 | | Mechanics of Solids
A Journal of Russian Academy of Sciences | | Founded
in January 1966
Issued 6 times a year
Print ISSN 0025-6544
Online ISSN 1934-7936 |
Archive of Issues
| Total articles in the database: | | 12804 |
| In Russian (Èçâ. ÐÀÍ. ÌÒÒ): | | 8044
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| In English (Mech. Solids): | | 4760 |
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| V.A. Babeshko, O.V. Evdokimova, and O.M. Babeshko, "Exact Solution to the Contact Problem in a Quarter-Plane of a Multilayer Medium by the Universal Simulation Method," Mech. Solids. 57 (8), 2058-2065 (2022) |
| Year |
2022 |
Volume |
57 |
Number |
8 |
Pages |
2058-2065 |
| DOI |
10.3103/S0025654422080039 |
| Title |
Exact Solution to the Contact Problem in a Quarter-Plane of a Multilayer Medium by the Universal Simulation Method |
| Author(s) |
V.A. Babeshko (Federal Research Centre the Southern Scientific Centre RAS, Rostov-on-Don, Russia; Kuban State University, Krasnodar, Russia, babeshko41@mail.ru)
O.V. Evdokimova (Federal Research Centre the Southern Scientific Centre RAS, Rostov-on-Don, Russia, evdokimova.olga@mail.ru)
O.M. Babeshko (Kuban State University, Krasnodar, Russia, babeshko49@mail.ru) |
| Abstract |
In this paper, for the first time, an exact solution to the contact problem posed on the surface of a multilayer medium in a quarter-plane is constructed. This is achieved by applying a new universal modeling method developed for studying and solving boundary value problems for partial differential equations. In this paper, the method is applied to two-dimensional Wiener–Hopf integral
equations in the quarter-plane arising in mixed problems of deformable solid mechanics, in contact
problems. A feature of mixed problems for layered media is the presence of meromorphic functions in
Fourier transformations of the kernels of integral equations. As in differential equations, this made it
possible to find fragments of differential equations in the representation of Wiener–Hopf integral
equations and to find a way to reduce a two-dimensional integral equation to one-dimensional. This
makes it possible to reduce integral equations in this field to infinite systems of linear algebraic equations having an inverse infinite matrix. This type of integral equations is not available for numerical
solution, due to the unlimited scope of the equation, and has not been studied analytically before. The
exact solution to the two-dimensional Wiener–Hopf equation in a quarter-plane makes it possible to
construct high-precision solutions to contact problems in limited domains, just like in the one-dimensional case. Wiener–Hopf integral equations are widely used in various fields for materials with complex rheology, including strength theory, diffraction, flaw detection, and tribology. |
| Keywords |
contact problem, block element, rigid stump, Wiener–Hopf integral equation |
| Received |
17 March 2022 | Revised |
18 May 2022 | Accepted |
18 May 2022 |
| Link to Fulltext |
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