limit state, plastic body, anisotropic plastic body.

The authors consider the limit state of anisotropic plastic bodies .The theory of limit state deals with statically determinate condition of solids. the System is closed due to the marginal conditions in this case. The system of equations has three tangential component of the stress tensor. Diagonal components of this system are equal. In this case, the authors are able to choose a velocity field that the system is also statically determinate. The system can be considered in terms of components of tensor of rate of deformation. The number of equations is not increased because the terms of jointness performs identically. For this system the authors found a group of point symmetries and conservation laws, considered some exact solutions, which can be used to describe the plastic swirl around the three orthogonal axes.

Senashov Sergei Ivanovich

e-mail: sen@sibsau.ru, Dr. Sci. Phys. & Math., Professor, Reshetnev Siberian State University of Science and Technology , Krasnoyarsk, Russia.

Savostyanova Irina Leonidovna

e-mail: savostyanova@sibsau.ru, Ph.D. in Pedagogy, Reshetnev Siberian State University of Science and Technology , Krasnoyarsk, Russia