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IssuesArchive of Issues2001-5pp.18-24

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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
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