Mechanics of Solids (about journal) Mechanics of Solids
A Journal of Russian Academy of Sciences
in January 1966
Issued 6 times a year
Print ISSN 0025-6544
Online ISSN 1934-7936

Russian Russian English English About Journal | Issues | Guidelines | Editorial Board | Contact Us

IPMech RASWeb hosting is provided
by the Ishlinsky Institute for
Problems in Mechanics
of the Russian
Academy of Sciences
IssuesArchive of Issues2018-4pp.397-410

Archive of Issues

Total articles in the database: 9179
In Russian (. . ): 6485
In English (Mech. Solids): 2694

<< Previous article | Volume 53, Issue 4 / 2018 | Next article >>
V.V. Vasiliev, "Singular Solutions in the Problems of Mechanics and Mathematical Physics," Mech. Solids. 53 (4), 397-410 (2018)
Year 2018 Volume 53 Number 4 Pages 397-410
DOI 10.3103/S0025654418040052
Title Singular Solutions in the Problems of Mechanics and Mathematical Physics
Author(s) V.V. Vasiliev (Ishlinsky Institute for Problems in Mechanics RAS, pr. Vernadskogo 101, str. 1, Moscow, 119526 Russia,
Abstract A problem of the solutions singularity for applied problems is discussed. It is proposed to qualify such solutions as formal mathematical results that arise from the discrepancy between the mathematical and physical models of the phenomenon or object being studied. As examples, we consider the singular solution of the Schwarzschild problem in the general theory of relativity (serving as the mathematical basis for the existence of objects called the Black Holes), the solution of the mathematical physics problem for a circular membrane loaded in the center by a concentrated force, and the solution for the problems of the theory of elasticity about a cylindrical punch and an expandable plate with a crack. A generalization of the classical definition for a function and its derivative is proposed. This generalization makes it possible to obtain regular solutions of traditional singular problems.
Keywords general theory of relativity, mathematical physics, theory of elasticity, singular solutions
1.  I.D. Novikov, Black Holes and the Universe (Molodaya Gvardia, Moscow, 1985) [in Russian].
2.  K. Thorne, Black Holes and Time Warps (Fizmatgiz, Moscow, 2009) [in Russian].
3.  S.L. Sobolev, Equations of Mathematical Physics (GITTL, Moscow, Leningrad, 1950) [in Russian].
4.  D. Singh, General Relativity (Izd-vo Inostr. Lit-ry, Moscow, 1963) [in Russian].
5.  A. Einstein, "On a Stationary System with Spherical Symmetry Consisting of Many Gravitating Masses," Ann. Math. 40 (4), 922-936 (1939).
7.  V.V. Vasiliev and L.V. Fedorov, "Stress State of an Elastic Ball in a Spherically Symmetric Gravitational Field," Izv. Akad. Nauk. Mekh. Tverd. Tela No. 4, 15-29 (2014) [Mech. Sol. (Engl. Transl.) 49 (4), 379-381 (2014)].
8.  S.G. Mikhlin, Linear Partial Differential Equations (Vyshshaya Shkola, Moscow, 1977) [in Russian].
9.  Theory of Flexible Round plates (IL, Moscow, 1967) [in Russian].
10.  V.V. Vasiliev and L.V. Fedorov, "Solution of a Spherically Symmetric Static Problem of General Relativity for an Elastic Solid Sphere," Appl. Phys. Res. 9 (6), 8-13 (2017).
11.  G.P. Cherepanov, "Singular Solutions in the Theory of Elasticity," in Mechanics of Solids (Sudostroenie, Leningrad, 1970), pp. 467-479 [in Russian].
12.  A. Love, Mathematical Theory of Elasticity (ONTTI, Moscow, Leningrad, 1935) [in Russian].
13.  A. Feppl and L. Feppl, Strength and Deformation. Applied Theory Elasticity (GTTI, Moscow, 1933) [in Russian].
14.  A.I. Lurie, Spatial Problems of Elasticity Theory (GITTL, Moscow, 1955) [in Russian].
15.  S.P. Timoshenko and J.N. Goodier, Theory of Elasticity (Nauka, Moscow, 1975) [in Russian].
16.  Yu.N. Rabotnov, Mechanics of a Deformable Solid (Nauka, Moscow, 1979) [in Russian].
17.  Fracture. Edited by E. Libowitz. Vol. 2. Mathematical Fundamentals (AcademicPress, New York and London, 1968).
18.  S.A. Lurie and V.V. Vasiliev, The Biharmonic Problem in the Theory of Elasticity (Gordon and Breach Publishers, 1995).
19.  V.V. Vasiliev and S.A. Lurie, "Continuous Model with Microstructure," Komp. Nanost. 7 (1), 25-33 (2015).
20.  V.V. Vasiliev and S.A. Lurie, "Generalized Theory of Elasticity," Izv. Akad. Nauk. Mekh. Tverd. Tela No. 4, 16-27 (2015) [Mech. Solids (Engl. Transl.) 50 (4), 379-388 (2015)]
21.  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. Solids (Engl. Transl.) 52 (5), 479-487 (2017)]
22.  A.V. Andreev, Engineering Methods for Determining Stress Concentration in Machine Elements (Mashinostroenie, Moscow, 1976) [in Russian].
23.  V.V. Vasiliev and S.A. Lurie, "Generalized Solution of the Problem on a Circular Membrane Loaded by a Concentrated Force," Izv. Akad. Nauk. Mekh. Tverd. Tela No. 3, 115-119 (2016) [Mech. Solids (Engl. Transl.) 51 (3), 334-338 (2016)].
24.  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. Solids (Engl. Transl.) 51 (5), 557-561 (2016)].
25.  G.P. Cherepanov, Mechanics of Brittle Fracture (Nauka, Moscow, 1974) [in Russian].
Received 05 March 2018
Link to Fulltext
<< Previous article | Volume 53, Issue 4 / 2018 | Next article >>
Orphus SystemIf you find a misprint on a webpage, please help us correct it promptly - just highlight and press Ctrl+Enter

101 Vernadsky Avenue, Bldg 1, Room 246, 119526 Moscow, Russia (+7 495) 434-3538
Founders: Russian Academy of Sciences, Branch of Power Industry, Machine Building, Mechanics and Control Processes of RAS, Ishlinsky Institute for Problems in Mechanics RAS
© Mechanics of Solids
Rambler's Top100