Robust design optimization of structures with multimodal responses using Taylor expansions

Abstract This paper shows how a combination of multiple linear approximations can efficiently capture non-linear and non-smooth response functions in the framework of robust design optimization. The basic idea is to split the domain of random parameters into multiple subdomains along the hypersurfaces that cause discontinuities in the response. For each subdomain, a linear approximation is used to determine the stochastic moments of the response function due to the scatter in that subdomain. The total stochastic distribution of the structural response is considered to be a multimodal distribution, and its moments are composed from the approximations in the subdomains. The application to use cases shows that indeed the structural response is multimodal in these cases, and the stochastic moment approximations are sufficiently accurate using the proposed method.