Combined Upper Bounds on the Effective Moduli of a Perforated Elastic Plate. Numerical Assessment by Genetic Algorithm

Abstract

A thin perforated plate with square symmetry is considered in the optimization context of finding the hole shapes which maximize the effective elastic moduli of the structure. In the literature, this is usually considered as a single-criterion problem when either of the moduli is optimized independently of the others. Here, we focus on the more realistic bi-criteria problem of optimizing the bulk modulus and the first shear modulus together. By combining the genetic algorithm (GA) with the weighted sums (WS) scheme, the set of Pareto optimal moduli is found numerically in the general case of interacting holes, even near the percolation limit. The GA part of the proposed approach was previously used by the author to separately optimize the shear and Young effective moduli in perforated plates.

Keywords

Plane elasticity problem shape optimization effective moduli extremal elastic structures genetic algorithm

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