Keywords: response surface approximation, fuzzy optimization, single level-cut strategy, structural optimization, MDO.

In the real-world structural engineering design problems, the allowable stresses or input parameters often contain fuzzy/imprecise characteristics so that the development of fuzzy nonlinear programming (FNLP) [1,2] is an essential task. Including constrained fuzzy limits is the task most confronted in the category of fuzzy design optimization (FDO) problems. The published literature [3] for FNLP indicate that the single level-cut method is successful for FDO problems to overcome the difficulty of prescribing a crisp design level.

On the other hand, some design optimization problems are not easy or impossible to compute sensitivity information or even difficult to have explicit system behaviour or performance functions. The approximation technique, particularly the response surface methodology (RSM), has been seriously developed for constructing the global approximation to system behaviour [4,5].

In the original single-cut strategy for a FNLP problem with an explicit function, the feasible value of minimum and maximum objective function must be solved before the computational optimization. However, it is impossible to do the same in the FNLP problems that contain implicit functions. Thus, this paper presents an integrating algorithm that can in parallel deal with the objective function and two extreme objective values simultaneously.

Four structural problems [6] are studied to demonstrate the presented multidisciplinary design optimization (MDO). Particularly, a 360-bar space truss design with fuzzy limits contains 81 variables, 744 inequality constraints and an equality constraint is solved without difficulty by the proposed response surface based FDO. Some numerical techniques such as a sampling method in the design of experiment, a successive reducing sub-region during the optimization process, and the single level-cut strategy are presented in concept and the methodology with illustrative examples. The algorithm presented is well developed and suitable for the large scale structural optimization with fuzzy limits.

1

H.J. Zimmermann, "Applications of Fuzzy Sets Theory to Mathematical Programming", Information Sciences, 36, 29-58, 1985. doi:10.1016/0020-0255(85)90025-8

2

S.S. Rao, "Description and Optimum Design of Fuzzy Mechanical Systems", J. of Mechanisms, Transmissions, and Automation in Design, 109, 126-132, 1987.

3

C.J. Shih and H.W. Lee, "Modified Level-Cut Approaches for Unique Design in Large-Scale Fuzzy Constrained Structural Optimization", in Proceedings of the Seventh International Conference on Computational Structures Technology, B.H.V. Topping and C.A. Mota Soares, (Editors), Civil-Comp Press, Stirling, United Kingdom, paper 292, 2004. doi:10.4203/ccp.79.292

4

G. Venter, R.T. Haftka, "Construction of Response Surface Approximations for Design Optimization", AIAA Journal, 36(12), 2242-2249, 1998. doi:10.2514/2.333

5

W.J. Roux, N. Stander, R.T. Haftka, "Response Surface Approximations for Structural Optimization", Int. J. for Numer. Meth. Engng, 42, 517-534, 1998. doi:10.1002/(SICI)1097-0207(19980615)42:3<517::AID-NME370>3.0.CO;2-L

6

R.T. Haftka, Z. Gürdal, Elements of Structural Optimization, Third Revised and Expanded Edition, Kluwer Academic, Dordrecht, 246-248, 1992.

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