 | | 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: | | 12949 |
| In Russian (Èçâ. ÐÀÍ. ÌÒÒ): | | 8096
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| In English (Mech. Solids): | | 4853 |
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| V.V. Vasiliev, S.A. Lurie, and V.A. Salov, "Nonlocal Solutions of the Theory of Elasticity Problems for an Infinite Space Loaded with Concentrated Forces," Mech. Solids. 59 (4), 1833-1840 (2024) |
| Year |
2024 |
Volume |
59 |
Number |
4 |
Pages |
1833-1840 |
| DOI |
10.1134/S0025654424700328 |
| Title |
Nonlocal Solutions of the Theory of Elasticity Problems for an Infinite Space Loaded with Concentrated Forces |
| Author(s) |
V.V. Vasiliev (Central Research Institute of Special Engineering, Khotkovo, Moscow Region, 141371 Russia, vvvas@dol.ru)
S.A. Lurie (Institute of Applied Mechanics RAS, Moscow, 125040 Russia, salurie@mail.ru)
V.A. Salov (Central Research Institute of Special Engineering, Khotkovo, Moscow Region, 141371 Russia, snegiricentral@yandex.ru) |
| Abstract |
Two classical problems of the theory of elasticity are considered in the paper. The first is the Kelvin problem for an infinite space loaded with a concentrated force. The classical solution is singular
and specifies an infinitely high displacement of the point of the force application which has no physical meaning. To obtain a physically consistent solution, the nonlocal theory of elasticity is used, which, in contrast to the classical theory, is based on the equations derived for an element of continuum that
has small but finite dimensions, and allows one to obtain regular solutions for traditional singular
problems. The equations of the nonlocal theory include an additional experimental constant, which
has the dimension of length and cannot be determined for a space problem. Consequently, the second
problem for an infinite plane loaded with two concentrated forces lying on the same straight line and
acting in the opposite directions is considered. The classical solution of this problem is also singular
and specifies an infinitely high elongation of the distance between the forces, irrespective of their magnitude. The solution of this problem is also obtained within the framework of the nonlocal theory of
elasticity, which specifies a regular dependence of this distance on the forces magnitude. This solution also includes an additional constant which is determined experimentally for a plane problem. |
| Keywords |
theory of elasticity, Kelvin problem, singular solution |
| Received |
26 December 2023 | Revised |
16 January 2024 | Accepted |
17 January 2024 |
| Link to Fulltext |
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