nonlinear elasticity, finite deformations, dynamics, shock waves, ray method.

The paper is devoted to an approximate solution of one-dimensional problem of nonlinear dynamic theory of elasticity about the torsional shock load on the cylindrical layer subjected to preliminary antiplane shear. It is shown that the boundary impact action extends in the environment in the form of the two surfaces of deformation discontinuities. The features of construction of frontline ray asymptotics for each surface ruptures and calculating the coefficients of the ray series according to the conditions of compatibility gaps and boundary conditions are specified.

1. Sevastyanov Georgiy Mamievich e-mail: akela.86@mail.ru, Ph. D., Researcher, Institute of Machine Engineering and Metallurgy FEB RAS, Komsomolsk-on-Amur, Russia. 2. Shtuka Victor Igorevich e-mail: onslice@mail.ru, Post-Graduate Student, Mathematician Engineer, Institute of Automation and Control Processes FEB RAS, Vladivostok, Russia. 3. Burenin Anatoly Aleksandrovich e-mail: burenin@iacp.dvo.ru, Corresponding Member of the Russian Academy of Sciences, Dr. Sci. Phys. & Math., Professor, Institute for Machine Engineering and Metallurgy of the Far Eastern Branch of Russian Academy of Science, Komsomolsk-on-Amur, Russia.