| ||Mechanics of Solids|
A Journal of Russian Academy of Sciences
in January 1966
Issued 6 times a year
Print ISSN 0025-6544
Online ISSN 1934-7936
Archive of Issues
|Total articles in the database:|| ||3639|
|In Russian (Èçâ. ÐÀÍ. ÌÒÒ):|| ||2053|
|In English (Mech. Solids):|| ||1586|
|M. I. Chebakov, "3D contact problem with friction for a layer," Mech. Solids. 37 (6), 48-56 (2002)|
||3D contact problem with friction for a layer|
||M. I. Chebakov (Rostov-on-Don)|
||A 3D contact problem of elasticity is considered to study the action
of a punch of an arbitrary shape on the surface of a layer
of thickness h. The contact region is not prescribed beforehand
but depends on the magnitudes of the normal force, P,
and the tangential force, T, acting on the punch.
Coulomb friction forces are assumed to act between the punch and the layer,
these forces being collinear to the tangential force T. The punch
does not rotate during the interaction. The surface acted upon by the punch
is stress-free outside the punch, while the other surface of the layer
is subject to zero displacement conditions. We consider the limiting
equilibrium case. The case of the quasi-static motion of the punch along
the surface of the layer in the moving reference frame can be considered
in a similar manner.|
An integral equation of this contact problem is obtained. To solve
this equation, we utilize the nonlinear boundary integral equation
method [1, 2]. The influence of the Coulomb friction coefficient,
the shape of the punch, the elastic constants, and the layer
thickness on the magnitude of contact stresses, the dependence
of the vertical displacement of the punch on the impressing force,
the contact region size and shape, and the displacement of points
of the layer surface outside the contact region is analyzed.
Plane problems [3, 4], 3D problems for a half-space [5, 6],
and 3D problems for a wedge [7, 8], with friction force
being taken into account,
have been considered previously by other authors.
|1. ||B. A. Galanov, "Hammerstein-type boundary equation method
for contact problems of elasticity in the case of unknown contact
PMM [Applied Mathematics and Mechanics], Vol. 49, No. 5, pp. 827-835, 1985.|
|2. ||B. A. Galanov, "Nonlinear boundary equations for contact problems
of elasticity," Doklady AN SSSR, Vol. 296, No. 4, pp. 812-815, 1987.|
|3. ||L. A. Galin, Contact Problems of Elasticity and Viscoelasticity
[in Russian], Nauka, Moscow, 1980.|
|4. ||V. M. Alexandrov, "On the plane contact problems of elasticity
with adhesion or friction,"
PMM [Applied Mathematics and Mechanics], Vol. 34, No. 2, pp. 246-257, 1970.|
|5. ||L. A. Galin and I. G. Goryacheva, "3D contact problem of the motion
of a punch with friction,"
PMM [Applied Mathematics and Mechanics], Vol. 46, No. 6, pp. 1016-1022, 1982.|
|6. ||A. S. Kravchuk, "The solution of some 3D contact problems
with friction on the contact surface,"
Trenie i Iznos, Vol. 2, No. 4, pp. 589-595, 1981.|
|7. ||D. A. Pozharskii, "3D contact problem for an elastic wedge
with friction in the unknown contact region,"
Doklady AN, Vol. 372, No. 3, pp. 333-336, 2000.|
|8. ||D. A. Pozharskii, "On the 3D contact problem for an elastic wedge
with friction forces,"
PMM [Applied Mathematics and Mechanics], Vol. 64, No. 1, pp. 151-159, 2000.|
|9. ||I. I. Vorovich, V. M. Alexandrov, and V. A. Babeshko,
Non-classical Mixed Problems of Elasticity [in Russian],
Nauka, Moscow, 1974.|
|10. ||A. I. Lur'e, Theory of Elasticity [in Russian],
Nauka, Moscow, 1970.|
||3 December 2001|