Numerical solution of generalized dynamic axisymmetric problems for elastoplastic shells of revolution under large deformations

We present a technique for solving numerically the nonlinear nonstationary problems of axisymmetric elastoplastic deformation of shells of revolution taking into consideration torsion under the prescribed kinematics and loads. The method is based on the geometrically nonlinear Timoshenko theory of shells and the plasticity theory with isotropic hardening. A variational difference method in combination with a scheme for explicit time integration of the equations of motion is used for solving the problem of interest. Stability estimates and a regularization technique for difference schemes that can increase the integration time step are given. The efficiency of the proposed method is verified by studying the stability of the elastoplastic deformation of a cylindrical metal shell under monotonic tension and torsion.