The Solution of Saint-Venant's Problem in the Theory of Cosserat Shells

This paper is concerned with the linear theory of thin elastic shells modelled as Cosserat surfaces. We formulate the corresponding Saint-Venant's problem with respect to cylindrical shells. Then, we determine the solution of the relaxed problem for both open and closed cylindrical surfaces. The edge curves perpendicular to the generator are not necessarily circular. Finally, some particular cases are discussed.