Design of Composite Plates of Extremal Rigidity

Abstract

We consider design problems for plates possessing an extremal rigidity. The plate is assumed to be assembled from two isotropic materials characterized by different values of their elastic moduli; the amount of each material is given. We look for a distribution of the materials which renders the plate’s rigidity for either its maximal or minimal value. The rigidity is defined here as work produced by an extremal load on deflection of the points of the plate. The optimal distribution of the materials is characterized by some infinitely often alternating sequences of domains occupied by each of the materials (see [1], [2]). This leads to the appearance of anisotropic composites; their structures are to be determined at each point of the plate.

The article is the translation of an article originally written in Russian and published as the report of Ioffe Physico-Technical Institute, Academy of Sciences of USSR, Publication 914, Leningrad, 1984.