On a Problem of Truesdell for Anisotropic Elastic Shells

Abstract

In this paper we study the equilibrium of cylindrical elastic shells under the action of resultant forces and moments on the end edges. We employ the linear theory of Cosserat surfaces to describe the deformation of anisotropic and inhomogeneous cylindrical shells with arbitrary (open or closed) cross-section. In this context, we prove a minimum energy characterization for the solution of the relaxed Saint-Venant's problem determined previously. Then, we treat the problem of Truesdell associated to the deformation of cylindrical shells.