 | | 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. I. Ostrik and A. F. Ulitko, "Contact problem for a rigid wedge and an elastic half-plane with adhesion and slip," Mech. Solids. 38 (1), 75-85 (2003) |
| Year |
2003 |
Volume |
38 |
Number |
1 |
Pages |
75-85 |
| Title |
Contact problem for a rigid wedge and an elastic half-plane with adhesion and slip |
| Author(s) |
V. I. Ostrik (Sumy)
A. F. Ulitko (Kiev) |
| Abstract |
Problems of contact interaction of a rigid cone or a wedge and an elastic
half-space,
with friction forces in the contact region neglected, were considered in [1-3].
Contact of a rigid and an elastic wedges with the initial contact point
at the vertex was studied in [4].
In the case of contact with friction
of two elastic (or an elastic and a rigid) bodies, the central part of the
contact region may contain a zone of complete adhesion in which the ratio
of the tangential stresses to the normal pressure does not exceed the
friction coefficient. On the other part of the contact region near its
boundary, sliding of the bodies is observed, with the tangential stresses
and the normal pressure related by the Amonton (Coulomb) law.
For the investigation of
contact with friction and partial adhesion
an incremental method was proposed in [5, 6].
According to this approach, the stress state is calculated step-by-step
as the contact region increases with the growth of the load,
under the assumption of static equilibrium on each step.
In contrast to the incremental method, a direct method of solving
the problem was proposed in [7] on the basis of the fact that
at all instants of loading, the stress field remains self-similar
and the ratio of the dimensions of the adhesion and the slip regions
remains constant. Similarity considerations can be used for
stating boundary condition for the tangential displacements in the
adhesion zone.
A contact problem for an elastic half-space penetrated by an indentor of
polynomial profile, in particular, by a cone, was solved in [8], with
friction forces, as well as adhesion and slip, in the contact region
taken into account. An approximate solution of this problem was obtained
under the condition that tangential stresses, being small, do not affect
the distribution of the normal pressure in the contact region. |
| References |
| 1. | A. E. H. Love, "Boussinesq's problem for a rigid cone,"
Quart. J. Math., Vol. 10, pp. 161-175, 1939. |
| 2. | I. N. Sneddon, "Boussinesq's problem for a rigid cone,"
Proc. Cambridge Phil. Soc., Vol. 44, pp. 492-507, 1948. |
| 3. | I. N. Sneddon, Fourier Transforms [Russian translation], Izd-vo Inostr. Lit-ry,
Moscow, 1955. |
| 4. | A. F. Ulitko and N. E. Kachalovskaya,
"Contact interaction between a rigid and an elastic wedge
with the initial single-point contact at their common vertex,"
Doklady NAN Ukrainy, No. 1, pp. 51-54, 1995. |
| 5. | L. E. Goodman,
"Contact stress analysis of normally loaded rough spheres,"
Trans. ASME. Ser. E.J. Appl. Mech., Vol. 29, No. 3, pp. 515-522, 1962. |
| 6. | V. I. Mossakovskii,
"Compression of Elastic Bodies with Adhesion," PMM [Applied Mathematics and Mechanics], Vol. 27, No. 3,
pp. 418-427, 1963. |
| 7. | D. A. Spence, "Self-similar solutions to adhesive contact
problems with incremental loading," Proc. Roy. Soc. London, Ser. A.
Vol. 35, No. 1480, pp. 55-80, 1973. |
| 8. | D. A. Spence,
"An eigenvalue problem for elastic contact with nite friction,"
Proc. Cambridge Phil. Soc., Vol. 73, No. 1, pp. 249-268, 1973. |
| 9. | K. L. Johnson, Contact Mechanics [Russian translation], Mir,
Moscow, 1989. |
| 10. | Ya. S. Uflyand, Integral Transforms in Elasticity Problems
[in Russian], Nauka, Leningrad, 1967. |
| 11. | F. D. Gakhov, Boundary Value Problems [in Russian], Fizmatgiz, Moscow, 1963. |
| 12. | B. Noble, Method Based of Wiener-Hopf Technique for the
Solution of Partial Differential Equations [Russian translation], Izd-vo Inostr. Lit-ry,
Moscow, 1962. |
| 13. | M. V. Fedoryuk, Asymptotics: Integrals and Series [in Russian], Nauka,
Moscow, 1987. |
| 14. | L. A. Galin, Contact Problems in Elasticity [in Russian],
Gostekhteorizdat, Moscow, 1953. |
|
| Received |
15 September 2000 |
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