 | | 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
|
| In English (Mech. Solids): | | 4760 |
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| 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 |
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10 (3), 345-354 (2014). |
| 10. | D. V. Georgievskii,
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[in Russian]. |
|
| Received |
26 August 2016 |
| Link to Fulltext |
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