Cantilever Beam Functions
Description:
Dimensions: 4The Cantilever Beam functions, used for uncertainty quantification, model a simple uniform cantilever beam with horizontal and vertical loads. The beam length L and displacement tolerance D0 at the free end of the beam are problem constants, with values L = 100 inches, and D0 = 2.2535 inches. The parameters w and t are width and thickness of the cross-section.
The responses are displacement (D) and stress (S). They have the following constraints: S ≤ R and D ≤ D0.
Input Distributions:
The input random variables and their distributions are:| R ~ N(μ=40000, σ=2000) | yield stress |
| E ~ N(μ=2.9E7, σ=1.45E6) | Young's modulus of beam material |
| X ~ N(μ=500, σ=100) | horizontal load |
| Y ~ N(μ=1000, σ=100) | vertical load |
Above, N(μ, σ) is the Normal distribution with mean μ and variance σ2.
Modifications and Alternative Forms:
The response values can be scaled as: S/R – 1 ≤ 0 and D/D0 – 1 ≤ 0, so that negative values will indicate safe regions, as in Eldred et al. (2007), Eldred & Burkardt (2009) and Eldred et al. (2008).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).
Sues, R., Aminpour, M., & Shin, Y. (2001, April). Reliability-based multidisciplinary optimization for aerospace systems. In Proc. 42rd AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference, number AIAA-2001-1521, Seattle, WA (Vol. 342).
Wu, Y. T., Shin, Y., Sues, R., & Cesare, M. (2001, April). Safety-factor based approach for probability-based design optimization. In Proc. 42nd AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference, number AIAA-2001-1522, Seattle, WA (Vol. 196, pp. 199-342).
For questions or comments, please email Derek Bingham at: dbingham@stat.sfu.ca.