Asymptotic Analysis of Shells via Γ-Convergence

Abstract

We give a new justification of the linear membrane and flexural shell models. We prove that the sequence of scaled energy functionals associated with the scaled problem Γ-converges to the energy functional associated with a two-dimensional model. This two-dimensional model is a membrane or flexural one, depending on the geometric and kinematic conditions. Then, a classical argument allows to give a new proof of the convergence theorems recently obtained by P.G. Ciarlet, V. Lods and B. Miara.