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V. D. Solovei

A VARIATIONAL PRINCIPLE FOR THE DISTURBANCES OF PARTICLE VELOCITIES IN THE FLOW OF A PERFECTLY PLASTIC STRIP UNDER ROLLING

DOI: 10.17804/2410-9908.2018.2.083-091

The slow plane flow of a perfectly plastic strip under rolling is considered. The Prandtl friction law is assumed to be valid on the contact surface between the strip and the roller. A variational principle enabling one to build a set of velocity disturbances in order to study the stability of the stationary flow of a perfectly plastic strip at an arbitrary time is proved.

Keywords: perfectly plastic strip rolling, stationary flow, disturbances of particle velocities in a stationary flow, variational principle

References:

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2.Shtremel M.A. In: Prochnost splavov. Ch. II. Deformatsiya [Srength of alloys. Part II. Deformation]. Moscow, MISIS Publ., 1997, 526 p. (In Russian).

3.Gubernatorov V.V., Sokolov B.K., Gervasieva I.V., Vladimirov L.R. On the Formation of Band Structures in Structurally Homogeneous Materials upon Deformation. Fizicheskaya Mezomekhanika, 1999, vol. 2, nos. 1–2, pp. 157–162. (In Russian).

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5.Glansdorff P., Prigogine I. Thermodynamic Theory of Structure, Stability, and Fluctuations. London, Wiley, 1971.

6.Solovei V.D., Trukhin V.B. The stability of upsetting of a viscoplastic parallelepiped without friction. Deformatsiya i Razrushenie Materialov, 2014, no. 2, pp. 9–13. (In Russian).

7.Lamb, Sir Horace. Hydrodynamics, 6th ed., Cambridge Univ. Press, London, 1932. (Reprinted by Dover Pubs., New York, 1945).

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11.Alekseev А.Е. Nonlinear laws of dry friction in contact problems for linear theory of elasticity. Prikladnaya Mekhanika i Tekhnicheskaya Fizika, 2002, vol. 43, no. 4. pp. 16–169.  (In Russian).

12.Solovei V.D. Possible velocity disturbances in the lag zone in the rolling of a perfectly plastic strip. Deformatsiya i Razrushenie Materialov, 2014, no. 12, pp. 23–26.  (In Russian).


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Article reference

Solovei V. D. A Variational Principle for the Disturbances of Particle Velocities in the Flow of a Perfectly Plastic Strip under Rolling // Diagnostics, Resource and Mechanics of materials and structures. - 2018. - Iss. 2. - P. 83-91. -
DOI: 10.17804/2410-9908.2018.2.083-091. -
URL: http://eng.dream-journal.org/issues/content/article_183.html
(accessed: 05/22/2024).

 

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