Construction of Response Surface Approximations for Design Optimization

Abstract

Using response surface approximations for design constraints in design optimization provides the designer with an overall perspective of the system response within the design space. Response surface approximations also reduce the numerical noise inherent in many numerical models and simplify the process of integrating several design codes, as is typically required in multidisciplinary optimization. Procedures are discussed for constructing accurate response surface approximations to represent design constraints in design optimization. Response surface approximations are constructed for the stresses and buckling loads of an isotropic plate with an abrupt change of thickness. These response surface approximations are constructed from numerical experiments conducted with a finite element analysis procedure and are used for minimum-weight optimum design of the plate. Nondimensional variahles and stepwise regression are used to reduce the complexity and increase the accuracy of the response surface approximations. Additionally, higher-order polynomials (cubic and quartic instead of the more traditional quadratic) are used as response surface approximations, and a detailed error analysis, using an independent data set, is performed. Finally, it is shown that, by making use of response surface approximations, the optimum weight of the plate may be presented in the form of a design chart for a wide range of geometric, loading, and material constants.