The ray method for solving the dynamics of the elastic-viscous-plastic shells

The processes of dynamic deformation of shells are actively studied by both domestic and foreign scientists [4; 11; 13; 14]. The work describes the ray method for solving systems of partial differential equations of hyperbolic type. This method consists in constructing the equations of discontinuity transfer along the propagation of perturbations on moving surfaces, as well as in representing the solution in the form of a Taylor power series in the variable distance behind the perturbation front while preserving a sufficient number of terms. The implementation of the method is shown by the example of a system of partial differential equations of hyperbolic type, which describe the process of dynamic deformation of thin cylindrical shells of revolution from elastoviscoplastic materials [10]. An algorithm for constructing a solution up to the required order is given.