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Mathematics and Mechanics of Solids
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Article

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

S. Vigdergauz*

The Israel Electric Corp. Ltd., PO Box 10, 31000, Hafia, Israel

* To whom correspondence should be addressed.


  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 we set previously used by the author to separate optimize the shear and Young effective moduli in perforated plates.

Key Words: Plane elasticity problem, shape optimization, effective moduli, external elastic structures, genetic algorithm.

First published on January 12, 2005, doi:10.1177/1081286504040404

Mathematics and Mechanics of Solids 2006;11:276.

A more recent version of this article appeared on June 1, 2006

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