 | | 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
|
| In English (Mech. Solids): | | 4760 |
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| V.V. Vasil'ev and S.A. Lurie, "New Solution of Axisymmetric Contact Problem of Elasticity," Mech. Solids. 52 (5), 479-487 (2017) |
| Year |
2017 |
Volume |
52 |
Number |
5 |
Pages |
479-487 |
| DOI |
10.3103/S0025654417050028 |
| Title |
New Solution of Axisymmetric Contact Problem of Elasticity |
| Author(s) |
V.V. Vasil'ev (Ishlinsky Institute for Problems in Mechanics of the Russian Academy of Sciences, pr. Vernadskogo 101, str. 1, Moscow, 119526 Russia, vvvas@dol.ru)
S.A. Lurie (Ishlinsky Institute for Problems in Mechanics of the Russian Academy of Sciences, pr. Vernadskogo 101, str. 1, Moscow, 119526 Russia; Institute of Applied Mechanics of the Russian Academy of Sciences, Leningradskii pr. 7, Moscow, 125040 Russia) |
| Abstract |
We consider two problems of elasticity, namely, the Boussinesq problem about the action of a lumped force on a half-space and the related problem about the interaction of the half-space with a cylindrical rigid punch with plane base. In the classical statement, these problems have singular solutions. In the Boussinesq problem, the displacement under the action of the force is infinitely large, and in the punch problem, the infinitely large variable is the pressure on the punch boundary. In the present paper, these problems are solved with the use of relations of generalized elasticity derived regarding a medium element of small but finite dimensions rather than a traditional infinitesimal element. The structure parameter of the medium contained in the solutions can be determined experimentally. The obtained generalized solutions of the problems under study are regular. |
| Keywords |
theory of elasticity, Boussinesq problem, punch problem |
| References |
| 1. | B. N. Zhemochkin,
Theory of Elasticity
(Stroivoenmorizdat, Moscow, 1948)
[in Russian]. |
| 2. | A. I. Lurie,
Spatial Problems of Theory of Elasticity
(GITTL, Moscow, 1955)
[in Russian]. |
| 3. | V. V. Vasiliev and S. A. Lurie,
"Model of a Solid with Microstructure,"
Kompoz. Nanostrukt.
7 (1), 25-33 (2015). |
| 4. | V. V. Vasil'ev and S. A. Lurie,
"Generalized Theory of Elasticity,"
Izv. Ross. Akad. Nauk. Mekh. Tverd. Tela,
No. 4, 16-27 (2015)
[Mech. Solids (Engl. Transl.)
50 (4), 379-388 (2015)]. |
| 5. | V. V. Vasil'ev and S. A. Lurie, "Generalized Solution of the
Problem of a Circular Membrane Loaded by a Lumped Force," Izv.
Ross. Akad. Nauk. Mekh. Tverd. Tela, No. 3, 115-119 (2016) [Mech.
Solids (Engl. Transl.) 51 (3), 334-338 (2016)]. |
| 6. | V. V. Vasil'ev and S. A. Lurie,
"New Solution of the Plane Problem for an Equilibrium Crack,"
Izv. Ross. Akad. Nauk. Mekh. Tverd. Tela,
No. 5, 61-67 (2016)
[Mech. Solids (Engl. Transl.)
51 (5), 557-561 (2016)]. |
| 7. | M. Abramowitz and I. Stegun (Editors),
Handbook of Mathematical Functions, with Formulas, Graphs, and Mathematical Tables
(Gov. Print off., Wasgington, 1964; Nauka, Moscow, 1979). |
|
| Received |
10 January 2017 |
| Link to Fulltext |
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