 | | 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.M. Alexandrov, "Spatial Contact Problems for a Prestressed Incompressible Elastic Layer," Mech. Solids. 46 (2), 275-279 (2011) |
| Year |
2011 |
Volume |
46 |
Number |
2 |
Pages |
275-279 |
| DOI |
10.3103/S0025654411020166 |
| Title |
Spatial Contact Problems for a Prestressed Incompressible Elastic Layer |
| Author(s) |
V.M. Alexandrov (Ishlinsky Institute for Problems in Mechanics, Russian Academy of Sciences, pr-t Vernadskogo 101, str. 1, Moscow, 119526 Russia, alexand@ipmnet.ru) |
| Abstract |
Two problems are considered on frictionless indentation of a stamp into the upper face of a layer with a homogeneous field of initial stresses present in the layer. The model of an isotropic incompressible nonlinearly-elastic material determined by the Mooney potential is used. The following two cases are studied: the lower face of the prestressed layer is rigidly fixed, and the lower face of a prestressed layer is supported by a rigid foundation without friction. It is assumed that the additional stresses due to the action of the stamp on the layer are small as compared with the initial stresses. This assumption makes it possible to linearize the problems of determining the additional stresses. In what follows, the problems are reduced to solving two-dimensional integral equations (IE) of the first kind with symmetric irregular kernels with respect to the pressure in the contact region. As an example, the case of an elliptic (in plan) stamp
acting on a layer is considered.
The spatial contact problem for a prestressed elastic half-space was first considered in [1]. |
| Keywords |
spatial problem, prestressed elastic body, indentation of elliptic stamp |
| References |
| 1. | K. M. Filippova,
"Three-Dimensional Contact Problem for a Prestressed Elastic Body,"
Prikl. Mat. Mekh.
42 (6), 1080-1084 (1978)
[J. Appl. Math. Mech. (Engl. Transl.)
42 (6), 1183-1188 (1978)]. |
| 2. | A. I. Lurie,
Nonlinear Theory of Elasticity
(Nauka, Moscow, 1980)
[in Russian]. |
| 3. | Ya. S. Ufland,
Integral Transforms in Elasticity Problems
(Nauka, Leningrad, 1967)
[in Russian]. |
| 4. | I. I. Vorovich, V. M. Alexandrov, and V. A. Babeshko,
Nonclassical Mixed Problems of Elasticity
(Nauka, Moscow, 1974)
[in Russian]. |
|
| Received |
06 December 2010 |
| Link to Fulltext |
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