Mechanics of Solids (about journal) Mechanics of Solids
A Journal of Russian Academy of Sciences
 Founded
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IssuesArchive of Issues2023-7pp.2694-2702

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V.A. Babeshko, O.V. Evdokimova, O.M. Babeshko, M.V. Zaretskaya, and V.S. Evdokimov, "On the Contact Problem with a Deformable Die in a Quadrant," Mech. Solids. 58 (7), 2694-2702 (2023)
Year 2023 Volume 58 Number 7 Pages 2694-2702
DOI 10.3103/S0025654423070026
Title On the Contact Problem with a Deformable Die in a Quadrant
Author(s) V.A. Babeshko (Southern Scientific Center of the Russian Academy of Sciences, Rostov-on-Don, Russia; Kuban State University, Krasnodar, Russia, babeshko41@mail.ru)
O.V. Evdokimova (Southern Scientific Center of the Russian Academy of Sciences, Rostov-on-Don, Russia, evdokimova.olga@mail.ru)
O.M. Babeshko (Kuban State University, Krasnodar, Russia, babeshko49@mail.ru)
M.V. Zaretskaya (Kuban State University, Krasnodar, Russia, zarmv@mail.ru)
V.S. Evdokimov (Kuban State University, Krasnodar, Russia, evdok_vova@mail.ru)
Abstract This paper is the first ever rigorous investigation of a two-dimensional dynamic contact problem of the action of a deformable die on a quadrant of a multilayer medium. Compared to an absolutely rigid die, its deformable counterpart introduces additional features. They consist in the potential occurrence of discrete resonances predicted by Academician I. I. Vorovich. The paper shows that a method based on using brick-level elements makes it possible to derive an equation describing resonant frequencies to study contact problems with a deformable die made of complex-rheology materials, including smart materials. First of all, the case of a deformable die made of a simple-rheology material described by the Helmholtz equations is considered. Solutions of the boundary problems for complex-rheology dies are represented as a combination of solutions of boundary problems for simple-rheology dies.
Keywords contact problem, brick element, deformable die, Wiener–Hopf integral equation
Received 16 January 2023Revised 02 March 2023Accepted 02 March 2023
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