Skip to main content
SpringerLink
Log in

Variational analysis of thermomechanically coupled steady-state rolling problem

  • Published:
Applied Mathematics and Mechanics Aims and scope Submit manuscript

Abstract

A steady-state, rigid-plastic rolling problem for temperature and strain-rate dependent materials with nonlocal friction is considered. A variational formulation is derived, coupling a nonlinear variational inequality for the velocity and a nonlinear variational equation for the temperature. The existence and uniqueness results are obtained by a proposed fixed point method.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Hill, R. The Mathematical Theory of Plasticity, Oxford University Press, Oxford (1950)

    MATH  Google Scholar 

  2. Kachanov, L. M. Fundamentals of the Theory of Plasticity, North-Holland, Amsterdam (1971)

    Google Scholar 

  3. Zienkiewicz, O. C., Onate, E., and Heinrich, J. C. A general formulation for coupled thermal flow of metals using finite elements. International Journal for Numerical Methods in Engineering, 17(10), 1497–1514 (1981)

    Article  MATH  Google Scholar 

  4. Kobayashi, S., Oh, S. I., and Altan, T. Metal Forming and the Finite Element Method, Oxford University Press, Oxford (1989)

    Google Scholar 

  5. Duvaut, G. and Lions, J. L. Les Inequations en Mecanique et en Physique, Dunod, Paris (1972)

    MATH  Google Scholar 

  6. Nečas, J. and Hlavaček, I. Mathematical Theory of Elastic and Elasto-Plastic Bodies: An Introduction, Elsevier, Amsterdam (1981)

    MATH  Google Scholar 

  7. Kikuchi, N. and Oden, J. T. Contact Problems in Elasticity: A Study of Variational Inequalities and Finite Element Methods, SIAM, Philadelphia (1988)

    Book  MATH  Google Scholar 

  8. Panagiotopoulos, P. D. Inequality Problems in Mechanics and Applications, Birkhäuser, Boston (1985)

    Book  MATH  Google Scholar 

  9. Glowinski, R. Numerical Methods for Nonlinear Variational Problems, Springer-Verlag, Berlin (1984)

    Book  MATH  Google Scholar 

  10. Han, W. and Sofonea, M. Quasistatic Contact Problems in Viscoelasticity and Viscoplasticity, American Mathematical Society and International Press, Providence (2002)

    MATH  Google Scholar 

  11. Shillor, M., Sofonea, M., and Telega, J. J. Models and Variational Analysis of Quasistatic Contact, Lecture Notes in Physics, Springer, Berlin (2004)

    Book  MATH  Google Scholar 

  12. Campo, M., Fernandez, J. R., and Kuttler, K. L. An elastic-viscoplastic quasistatic contact problem: existence and uniqueness of a weak solution. Archive for Rational Mechanics and Analysis, 191(3), 423–445 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  13. Angelov, T. A. A thermomechanically coupled rolling problem with damage. Mechanics Research Communications, 26(3), 287–293 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  14. Angelov, T. A. Variational analysis of a rigid-plastic rolling problem. International Journal of Engineering Science, 42(17–18), 1779–1792 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  15. Angelov, T. A. Variational and numerical approach to a steady-state rolling problem. Journal of Engineering Mathematics, 66(4), 311–323 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  16. Kantorovich, L. B. and Akilov, G. P. Functional Analysis (in Russian), Nauka, Moscow (1984)

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute of Mechanics, Bulgarian Academy of Sciences, Sofia, 1113, Bulgaria

    T. A. Angelov

Authors
  1. T. A. Angelov
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to T. A. Angelov.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Angelov, T.A. Variational analysis of thermomechanically coupled steady-state rolling problem. Appl. Math. Mech.-Engl. Ed. 34, 1361–1372 (2013). https://doi.org/10.1007/s10483-013-1751-6

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10483-013-1751-6

Key words

Chinese Library Classification

2010 Mathematics Subject Classification

Search

Navigation