short: Short Column Function

In gek: Gradient-Enhanced Kriging

Short Column Function

Description

The short column function is defined by

f_{\rm short}(x) = 1 - \frac{4M}{b h^2 Y} - \frac{P^2}{b^2 h^2 Y^2}

with x = (Y, M, P).

Usage

short(x, b = 5, h = 15)
shortGrad(x, b = 5, h = 15)

Arguments

x	a numeric vector of length 3 or a numeric matrix with n rows and 3 columns.
b	width of the cross-section in \rm mm of the short column. Default is 5.
h	depth of the cross-section in \rm mm of the short column. Default is 15.

Details

The short column function describes the limite state function of a short column with uncertain material properties and loads.

Input	Distribution	Mean	Standard deviation	Description
Y	\mathcal{LN}	5	0.5	yield stress in \rm MPa
M	\mathcal{N}	2000	400	bending moment in \rm MNm
P	\mathcal{N}	500	100	axial force in \rm MPa

The bending moment and the axial force are correlated with \rm{Cor}(M, P) = 0.5. Note, \mathcal{N} represents the normal distribution and \mathcal{LN} is the log-normal distribution.

Value

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

shortGrad returns the gradient of short 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.