Sur l'analyse asymptotique du modèle bidimensionnel de Koiter d'une coque en flexion linéairement élastique

Abstract

To compute the displacement vector of a linearly elastic shell, we can use the twodimensional Koiter's model. An asymptotical analysis allows to justify this model in the sense that the solution ζ ε of the Koiter's model converges, when the thickness 2ε of the shell goes to zero, to the same limit ζ F as the three-dimensional displacement vector (under some asumptions on the loads and with adapted scalings). The function ζ F solves the flexural shell equations. We prove the convergence of (ζ ε- ζ F)/ε under a specific assumption on the loads, which is always verified in the particular case of an arch. To this end, we associate a mixed formulation with the flexural problem.