UN PROBLEME DE COQUES ELASTIQUES MINCES AVEC PROBLEME LIMITE A ENERGIE NON BORNEE

Abstract

We study in this work a singular perturbation problem depending on a small parameter ! 0 , which characterizes the balance of a linearly elastic thin shell of thickness 2 and elliptic middle surface, within the framework of the theory of Koiter. For ! 0 this problem is well posed in the space of admissible displacements. On the other hand if " 0 the limit problem is ill-posed for a choice of singular loadings, i.e., which are not in the dual of the space of the limit problem. Thus the deformation energy of the shell tends towards the infinite one and it concentrates in internal layers. Then we determine the structure of these internal layers and we justifie the convergence.