Short Column Function
Description:
Dimensions: 3The Short Column function models a short column with uncertain material properties and subject to uncertain loads (Eldred et al., 2007). The parameters b (width of the cross-section, in mm) and h (depth of the cross-section, in mm) have nominal values b = 5 and h = 15.
Input Distributions:
The input random variables and their distributions are:| Y ~ Lognormal(mean=5, standard deviation=0.5) | yield stress |
| M ~ N(μ=2000, σ=400) | bending moment |
| P ~ N(μ=500, σ=100) | axial force |
Above, N(μ, σ) is the Normal distribution with mean μ and variance σ2. The input variables are uncorrelated, except for a correlation coefficient of 0.5 between M and P.
Code:
References:
Eldred, M. S., Agarwal, H., Perez, V. M., Wojtkiewicz Jr, S. F., & Renaud, J. E. (2007). Investigation of reliability method formulations in DAKOTA/UQ. Structure and Infrastructure Engineering, 3(3), 199-213.
Eldred, M. S., & Burkardt, J. (2009, January). Comparison of non-intrusive polynomial chaos and stochastic collocation methods for uncertainty quantification. In Proceedings of the 47th AIAA Aerospace Sciences Meeting and Exhibit, number AIAA-2009-0976, Orlando, FL (Vol. 123, p. 124).
Eldred, M. S., Webster, C. G., & Constantine, P. (2008, April). Evaluation of non-intrusive approaches for Wiener-Askey generalized polynomial chaos. In Proceedings of the 10th AIAA Non-Deterministic Approaches Conference, number AIAA-2008-1892, Schaumburg, IL (Vol. 117, p. 189).
Kuschel, N., & Rackwitz, R. (1997). Two basic problems in reliability-based structural optimization. Mathematical Methods of Operations Research, 46(3), 309-333.
For questions or comments, please email Derek Bingham at: dbingham@stat.sfu.ca.