 | | 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 |
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| In English (Mech. Solids): | | 4760 |
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| V. M. Alexandrov, M. Bach, and D. A. Pozharskii, "To three-dimensional contact problems with friction for an elastic wedge," Mech. Solids. 36 (5), 18-24 (2001) |
| Year |
2001 |
Volume |
36 |
Number |
5 |
Pages |
18-24 |
| Title |
To three-dimensional contact problems with friction for an elastic wedge |
| Author(s) |
V. M. Alexandrov (Moscow)
M. Bach (Stuttgart)
D. A. Pozharskii (Moscow) |
| Abstract |
A three-dimensional elastic wedge is considered, one surface of which is
acted on by normal and tangential (perpendicular to the edge of the wedge)
loads, whereas the other surface is in the conditions of either rigid or
sliding fixing. The relations permitting one to completely
calculate the displacement vector and stress tensor in this wedge
are presented. Previously in [1], the boundary value
problems for such a wedge were
reduced to Fredholm integral equations of the second kind.
Relations for the wedge one surface of which is free of stress are given
in [2]. On the basis of the solutions obtained, we consider
quasi-static contact problems for a punch moving along a surface of the
elastic wedge in the direction perpendicular to the edge of the wedge. The
punch is an elliptic paraboloid which is strongly extended along the edge.
For this reason, the friction forces are assumed to be collinear to the
direction of the punch motion. The influence of the Coulomb friction
coefficient and the wedge angle on the contact pressure
distribution, relation between the indentation force and upsetting of the
punch, and surface shape (normal displacement) outside the contact region
is analyzed by means of the Galanov-Newton method of nonlinear boundary
integral equations [3, 4]. This method was used in [2] for solving a
similar contact problem for the case where one surface of the wedge is free
of stress. The three-dimensional contact problem with friction for
a half-space was analyzed in [5] by using the method of successive
approximations. The authors of this paper considered the symmetric contact
problem with friction for two punches on a half-space. This problem
corresponds to a quarter-space (a particular case of the wedge) in the
conditions of sliding fixing. (The contact problem for a wedge in the
conditions of sliding fixing is equivalent to the symmetric contact problem
for two punches applied to different surfaces of the wedge with double
angle). |
| References |
| 1. | I. A. Lubyagin, D. A. Pozharskii, and M. I. Chebakov,
"The generalization of the Boussinesq and Cerruti problems for an elastic
three-dimensional wedge," Doklady AN SSSR, Vol. 321, No. 1, pp. 58-62,
1991. |
| 2. | D. A. Pozharskii, "On a three-dimensional contact problem for
an elastic wedge taking into account the friction forces," PMM [Applied
Mathematics and Mechanics], Vol. 64, No. 1, pp. 151-159, 2000. |
| 3. | B. A. Galanov, "Method of boundary equations of Hammerstein
type for contact problems of elasticity in the case of unknown
contact areas," PMM [Applied Mathematics and Mechanics], Vol. 49, No. 5,
pp. 827-835, 1985. |
| 4. | D. A. Pozharskii, "On a three-dimensional contact problem for
an elastic wedge with unknown contact area," PMM [Applied Mathematics and
Mechanics], Vol. 59, No. 5, pp. 812-818, 1995. |
| 5. | L. A. Galin and I. G. Goryacheva, "Three-dimensional contact
problem on a punch moving with friction," PMM [Applied Mathematics and
Mechanics], Vol. 46, No. 6, pp. 1016-1022, 1982. |
| 6. | V. M. Alexandrov and D. A. Pozharskii, Nonclassical
Three-Dimensional Problems of the Mechanics of Contact Interactions of
Elastic Bodies [in Russian], Faktorial, Moscow, 1998. |
| 7. | A. P. Prudnikov, Yu. A. Brychkov, and O. I. Marichev, Integrals and
Series. Special Functions [in Russian], Nauka, Moscow, 1983. |
| 8. | H. G. Hahn, Elastizitätstheorie, Teubner, Stuttgart, 1985. |
|
| Received |
03 May 2001 |
| << Previous article | Volume 36, Issue 5 / 2001 | Next article >> |
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