Calculations in dynamics of incompressible elastic medium under antiplane and twisting shock loading

This paper is devoted to using the ray method in constructing numerical solution schemes for one-dimensional problems on shock loading of a cylindrical surface. The ray method is applied to localize the shock wave, which is a moving boundary in the boundary-value problem for the equation of medium motion, and to find a solution near the wave front. The approximate analytical solutions of antiplane and twisted shock loading problems for a short time passed after the impact are given. The method of matching the front analytical solution and the numerical solution using the least-square technique is presented. Numerical solutions for the problems under study are given.