Skip to main content

On the Solvability of the Steady-State Rolling Problem

  • Conference paper
Numerical Analysis and Its Applications (NAA 2004)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 3401))

Included in the following conference series:

  • 2692 Accesses

Abstract

In this paper a steady-state rolling problem with nonlinear friction, for rigid-plastic, rate sensitive and slightly compressible materials is considered. Its variational formulation is given and existence and uniqueness results, obtained with the help of successive iteration methods are presented. Considering the slight material compressibility as a method of penalisation, it is further shown, that when the compressibility parameter tends to zero the solution of the rolling problem for incompressible materials is approached.

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

Access this chapter

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Similar content being viewed by others

References

  1. Zienkiewicz, O.C.: Flow formulation for numerical solution of forming processes. In: Pittman, J.F.T., Zienkiewicz, O.C., Wood, R.D., Alexander, J.M. (eds.) Numerical Analysis of Forming Processes, pp. 1–44. John Wiley & Sons, Chichester (1984)

    Google Scholar 

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

    Google Scholar 

  3. Mori, K.-I.: Rigid-plastic finite element solution of forming processes. In: Pietrzyk, M., Kusiak, J., Sadok, L., Engel, Z. (eds.) Huber’s Yield Criterion in Plasticity, pp. 73–99. AGH, Krakow (1994)

    Google Scholar 

  4. Angelov, T., Baltov, A., Nedev, A.: Existence and uniqueness of the solution of a rigid-plastic rolling problem. Int. J. Engng. Sci. 33, 1251–1261 (1995)

    Article  MATH  MathSciNet  Google Scholar 

  5. Angelov, T.: A secant modulus method for a rigid-plastic rolling problem. Int. J. Nonl. Mech. 30, 169–178 (1995)

    Article  MATH  MathSciNet  Google Scholar 

  6. Angelov, T., Liolios, A.: Variational and numerical approach to a steady-state rolling problem (submitted)

    Google Scholar 

  7. Duvaut, G., Lions, J.-L.: Les Inequations en Mechanique en Physique. Dunod, Paris (1972)

    Google Scholar 

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

    MATH  Google Scholar 

  9. Glowinski, R., Lions, J.-L., Tremolieres, R.: Numerical Analysis of Variational Inequalities. North-Holland, Amsterdam (1981)

    MATH  Google Scholar 

  10. Glowinski, R.: Numerical Methods for Nonlinear Variational Problems. Springer, Berlin (1984)

    MATH  Google Scholar 

  11. Mikhlin, S.G.: The Numerical Performance of Variational Methods. Walters-Noordhoff, The Netherlands (1971)

    MATH  Google Scholar 

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

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2005 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Angelov, T.A. (2005). On the Solvability of the Steady-State Rolling Problem. In: Li, Z., Vulkov, L., Waśniewski, J. (eds) Numerical Analysis and Its Applications. NAA 2004. Lecture Notes in Computer Science, vol 3401. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-31852-1_13

Download citation

  • DOI: https://doi.org/10.1007/978-3-540-31852-1_13

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-24937-5

  • Online ISBN: 978-3-540-31852-1

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics