Optimization formulation for determining and maximizing wrinkling stress of the sandwich beam

Abstract

Face-sheet wrinkling is a standard failure mode for sandwich structures with thin, stiff face sheets and a thick, soft core under in-plane compression. Constructing a core with a multi-layer material and placing the stiffest material in the outermost region of the core can efficiently improve the wrinkling stress. However, complex engineering requirements may hinder this ideal core design. Hence, the design of sandwich structures for maximum wrinkling stress requires a systematic structural optimization method. This study proposes a max-min structural optimization model for the design of the multi-layer core thickness distribution in a sandwich beam, aiming at the maximization of wrinkling stress. Two series of layers are introduced: virtual and physical. The thicknesses of the former serve to compute the wrinkling stress, whereas those of the latter serve to describe the thickness distribution of the multi-layer core. The optimization is structured in two levels: the inner level is formulated as a minimization problem to compute the wrinkling stress, and the outer level as a maximization problem to obtain the optimal thickness distribution. The proposed max-min optimization model determines the optimal thickness distribution of a sandwich beam with a multi-layer core to achieve maximum wrinkling stress, independent of specific engineering requirements. For example, simple mass requirements in engineering may prevent the stiffest material from being placed on the outermost layer. Moreover, the method is highly computationally efficient, owing to the simple convex feasible domains of its optimization model and the elimination of matrix eigenvalue solutions and finite element mesh operations. We therefore recommend its adoption in engineering design because the method can explicitly incorporate complex constraints into its formulation.