S. and Bingham, D. (2013). Virtual Library of Simulation Experiments: Test Functions and Datasets. https://www.sfu.ca/~ssurjano/ (retrieved January 19, 2024).

gek documentation built on April 4, 2025, 12:35 a.m.