Mechanics of Solids (about journal) 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

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


IssuesArchive of Issues2017-4pp.465-472

Archive of Issues

Total articles in the database: 12855
In Russian (Èçâ. ÐÀÍ. ÌÒÒ): 8044
In English (Mech. Solids): 4811

<< Previous article | Volume 52, Issue 4 / 2017 | Next article >>
D.V. Georgievskii and G.S. Tlyustangelov, "Exponential Estimates of Perturbations of Rigid-Plastic Spreading-Sink of an Annulus," Mech. Solids. 52 (4), 465-472 (2017)
Year 2017 Volume 52 Number 4 Pages 465-472
DOI 10.3103/S0025654417040148
Title Exponential Estimates of Perturbations of Rigid-Plastic Spreading-Sink of an Annulus
Author(s) D.V. Georgievskii (Lomonosov Moscow State University, 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)
G.S. Tlyustangelov (Lomonosov Moscow State University, Moscow, 119992 Russia, gs_angelov@mail.ru)
Abstract The time evolution of the plane picture of small perturbations imposed on the radial spreading or sink of an annulus made of incompressible ideally rigid-plastic material obeying the Mises-Hencky plasticity criterion is studied. The adhesion conditions are posed on the extending (contracting) boundaries of the annulus in both the ground and perturbed processes. The method of integral relations, which is based on variational inequalities in the corresponding complex Hilbert space, is used to reduce the linearized problem in perturbations to a single relation for quadratic functionals, which permits deriving new exponential upper bounds for the growth or decay of kinematic perturbations. It is shown that the evolution of angular harmonics with distinct numbers is qualitatively distinct.
Keywords rigid-plastic body, yield point, annulus, spreading, sink, perturbation, stability, method of integral relations, quadratic functional
References
1.  A. A. Il'yushin, "Deformation of Viscoplastic Bodies," Uchen. Zap. MGU. Mekh. No. 39, 3-81 (1940).
2.  V. V. Sokolovskii, Theory of Plasticity (Vysshaya Shkola, Moscow, 1969) [in Russian].
3.  M. A. Zadoyan, Spatial Problems of Plasticity Theory (Nauka, Moscow, 1992) [in Russian].
4.  A. Yu. Ishlinskii and D. D. Ivlev, The Mathematical Theory of Plasticity (Fizmatlit, Moscow, 2001) [in Russian].
5.  B. A. Druyanov and R. I. Nepershin, Problems of Technological Plasticity (Mashinostroenie, Moscow, 1990; Elsevier, Amsterdam, 1994).
6.  I. A. Kiiko, Viscoplastic Flow of Materials. Physical-Mathematical Foundations of Plastic Working Technology (Izdat. Mekh.-Mat. MGU, Moscow, 2001) [in Russian].
7.  V. L. Kolmogorov, Mechanics of Metal Plastic Working (Metallurgiya, Moscow, 1986) [in Russian].
8.  D. M. Klimov, A. G. Petrov, and D. V. Georgievskii, Viscoplastic Flows: Dynamical Chaos, Stability, Mixing (Nauka, Moscow, 2005) [in Russian].
9.  D. V. Georgievskii, "Evolution of Three-Dimensional Picture of Perturbations Imposed on Rotational-Axial Flow in a Cylindrical Gap," Nelin. Din. 10 (3), 345-354 (2014).
10.  D. V. Georgievskii, "A Generalized Analysis of Perturbation Patterns for the Poiseuille Flow in a Tube," Vestnik Moskov. Univ. Ser. I. Mat. Mekh., No. 4, 40-45 (2015). [Moscow Univ. Mech. Bull. (Engl. Transl.) 70 (4), 86-91 (2015)].
11.  K. Rektorys, Variational Methods in Mathematics, Science, and Engineering (Reidel, Dordrecht, 1983; Mir, Moscow, 1985).
12.  A. S. Kravchuk, Variational and Quasivariational Inequalities in Mechanics (Izdat. MGAPI, Moscow, 1997) [in Russian].
Received 26 August 2016
Link to Fulltext
<< Previous article | Volume 52, Issue 4 / 2017 | 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 mechsol@ipmnet.ru https://mtt.ipmnet.ru
Founders: Russian Academy of Sciences, Ishlinsky Institute for Problems in Mechanics RAS
© Mechanics of Solids
webmaster
Rambler's Top100