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V. D. Solovei

VARIATIONAL PRINCIPLE FOR THE VELOCITIES OF PARTICLES OF A VISCOPLASTIC STRIP UNDER ROLLING

Plane flow of a viscoplastic strip under rolling is considered. Tangential friction stresses at the flow–roll interface and at contact of the flow region with the rigid strip ends are specified approximately by the Prandtl friction law. A variational principle is proved for particle velocities with account of the convection flow.

Keywords: viscoplastic strip rolling, stationary flow of a strip, convective flow, variational principle, local potential

Bibliography:

1. Ilyushin A.A. The Deformation of a Visco-Plastic Solid. Uchenye Zapiski Mosk. Gos. Univ., Ser. 2, 1940, vol. 39, pp. 3–81. (In Russian).

2. Моsolov P.P., Miasnikov V.P. Variational methods in the theory of the fluidity of a viscous-plastic medium. Journal of Applied Mathematics and Mechanics, 1965, vol. 29, no. 3, pp. 545–577. DOI: 10.1016/0021-8928(65)90063-8.

3. Freydental A., Geyringer Kh. Matematicheskie teorii neuprugoy sploshnoy sredy [Freudenthal Alfred M., Geiringer Hilda. The Mathematical Theories of the Inelastic Continuum. In: Handbuch der Physik, Bd.VI, Berlin, Göttingen, Heidelberg, Springer-Verlag, 1958, pp. 229–433]. Moscow, Fizmatgiz Publ., 1962, 432 p. (In Russian).

4. Kolmogorov V.L. Mekhanika obrabotki metallov davleniem [Mechanics of Metal Forming]. Moscow, Metallurgiya Publ., 1986, 688 p. (In Russian).

5. Alekseev A.E. Nonlinear laws of dry friction in contact problems of linear theory of elasticity. Journal of Applied Mechanics and Technical Physics, 2002, vol. 43, iss. 4, pp. 622–629. DOI: 10.1023/A:1016018118184.


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Founder:  Institute of Engineering Science, Russian Academy of Sciences (Ural Branch)
Chief Editor:  E.S. Gorkunov
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