 | | 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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| D. A. Pozharskii, "Contact with adhesion between flexible plates and an elastic wedge," Mech. Solids. 39 (4), 46-54 (2004) |
| Year |
2004 |
Volume |
39 |
Number |
4 |
Pages |
46-54 |
| Title |
Contact with adhesion between flexible plates and an elastic wedge |
| Author(s) |
D. A. Pozharskii (Rostov-on-Don) |
| Abstract |
The tree-dimensional problem of equilibrium of an elastic wedge whose surfaces are reinforced (with complete adhesion) by thin plates which are rigid in tension but perfectly flexible. The problem is symmetric with respect to the bisecting half-plane of the wedge. The plates are subjected to prescribed tangential forces. The desired quantities are the tangential stresses in the contact region, translational displacement, and angle of rotation of a plate. The relations that enable one to calculate completely the displacement vector and stress tensor in the three-dimensional elastic wedge whose surfaces are subjected to symmetric tangential loads directed arbitrarily are presented. These relations generalize the solutions obtained in [1-3] in which the tangential load is perpendicular to the edge of the wedge. With the aid of two Green's functions obtained, the contact problem is reduced to the system of two integral equations for the tangential stresses. In the case of elliptic plates, this system is solved by using the regular asymptotic method. As the zero term of the asymptotic relation, the exact solution of a similar problem for plates on the elastic half-space [4] is used. Numerical examples are presented.
For two-dimensional contact problems with friction and adhesion, asymptotic methods were used in [5, 6]. |
| References |
| 1. | I. A. Lubyagin, D. A. Pozharskii, and M. I. Chebakov,
"Generalization of the Boussinesq and Cerruti problems for the case of an elastic three-dimensional wedge," Doklady AN SSSR, Vol. 321, No. 1,
pp. 58-62, 1991. |
| 2. | D. A. Pozharskii, "On the 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. | V. M. Alexandrov and D. A. Pozharskii, Three-Dimensional Contact
Problems, Kluwer Academic Publishers, Dordrecht, 2001. |
| 4. | V. M. Alexandrov, B. I. Smetanin, and B. V. Sobol', Thin Stress Concentrators in Elastic Bodies [in Russian], Nauka, Moscow, 1993. |
| 5. | A. S. Solov'ev, "On an integral equation and its applications to contact problems of elasticity taking into account the forces of friction and adhesion," PMM [Applied Mathematics and Mechanics], Vol. 33, No. 6, pp. 1042-1050, 1969. |
| 6. | V. M. Alexandrov, "On two-dimensional problems of elasticity in the presence of adhesion or friction," PMM [Applied Mathematics and Mechanics],
Vol. 34, No. 2, pp. 246-257, 1970. |
| 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. |
| 9. | S. G. Mikhlin, Variational Methods in Mathematical Physics [in Russian], Gostekhizdat, Moscow, 1957. |
| 10. | B. I. Smetanin and B. V. Sobol', "Equilibrium of an elastic layer weakened by flat cracks," PMM [Applied Mathematics and Mechanics], Vol. 48,
No. 6, pp. 1030-1038, 1984. |
|
| Received |
21 May 2002 |
| << Previous article | Volume 39, Issue 4 / 2004 | Next article >> |
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