Source: https://vestnik.sibsau.ru/en_US/item/?id=942
Timestamp: 2019-04-19 14:35:45+00:00

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In this paper we study equations describing a slow plastic flow of material. In this case the material is in the flat state of stress. The paper presents the equations that can be used to simulate slow plastic material flows compressed between rigid plates, converging with constant acceleration. In the above equations we neglect convective terms, which greatly simplifies all calculations. The Lie algebra of point symmetries admitted by these equations is calculated for reduced equations. It has dimension eight. The optimal system of one-dimensional subalgebras is constructed for this algebra. It allows to give a view of all the different invariant solutions of rank two. That means such solutions depend only on two independent variables. To demonstrate this we offer a table of switches of all basis operators, as well as a table of all internal automorphisms functioning. One of the solutions, which simulates the slow plastic flow of the material compressed between rigid plates, converging with constant acceleration, built in. Among the most popular solutions in the flat theory of ideal plasticity is the Prandtl’s solution, which describes the compression of a plastic layer between rigid plates. In this case, the plates approach at a constant speed. The popularity of the solution is explained by its simplicity, as well as the fact that it can be used to describe various technological processes. The analogue of such a solution for the plane stress state cannot be constructed. In general, there are big problems with finding analytical solutions for the plane state of stress. It is caused by the fact that the equations describing this state are quite complex, even in spite of their linearization. In one of the previous works, one of the authors of the present article managed to find a solution that describes compression of a plastic layer between rigid plates which converge with constant acceleration. In this work the analogue of such a solution is found for the plane stress state. The authors hope that the suggested solution can also be used for the analysis of real technological processes.
Keywords: plane stress, the exact solution, non-stationary process.
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Senashov Sergey Ivanovich – Dr. Sc., professor, head of Department of Information Economic Systems, Reshetnev Siberian State University of Science and Technology. E-mail: sen@sibsau.ru.
Filyushina Elena Vladimirovna – Cand. Sc., Docent, Department of Information Economic Systems, Reshetnev Siberian State University of Science and Technology. E-mail: filyushina@sibsau.ru.

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