Non-dimensional response surfaces for structural optimization with uncertainty
Gerhardus Venter, Raphael T. Haftka · University of Florida Digital Collections (University of Florida) · 1998
Approximation concepts are an effective approach for alleviating some of the problems associated with the direct use of modern computerized analysis techniques in an optimization environment. Recently, response surface approximations have gained popularity as polynomial approximations that are global in nature. Response surface approximations shift the computational burden from the optimization problem to the problem of constructing the approximations, and accommodate the use of detailed analysis techniques without the need of derivative information. Additionally, response surface approximations filter out numerical noise inherent to most numerical analysis procedures, by providing a smooth approximate response function, and simplify the integration of the analysis and the optimization codes. The present dissertation investigates the use of response surface approximations in expensive structural optimization problems and aims to suggest techniques for improving both the accuracy of response surface approximations as well as the efficiency with which they are constructed. A stepped plate design problem is considered and response surface approximations are constructed for different failure mechanisms using numerical experiments conducted with a finite element analysis. Both an isotropic and a composite laminated plate, where the change in thickness is a result of internal ply drop off, are considered. The proposed methodology uses a combination of dimensional analysis, higher order response surface approximations, stepwise regression, a detailed error analysis and statistical design of experiments to improve both accuracy and efficiency. Dimensional analysis identifies variables intrinsic to the problem, and thus reduces the number of variables in the resulting response surface approximation. Stepwise regression is used to eliminate insignificant parameters from a response surface approximation and statistical design of experiments is used to identify a small set of data points for constructing the response surface approximations, while maintaining accuracy. The result of the proposed methodology is response surface approximations that are highly accurate over the entire design space. The use of response surface approximations in expensive structural optimization problems is demonstrated by using the developed response surface approximations in designing for uncertainty. The uncertainty is modeled using fuzzy set theory and the optimization results are presented in the form of design charts.