Approximation of structural optimization problems by means of designed numerical experiments

In this paper we describe an approach in which the Experimental Design Theory (EDT) (see Montgomery and Wiley 1984; Kiefer and Wolfowitz 1959; Fedorov 1972) is used as a tool in building approximate analysis models to be applied in structural optimization problems. This theory has been developed for the planning and analysis of comprehensive physical experiments in order to reduce the number of required experiments while preserving the amount of information that can be extracted from them. This situation is very similar to that of structural optimization, where the number of expensive finite element (FEM) analyses has to be minimized (Schoofs 1987). FEM computations can be regarded as numerical experiments, where the design variables are treated as input quantities. All computable properties of the structure, such as weight, displacements, stresses, etc. can be regarded as response quantities of the numerical experiment. The approximating models will be derived for these responses by using regression techniques, and they can be substituted in the optimization problem for the definition of the objective and the constraint functions. The application of the proposed method is illustrated with two case studies.