Mechanics of Solids (about journal) Mechanics of Solids
A Journal of Russian Academy of Sciences
in January 1966
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IssuesArchive of Issues2012-6pp.690-694

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Total articles in the database: 4725
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V.M. Alexandrov and L.A. Kostyreva, "Plane Contact Problem for a Prestressed Incompressible Elastic Layer Clamped along the Base," Mech. Solids. 47 (6), 690-694 (2012)
Year 2012 Volume 47 Number 6 Pages 690-694
DOI 10.3103/S0025654412060118
Title Plane Contact Problem for a Prestressed Incompressible Elastic Layer Clamped along the Base
Author(s) V.M. Alexandrov (Ishlinsky Institute for Problems in Mechanics, Russian Academy of Sciences, pr-t Vernadskogo 101, str. 1, Moscow, 119526 Russia)
L.A. Kostyreva (Lomonosov Moscow State University, GSP-2, Leninskie Gory, Moscow, 119992 Russia,
Abstract The problem of a rigid punch penetration into the upper face of a layer is considered in the case of a homogeneous field of initial stresses. The model of isotropic incompressible nonlinearly elastic material determined by the Mooney potential is used. The case of rigid clamping of the layer along its lower face is considered under the assumption that the additional stresses caused by the penetrating punch are small compared with the initial ones. This assumption allows one to linearize the problem of determining the additional stresses. This problem is then reduced to solving an integral equations of the first kind with a difference kernel which allows one to determine the pressure in the contact region. An asymptotic solution is constructed for large values of the parameter characterizing the relative thickness of the layer. A modified Multhopp-Kalandiya method is also used to obtain a solution for a wider range of the parameter.
Keywords contact problem, preliminary stress, layer, Mooney potential
1.  V. M. Alexandrov and L. M. Filippova, "The Contact Problem for a Heavy Half-Plane," Prikl. Mat. Mekh. 44 (3), 535-539 (1980) [J. Appl. Math. Mech. (Engl. Transl.) 44 (3), 375-378 (1980)].
2.  V. M. Alexandrov, "Axially Symmetric Contact Problem for an Elastic Infinite Cylinder," Izv. Akad. Nauk SSSR. Mekh. Mashinostr. No. 5, 91-94 (1962).
3.  I. I. Vorovich, V. M. Alexandrov, and V. A. Babeshko, Nonclassical Mixed Problems of Elasticity (Nauka, Moscow, 1974) [in Russian].
Received 01 February 2010
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