Une justification d'un modèle d'assemblages de coques cylindriques collées

Abstract

We consider two thin linearly elastic cylindrical shells, bonded to each other. The thickness of each shell is 2ε, ε being small. The adhesive material is assumed to be a linearized Saint-Venant Kirchhoff material, with Lamé constants of order ε^q with q>0 as in [1,2]. This material then constitutes a cylindrical shell with a thickness ε^r with r>1. The upper shell is loaded with a volumic density of order ε². We consider the case q=3+r. We then establish the convergence, in appropriate spaces, of the scaled displacements and scaled stress tensors when ε goes to zero. The limit displacement satisfies a flexural model which involve the shear and the normal stress of the adhesive part. These stresses depend on the jump of the tangential and normal displacements of the bonded shells.