Robust design of structures using optimization methods. (English) Zbl 1067.74554

Summary: The robust design of structures with stochastic parameters is studied using optimization techniques. The first two statistical moments of the stochastic parameters including design variables are considered in conjunction with the second-order perturbation method for the approximation of mean value and variance of the structural response. In this framework, the sensitivities of the mean values and variances of the structural performance function with respect to the design variables are calculated for use in the optimization task. The robust design of structures is formulated as a multi-criteria optimization problem, in which both the expected value and the standard deviation of the objective function are to be minimized. The robustness of the feasibility is also taken into account by involving the variability of the structural response in the constraints. The two-criteria optimization problem is converted into a scalar one and is then solved by a gradient based optimization algorithm. To demonstrate the applicability of the presented method, numerical examples are given, involving static and dynamic response.


74P10 Optimization of other properties in solid mechanics
74P05 Compliance or weight optimization in solid mechanics
74S05 Finite element methods applied to problems in solid mechanics


Full Text: DOI


[1] Kuschel, N.; Rackwitz, R., Optimal design under time-variant reliability constraints, Struct. safety, 22, 113-127, (2000)
[2] R. Rackwitz, G. Augusti, A. Borii (Eds.), Reliability and Optimization of Structural Systems, Proc. IFIP WG 7.5 Working Conference, Assisi, Italy, 1995. Chapman & Hall
[3] Elishakoff, I.; Haftka, R.T.; Fang, J., Structural design under bounded uncertainty-optimization with anti-optimization, Comput. struct., 53, 1401-1405, (1994) · Zbl 0878.73041
[4] Venter, G.; Haftka, R.T., Using response surface approximations in fuzzy set based design optimization, Struct. optim., 18, 218-227, (1999)
[5] Tsui, K.L., An overview of Taguchi method and newly developed statistical methods for robust design, IIE trans., 24, 44-57, (1992)
[6] Chi, H.W.; Bloebaum, C.L., Mixed variable optimization using Taguchi’s orthogonal arrays, Struct. optim., 12, 147-152, (1996)
[7] Lee, K.H.; Eom, I.S.; Park, G.J.; Lee, W.I., Robust design for unconstrained optimization problems using the Taguchi method, Aiaa j., 34, 1059-1063, (1996) · Zbl 0900.73481
[8] Lee, K.H.; Park, G.J., Robust optimization considering tolerances of design variables, Comput. struct., 79, 77-86, (2001)
[9] Lautenschlager, U.; Eschenauer, H.A., Design-of-experiments methods and their application to robust multi-criteria optimization problems, Z. angew. math. mech., 79, S1, 71-74, (1999) · Zbl 0939.74053
[10] Sandgren, E.; Cameron, T.M., Robust design optimization of structures through consideration of variation, Comput. struct., 80, 1605-1613, (2002)
[11] C.R. Gumbert, G.J.W. Hou, P.A. Newman, Reliability assessment of a robust design under uncertainty for a 3-D flexible wing, in: Proc. 16th AIAA Computational Fluid Dynamics Conference, Orlando, Florida, AIAA 2003-4094, 2003, p. 11
[12] Shinozuka, M.; Lenoe, E., A probabilistic model for spatial distribution of material properties, Engrg. fract. mech., 8, 217-227, (1976) · Zbl 0354.73061
[13] Stefanou, G.; Papadrakakis, M., Stochastic finite element analysis of shells with combined random material and geometric properties, Comput. methods appl. mech. engrg., 193, 139-160, (2004) · Zbl 1075.74681
[14] Liu, W.K.; Belytschko, T.; Mani, A., Random field finite element, Int. J. numer. methods engrg., 23, 1831-1845, (1986) · Zbl 0597.73075
[15] Schueller, G.I., Computational stochastic mechanics–recent advances, Comput. struct., 79, 2225-2234, (2001)
[16] Liu, W.K.; Besterfield, G.; Belytschko, T., Transient probabilistic systems, Comput. methods appl. mech. engrg., 67, 27-54, (1988) · Zbl 0619.73085
[17] C. Lawrence, J.L. Zhou, A.L. Tits, User’s Guide for CFSQP Version 2.5. Available from <http://www.aemdesign.com>
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