On Saint-Venant's principle in the theory of Cosserat elastic shells

摘要

In this paper, we consider the linear theory of Cosserat elastic shells made from an homogeneous and anisotropic material. We study the equilibrium of cylindrical shells loaded by contact forces and couples acting on the end edges. We prove the principle of Saint-Venant in the following formulation: if a system of loads has zero resultant force and moment at each end edge, then the strain energy U_z contained in that portion of the cylindrical shell situated beyond a distance z from the load region has an exponential decay as a function of z.