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Сибирский государственный университет
науки и технологий имени академика М.Ф. Решетнева

Сибирский аэрокосмический журнал
ISSN 2712-8970 (Print) ISSN 2782-5760 (on-line)

Сведения об образовательной организации

UDK 539.374 Doi: 10.31772/2712-8970-2021-22-3-452-456
3-dimensional solutions from two variables
Senashov S. I., Savostyanova I. L.
Reshetnev Siberian State University of Science and Technology, 31, Krasnoyarskii rabochii prospekt, Krasnoyarsk, 660037, Russian Federation
In this paper, we consider stationary 3-dimensional equations of ideal plasticity with the Mises flow condition. The material is assumed to be incompressible. The case when all three components of the veloc-ity vector and hydrostatic pressure depend only on two coordinates x, y is studied in detail. For this case, a new name is introduced – 3-dimensional solutions from two variables, to distinguish it from the generally accepted two-dimensional state, when only two components of the velocity vector and hydrostatic pressure differ from zero. It is proved that the system admits, in the sense of S. Lie, a Lie algebra of dimension 10. It is shown that all 3-dimensional solutions from two variables is a superposition of the plane stress state and plastic torsion around the z-axis. Two invariant solutions of the equations describing the 3-dimensional deformed state are constructed. The first solution can be used to describe plastic flows between two rigid plates that approach at different speeds. The second solution is used to describe the stress-strain state of the material inside a flat channel formed by converging plates.
Keywords: 3-dimensional solutions of ideal plasticity equations, point symmetries, invariant solutions.
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Senashov Sergei Ivanovich – Dr. Sc, Professor, Head of the Department of IES; Siberian State University of Science and Technology. E-mail: sen@sibsau.ru.

Savostyanova Irina Leonidovna – Cand. Sc., Associate Professor of the Department of IES, Siberian State University of Science and Technology. E-mail: savostyanova@sibsau.ru.