The effective properties of a perforated elastic plate Numerical optimization by genetic algorithm

We consider a perforated elastic plate in which identical traction-free holes form square or hexagonal periodic arrays. The optimization problem of finding the hole shape in this structure that maximizes either of its effective moduli is posed as a full scale inverse problem of elasticity. In this context, only limiting cases of a single hole and cellular solids with thin cell walls have been studied thus far. Here, we cover the gap between these cases numerically solving the problem by the genetic algorithm approach. A new time-saving scheme of the fitness evaluation provides reliable data even near the percolation limit. The presented numerical results comprehensively describe the optimal behavior of perforated plates in terms of equivalent homogeneous medium. Similar, though less sophisticated approach was used by the author Vigdergauz, (Int. J. Solids Struct. 38 (2001) 6851) to optimize an isolated inclusion in a plate.