Сибирский федеральный университет

Тип публикации: статья из журнала

Год издания: 2020

Идентификатор DOI: 10.17516/1997-1397-2020-13-6-792-796

Ключевые слова: differential equation, dynamical problem, exact solution, plasticity, symmetries

Аннотация: Dynamical problems of the theory of plasticity have not been adequately studied. Dynamical problems arise in various fields of science and engineering but the complexity of original differential equations does not allow one to construct new exact solutions and to solve boundary value problems correctly. One-dimensional dynamical problems are studied rather well but two-dimensional problems cause major difficulties associated with nonlinearity of the main equations. Application of symmetries to the equations of plasticity allow one to construct some exact solutions. The best known exact solution is the solution obtained by B.D. Annin. It describes non-steady compression of a plastic layer by two rigid plates. This solution is a linear one in spatial variables but includes various functions of time. Symmetries are also considered in this paper. These symmetries allow transforming exact solutions of steady equations into solutions of non-steady equations. The obtained solution contains 5 arbitrary functions. © Siberian Federal University. All rights reserved.

Журнал: Journal of Siberian Federal University - Mathematics and Physics

Выпуск журнала: Vol. 13, Is. 6

Номера страниц: 792-796

ISSN журнала: 19971397

Издатель: Siberian Federal University

• Senashov Sergei (Reshetnev Siberian State Univ Sci & Technol, Dept Econ Informat Syst, 31 Krasnoyarsky Rabochy Av, Krasnoyarsk 660037, Russia)
• Gomonova Olga (Reshetnev Siberian State Univ Sci & Technol, Dept Econ Informat Syst, 31 Krasnoyarsky Rabochy Av, Krasnoyarsk 660037, Russia)
• Savostyanova Irina L. (Reshetnev Siberian State Univ Sci & Technol, Dept Econ Informat Syst, 31 Krasnoyarsky Rabochy Av, Krasnoyarsk 660037, Russia)
• Cherepanova Olga N. (Siberian Fed Univ, Dept Math Anal & Differential Equat, Svobodny 79, Krasnoyarsk 660041, Russia)

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