Plate theory as the variational limit of the complementary energy functionals of inhomogeneous anisotropic linearly elastic bodies

Abstract

We consider a sequence of linear hyper-elastic, inhomogeneous and fully anisotropic bodies in a reference configuration occupying a cylindrical region of height . We study, by means of Γ-convergence, the asymptotic behavior as goes to zero of the sequence of complementary energies. The limit functional is identified as a dual problem for a two-dimensional plate. Our approach gives a direct characterization of the convergence of the equilibrating stress fields.