Two-Dimensional Grained Composites of Extreme Rigidity

Abstract

A thin elastic plate with nonidentical periodical inclusions is considered as an adequate model to optimize mechanical characteristics of a two-phase composite, given the mean stresses and phase volume fraction. Geometrical forms of these inclusions minimizing the total stress energy are obtained explicitly through the analytical solution of a specific boundary value problem so their parametrical equations are expressed in terms of elliptic functions. Such approach is used also to find the effective moduli of the composite. Finally, the similar finite-step procedure is suggested to construct multiphase optimal structure with macroisotropy.