 | | 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 |
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| D.V. Georgievskii, "The Problems in Terms of Stresses of Diffusion-Vortex Class in Infinite Rigid Viscoplastic Space," Mech. Solids. 53 (5), 520-526 (2018) |
| Year |
2018 |
Volume |
53 |
Number |
5 |
Pages |
520-526 |
| DOI |
10.3103/S002565441808006X |
| Title |
The Problems in Terms of Stresses of Diffusion-Vortex Class in Infinite Rigid Viscoplastic Space |
| Author(s) |
D.V. Georgievskii (Lomonosov Moscow State University, Leninskie Gory 1, Moscow, 119992 Russia; Ishlinsky Institute for Problems in Mechanics of the Russian Academy of Sciences, pr. Vernadskogo 101, str. 1, Moscow, 119526 Russia, georgiev@mech.math.msu.su) |
| Abstract |
The statements and exact self-similar solutions of diffusion-vortex problems in terms of stresses simulating a nonstationary one-dimensional shear in some curvilinear orthogonal coordinate systems of a two-constant stiff-viscous plastic medium (Bingham body) are analyzed. Such problems include the diffusion of plane and axisymmetric vortex layers, as well as the diffusion of a vortex filament. The shear occurs in regions of unlimited space expanding with time with a pre-unknown boundary, and a possible way of specifying an additional condition at infinity is described. A generalized vortex diffusion is introduced into consideration, containing a formulation with several parameters, including the order of the singularity peculiarities at zero. Self-similar solutions are constructed in which the order of the singularity corresponds to or does not correspond to the type of shift in the selected coordinate system. |
| Keywords |
nonstationary shear, vortex diffusion, stiff-viscous-plastic body, yield strength, viscosity, self-similarity, parabolic systems |
| References |
| 1. | D.M. Klimov, A.G. Petrov, and D.V. Georgievskii,
Viscous-Plastic Flows: Dynamic Chaos, Stability, Mixing
(Nauka, Moscow, 2005) [in Russian]. |
| 2. | D.V. Georgievskii,
"The Diffusion of a Discontinuity of the Shear Stress at the Boundary of a Viscoplastic Half-Plane,"
Prikl. Mat. Mekh.
70 (5), 884-892 (2006)
[J. Appl. Math. Mech. (Engl. Transl.)
70 (5), 796-803 (2006)]. |
| 3. | S.N. Kruzhkov,
"On Some Problems with Unknown Boundaries for the Heat Conduction Equation,"
Prikl. Mat. Mekh.
31 (6), 1009-1020 (1967)
[J. Appl. Math. Mech. (Engl. Transl.)
31 (6), 1014-1024 (1967)]. |
| 4. | P.M. Ogibalov and A.Kh. Mirzadzhanzade,
Unsteady Motions of Visco-Plastic Media
(Nauka, Moscow, 1977) [in Russian]. |
| 5. | A.N. Tikhonov and A.A. Samarsky,
Equations of Mathematical Physics
(Izd-vo MGU, Moscow, 1999) [in Russian]. |
| 6. | D.V. Georgievskii,
"Self-Similar Solutions in the Problem of Generalized Vortex Diffusion,"
Izv. Akad. Nauk. Mekh. Zhid. Gaz.,
No. 2, 3-12 (2007)
[Fluid Dyn. (Engl. Transl.)
42 (2), 151-159 (2007)]. |
| 7. | E. Kamke,
Handbook of Ordinary Differential Equations
(Mir, Moscow, 1991) [Differentialgleichungen. Lösungsmethoden und Lösungen. I. Gewöhnliche Differentialgleichungen (Academische Verlag., Leipzig, 1959)] |
|
| Received |
23 April 2018 |
| Link to Fulltext |
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