Journal of Applied Mathematics and Mechanics (about journal) Journal of Applied
Mathematics and Mechanics

Russian Academy of Sciences
 Founded
in January 1936
(Translated from 1958)
Issued 6 times a year
ISSN 0021-8928
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IssuesArchive of Issues2015-6pp.611-617

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Total articles in the database: 10440
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Ye.V. Kovalenko, "An approximate analytical solution of the integral equations of non-axisymmetric contact problems for a ring-shaped domain," J. Appl. Math. Mech. 79 (6), 611-617 (2015)
Year 2015 Volume 79 Issue 6 Pages 611-617
DOI 10.1016/j.jappmathmech.2016.04.008
Title An approximate analytical solution of the integral equations of non-axisymmetric contact problems for a ring-shaped domain
Author(s) Ye.V. Kovalenko (Financial University at the Government of the Russian Federation, Moscow, Russia, evg.koval@mail.ru)
Abstract An algorithm is developed for solving the integral equations of the first and third kind to which non-axisymmetric mixed problems in continuum mechanics and mathematical physics reduce on replacing the boundary conditions in a ring-shaped domain. The use of the Bubnov-Galerkin procedure in conjunction with addition theorems for Bessel functions is the basis of this method. In the final stage of solving integral equations corresponding to arbitrary harmonics of a mixed problem for a ring-shaped domain, the method enables the coefficients of the linear algebraic systems to be represented in the form of simple quadratures that are convenient for numerical implementation. The discussion is carried out using the example of a contact problem in the theory of elasticity for a linearly deformable base of a general type strengthened by a thin coating along its boundary. The effect of the relative thickness of the coating, its stiffness and the shape of the bottom of a ring-shaped punch on the basic contact characteristics is investigated. Publications on the known results are available in the special case of axisymmetric problems and the problem of an inclined ring-shaped punch.
Received 02 February 2015
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