Optimal bounds for Kirchhoff-Love plate

Abstract

In this paper, we consider the fourth-order elliptic equation describing the Kirchhoff-Love model for the pure bending of a thin, solid, symmetric plate under a transverse load. We address optimal bounds on the effective energy of a composite material using the translation method, without assuming that the given materials are well-ordered or isotropic. Moreover, we provide an alternative approach to deriving the Hashin-Shtrikman bounds. These results pave the way for numerous applications of homogenization theory in optimal design problems for stationary elastic plates, especially when the elastic composite material is obtained by mixing two phases that are not well-ordered.