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 prПоказать полностьюoblems 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