 | | 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: | | 11223 |
| In Russian (Èçâ. ÐÀÍ. ÌÒÒ): | | 8011
|
| In English (Mech. Solids): | | 3212 |
|
| << Previous article | Volume 53, Issue 4 / 2018 | Next article >> |
| 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 |
| 1. | V.V. Vasiliev,
"Stress Tensor Symmetry and Singular Solutions in the Theory of Elasticity,"
Izv. Akad. Nauk. Mekh. Tverd. Tela,
No. 2, 62-72 (2010)
[Mech. Sol. (Engl. Transl.)
45 (2), 205-213 (2010)]. |
| 2. | V.V. Vasiliev and S.A. Lurie,
"On the Solution Singularity in the Plane Elasticity Problem for a Cantilever Strip,"
Izv. Akad. Nauk. Mekh. Tverd. Tela,
No. 4, 40-49 (2013)
[Mech. Sol. (Engl. Transl.)
48 (4), 388-396 (2013)]. |
| | |
| 3. | V.V. Vasiliev and S.A. Lurie,
"Continuous Model with Microstructure,"
Comp. Nanostruct.
7 (1), 2-10 (2015). |
| 4. | V.V. Vasiliev and S.A. Lurie,
"Generalized Theory of Elasticity,"
Izv. Akad. Nauk. Mekh. Tverd. Tela,
No. 4, 16-27 (2015)
[Mech. Sol. (Engl. Transl.)
50 (4), pp. 379-388 (2015)]. |
| 5. | V.V. Vasiliev and S.A. Lurie,
"Generalized Solution of the Problem on a Circular Membrane Loaded by a Lumped Force,"
Izv. Akad. Nauk. Mekh. Tverd. Tela,
No. 3, 115-119 (2061)
[Mech. Sol. (Engl. Transl.)
51 (3), 334-338 (2011)]. |
| 6. | V.V. Vasiliev and S.A. Lurie,
"New Solution of the Plane Problem for an Equilibrium Crack,"
Izv. Akad. Nauk. Mekh. Tverd. Tela,
No. 5, 61-67 (2016)
[Mech. Sol. (Engl. Transl.)
51 (5), 557-561 (2016)]. |
| 7. | V.V. Vasiliev and S.A. Lurie,
"New Solution of Axisymmetric Contact Problem of Elasticity,"
Izv. Akad. Nauk. Mekh. Tverd. Tela,
No. 5, 12-21 (2017)
[Mech. Sol. (Engl. Transl.)
52 (5), 479-487 (2017)]. |
| 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). |
| 9. | M.Yu. Gutkin,
"Nanoscopics of Dislocations and Disclinations in Gradient Elasticity,"
Rev. Adv. Mater. Sci.
No. 1, 27-60 (2000). |
| 10. | M. Lazar and G.A. Maugin,
"A Note on Line Forces in Gradient Elasticity,"
Mech. Res. Commun.
33, 674-680 (2006). |
| 11. | M. Lazar,
"The Fundamentals of Non-singular Dislocations in the Theory of Gradient Elasticity: Dislocation Loops and Straight Dislocations,"
Int. J. Sol. Struct.
50, 352-362 (2013). |
| 12. | P.F. Papkovich,
Theory of Elasticity
(Oborongiz, Moscow-Leningrad, 1939) [in Russian]. |
| 13. | V. Novatskii,
Theory of elasticity
(Nauka, Moscow, 1975) [in Russian]. |
| 14. | L.D. Landau and E.M. Lifschitz,
Fluid Mechanics
(Nauka, Moscow, 1986) [in Russian]. |
|
| Received |
02 March 2018 |
| Link to Fulltext |
|
| << Previous article | Volume 53, Issue 4 / 2018 | Next article >> |
|
 If you find a misprint on a webpage, please help us correct it promptly - just highlight and press Ctrl+Enter
|
|
Russian 
English