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IssuesArchive of Issues2017-4pp.465-472

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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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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)].
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Received 26 August 2016
Link to Fulltext https://link.springer.com/article/10.3103/S0025654417040148
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