 | | 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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| V.V. Vasiliev and S.A. Lurie, "Nonlocal Solutions to Singular Problems of Mathematical Physics and Mechanics," Mech. Solids. 53 (S2), 135-144 (2018) |
| Year |
2018 |
Volume |
53 |
Number |
S2 |
Pages |
135-144 |
| DOI |
10.3103/S0025654418050163 |
| Title |
Nonlocal Solutions to Singular Problems of Mathematical Physics and Mechanics |
| Author(s) |
V.V. Vasiliev (Ishlinsky Institute for Problems in Mechanics, Russian Academy of Sciences, Moscow, 119526 Russia; Institute of Applied Mechanics, Russian Academy of Sciences, Moscow, 125040 Russia, vvvas@dol.ru)
S.A. Lurie (Ishlinsky Institute for Problems in Mechanics, Russian Academy of Sciences, Moscow, 119526 Russia; Institute of Applied Mechanics, Russian Academy of Sciences, Moscow, 125040 Russia, salurie@mail.ru) |
| Abstract |
Second-order partial differential equations are considered that describe the behavior of
elastic bodies and have singular solutions. In contrast to the common differential calculus based on the
analysis of the function behavior in the neighborhood of a point at infinitesimal variation of arguments, the nonlocal function and its derivative, which describe the behavior of the function in a small,
but finite, interval of variation of the argument, are introduced. As a result, the order of the equations
under consideration increases up to fifth, and the solution to the traditionally singular problems of
mathematical physics appears regular. The solution to the nonlocal problem depends on the constant
coefficient, which is suggested to be determined experimentally. Possible applications we consider
include the generalized solutions to the equation of mathematical physics and mechanics in Cartesian,
polar, and spherical coordinates, governing the bending of the thin membrane and the stress state of
the elastic orthotropic sphere. |
| Received |
16 May 2017 |
| Link to Fulltext |
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