 | | 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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| S.A. Lurie and D.B. Volkov-Bogorodskii, "Green Tensor and Solution of the Boussinesq Problem in the Generalized Theory of Elasticity," Mech. Solids. 53 (4), 440-453 (2018) |
| Year |
2018 |
Volume |
53 |
Number |
4 |
Pages |
440-453 |
| DOI |
10.3103/S0025654418040106 |
| Title |
Green Tensor and Solution of the Boussinesq Problem in the Generalized Theory of Elasticity |
| Author(s) |
S.A. Lurie (Ishlinsky Institute for Problems in Mechanics RAS, pr. Vernadskogo 101, str. 1, Moscow, 119526 Russia; Institute of Applied Mechanics of Russian Academy of Sciences, Leningradsky pr. 7, Moscow, 125040, Russia, salurie@mail.ru)
D.B. Volkov-Bogorodskii (Institute of Applied Mechanics of Russian Academy of Sciences, Leningradsky pr. 7, Moscow, 125040, Russia) |
| Abstract |
The fundamental spatial problems of the theory of elasticity such as the problem of constructing Green tensor and the Boussinesq problem of the action of a concentrated force on a half-space are considered. According to the classical theory of elasticity, these problems are singular. It is shown that an analytical solution of such problems can be constructed by the Papkovich-Neuber representation without invoking symmetry conditions. This makes it possible to present the solution of the problems under consideration in a single form and allows us to write an explicit solution of half-space loaded by a concentrated vector-force having non-zero projections onto the normal to the plane bounding the half-space and onto the plane itself.
This paper deals with the generalized regular solutions of the considered fundamental problems of the elasticity. The solutions are limited at a singular point and damp at infinity. |
| Keywords |
generalized theory of elasticity, Papkovich-Neuber representation, regular solution, Green tensor, Boussinesq problem |
| References |
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[Mech. Sol. (Engl. Transl.)
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| 2. | V.V. Vasiliev and S.A. Lurie,
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| | |
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| 5. | V.V. Vasiliev and S.A. Lurie,
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| 6. | V.V. Vasiliev and S.A. Lurie,
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| 7. | V.V. Vasiliev and S.A. Lurie,
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[Mech. Sol. (Engl. Transl.)
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| 8. | V.V. Vasiliev and S.A. Lurie,
"Non-local Solutions of Singular Problems of Mathematical Physics and Mechanics,"
Prikl. Mat. Mech.
82 (4), 459-471 (2018). |
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(Oborongiz, Moscow-Leningrad, 1939) [in Russian]. |
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|
| Received |
02 March 2018 |
| Link to Fulltext |
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