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 Issues2012-5pp.604-610

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Total articles in the database: 10482
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I.I. Argatov, "The contact problem for a periodic cluster of microcontacts," J. Appl. Math. Mech. 76 (5), 604-610 (2012)
Year 2012 Volume 76 Issue 5 Pages 604-610
Title The contact problem for a periodic cluster of microcontacts
Author(s) I.I. Argatov (St Petersburg, Russia, ivan.argatov@gmail.com)
Abstract The three-dimensional contact problem of the linear theory of elasticity is investigated for a system consisting of a large number of small punches, periodically arranged within a limited area on the boundary of an elastic semi-infinite body. The problem is investigated by a method which combines the averaging method and the method of matched asymptotic expansions. It is assumed that the ratios of the diameters of the actual contact areas to the distance between them are small, and each such ratio for neighbouring contact areas is in proportion to the ratio of the dimension of the periodic cell to the diameter of the nominal contact area. The asymptotic form of the doubly periodic contact problem for an elastic half-space is constructed. An approximate solution, in explicit form, is constructed for circular and elliptic contact areas. In the first case, the results agree with the well-known solution in the literature, obtained by another method.
Received 11 March 2012
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