Nonlinear Saint-Venant problem of torsion and tension of the cylindrical shell

Within the framework of the nonlinear theory of elastic micropolar shells with kinematically independent fields of translations and rotations, we consider the Saint-Venant problem for a cylindrical shell with an arbitrary cross-section. Using the special representation of deformation of the cylinder we reduce the problem to the one-dimensional nonlinear boundary value problem (BVP). We prove that the proposed family of deformations satisfies the equilibrium equations and boundary conditions at the rectilinear part of the cylinder boundaries. The boundary conditions at the shell edges are satisfied in the sense of Saint-Venant. We obtain energetic relations for the total tensile force and torsional moment acting on the shell cross-section. For an elastic circular cylindrical shell subjected to the torsional moment, the exact solution of the nonlinear BVP is presented.