Le modèle de Novozhilov-Donnell linéaire déduit de l'élasticité tridimensionnelle non linéaire

Abstract

In this paper, we present a justification of the linear Novozhilov-Donnell model using an asymptotic approach. This model has already been obtained from linearized three-dimensional elasticity. We propose here to justify this model directly from the nonlinear three-dimensional elasticity equations. In the case of shallow shells and for small enough applied loads, we prove that the first term of the strain measures is linear with respect to the displacements. The equilibrium equations of the asymptotic model are those of the Novozhilov-Donnell model. So, the domain of validity of the linear Novozhilov-Donnell model is clearly determined.