Skip to main content

Domain Decomposition Schemes for Frictionless Multibody Contact Problems of Elasticity

Abstract

The class of parallel Robin (Poincaré) domain decomposition schemes which are based on the penalty method and the simple iteration method for variational equations is proposed for solution of frictionless multibody contact problems of elasticity. The convergence of these schemes is proved. The numerical analysis is made for 2D contact problems using FEM approximations.

This is a preview of subscription content, access via your institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • DOI: 10.1007/978-3-642-11795-4_31
  • Chapter length: 9 pages
  • Instant PDF download
  • Readable on all devices
  • Own it forever
  • Exclusive offer for individuals only
  • Tax calculation will be finalised during checkout
eBook
USD   219.00
Price excludes VAT (USA)
  • ISBN: 978-3-642-11795-4
  • Instant PDF download
  • Readable on all devices
  • Own it forever
  • Exclusive offer for individuals only
  • Tax calculation will be finalised during checkout
Softcover Book
USD   279.99
Price excludes VAT (USA)
Hardcover Book
USD   279.99
Price excludes VAT (USA)

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Céa, J.: Optimisation. Théorie et algorithmes. Dunod, Paris (1971)

    MATH  Google Scholar 

  2. Dyyak, I. I., Prokopyshyn, I. I.: The convergence of parallel Neumann domain decomposition scheme for frictionless multibody contact problems of elasticity. Mat. Met. Fiz.-Mekh. Polya. 52(3), 78–89 (2009) [In Ukrainian]

    Google Scholar 

  3. Glowinski, R., Lions, J. L., Trémolières, R.: Analyse numérique des inéquations variationnelles. Dunod, Paris (1976)

    MATH  Google Scholar 

  4. Hüeber, S., Wohlmuth, B. I.: A primal-dual active set strategy for non-linear multibody contact problems. Comput. Meth. Appl. Mech. Engrg. 194(27–29), 3147–3166 (2005)

    MATH  CrossRef  Google Scholar 

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

    Google Scholar 

  6. Kravchuk, A. S.: The formulation of the contact problem for several deformable bodies as the nonlinear programming problem. PMM. 42(3), 466–474 (1978) [In Russian]

    Google Scholar 

  7. Kuzmenko, V. I.: On variational approach to the theory of contact problems for nonlinear elastic multilayer bodies. PMM. 43(5), 893–901 (1979) [In Russian]

    Google Scholar 

  8. Lions, J. L.: Quelques méthodes de résolution des problèmes aux limites non linéaire. Dunod, Gauthier-Villars, Paris (1969)

    Google Scholar 

  9. Prokopyshyn, I.: Parallel domain decomposition schemes for frictionless contact problems of elasticity. Visnyk Lviv Univ. Ser. Appl. Math. Comp. Sci. 14, 123–133 (2008) [In Ukrainian]

    Google Scholar 

  10. Wriggers, P.: Computational Contact Mechanics, second ed. Springer, Heidelberg (2006)

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Ivan I. Dyyak .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and Permissions

Copyright information

© 2010 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Dyyak, I.I., Prokopyshyn, I.I. (2010). Domain Decomposition Schemes for Frictionless Multibody Contact Problems of Elasticity. In: Kreiss, G., Lötstedt, P., Målqvist, A., Neytcheva, M. (eds) Numerical Mathematics and Advanced Applications 2009. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-11795-4_31

Download citation