Pure bending of a cylindrical membrane with internal pressure

The nonlinear bending by end moments of the closed cylindrical shell prestressed by internal pressure is considered. The shell is made of the incompressible isotropic hyperelastic material. The nonlinear membrane theory of shells is used. The set of basic equations is derived from the variational principle of stationary potential energy. With the help of special substitution the bending problem is reduced to the system of nonlinear ordinary differential equations, which are analysed by a numerical method. The numerical results are obtained for the circular cylindrical shell made of the neo-Hookean material. The influence of the internal pressure on the curvature of the cylinder axis deformed by the bending moment is studied.