On Saint–Venant’s problem for anisotropic, inhomogeneous, cylindrical Cosserat elastic shells

We investigate the static deformation of cylindrical elastic shells, using the theory of Cosserat surfaces. We consider anisotropic and inhomogeneous cylindrical shells with arbitrary (open or closed) cross-section. The constitutive coefficients are assumed to be independent of the axial coordinate. In the context of linearized theory, we determine a solution of the relaxed Saint–Venant’s problem. Finally, we apply the general results in the special cases of circular cylindrical shells and of Cosserat plates made from an orthotropic material.