Développements asymptotiques dans les coques elliptiques : Modèle de Koiter

Abstract

We study the asymptotic expansion of the solution of the two-dimensional Koiter model (see [7]) in linear elasticity, for an elliptic shell clamped along its whole lateral face. We show that for smooth data, this solution admits an asymptotic expansion in powers of ε 1/2 where ε represents the (half-)thickness of the shell. This expansion contains terms independent on ε and boundary layer terms exponentially decaying with respect to r/ ε where r denotes the geodesic distance to the boundary of the mean surface.