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

Russian Academy of Sciences
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in January 1936
(Translated from 1958)
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ISSN 0021-8928
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IssuesArchive of Issues2012-1pp.120-124

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V.M. Aleksandrov, "Axisymmetric contact problems for a prestressed incompressible elastic layer," J. Appl. Math. Mech. 76 (1), 120-124 (2012)
Year 2012 Volume 76 Issue 1 Pages 120-124
Title Axisymmetric contact problems for a prestressed incompressible elastic layer
Author(s) V.M. Aleksandrov (Moscow, Russia)
Abstract Two axisymmetric problems of the indentation without friction of an elastic punch into the upper face of a layer when there is a uniform field of initial stresses in the layer are considered. The model of an isotropic incompressible non-linearly elastic material, specified by a Mooney potential, is used. Two cases are investigated: when the lower face of the layer is rigidly clamped after it is prestressed, and when the lower face of the layer is supported on a rigid base without friction after it is prestressed. It is assumed that the additional stresses due to the action of the punch on the layer are small compared with the initial stresses; this enables the problem of determining the additional stresses to be linearized. The problem is reduced to solving integral equations of the first kind with symmetrical irregular kernels relative to the pressure in the contact area. Approximate solutions of the integral equations are constructed by the method of orthogonal polynomials for large values of the parameter characterizing the relative layer thickness. The case of a punch with a plane base is considered as an example.
Received 29 April 2010
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