Structural Optimum Design in Conjunction with Transient Dynamic Analysis using Global Direct Search

In structural design, nonlinear transient dynamic analysis is widely used. Establishing optimization techniques suited for application with transient dynamic analysis is important from both a theoretical and a practical point of view. In particular, we consider a minimization problem of maximum transient dynamic response. This class of problem is referred to as an unsmooth and noisy problem and this is often needed in practical design. As many optimization techniques require accurate design sensitivity information, transient dynamic analysis hinders optimization. In order to overcome these difficulties, we propose an approach to combine the direct search method, which is one of the derivative-free methods, with the global optimization method, based on sequential design of computer experiments. Our new propositions are mainly following two lines: a) enhancement by expected improvement criterion of direct search method b) using an equivalent expected improvement for maximum function. We illustrate the efficiency of our method comparing with other methods through numerical examples.