Numerical analysis and simulations of quasistatic frictionless contact problems

José Fernández García; Weimin Han; Meir Shillor; Mircea Sofonea

International Journal of Applied Mathematics and Computer Science (2001)

  • Volume: 11, Issue: 1, page 205-222
  • ISSN: 1641-876X

Abstract

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A summary of recent results concerning the modelling as well as the variational and numerical analysis of frictionless contact problems for viscoplastic materials are presented. The contact is modelled with the Signorini or normal compliance conditions. Error estimates for the fully discrete numerical scheme are described, and numerical simulations based on these schemes are reported.

How to cite

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Fernández García, José, et al. "Numerical analysis and simulations of quasistatic frictionless contact problems." International Journal of Applied Mathematics and Computer Science 11.1 (2001): 205-222. <http://eudml.org/doc/207500>.

@article{FernándezGarcía2001,
abstract = {A summary of recent results concerning the modelling as well as the variational and numerical analysis of frictionless contact problems for viscoplastic materials are presented. The contact is modelled with the Signorini or normal compliance conditions. Error estimates for the fully discrete numerical scheme are described, and numerical simulations based on these schemes are reported.},
author = {Fernández García, José, Han, Weimin, Shillor, Meir, Sofonea, Mircea},
journal = {International Journal of Applied Mathematics and Computer Science},
keywords = {finite element method (FEM); normalcompliance; quasistatic contact; viscoplasticity; numerical approximation; Signorini condition; variational inequality; error estimate; normal compliance condition; finite element method; frictionless contact},
language = {eng},
number = {1},
pages = {205-222},
title = {Numerical analysis and simulations of quasistatic frictionless contact problems},
url = {http://eudml.org/doc/207500},
volume = {11},
year = {2001},
}

TY - JOUR
AU - Fernández García, José
AU - Han, Weimin
AU - Shillor, Meir
AU - Sofonea, Mircea
TI - Numerical analysis and simulations of quasistatic frictionless contact problems
JO - International Journal of Applied Mathematics and Computer Science
PY - 2001
VL - 11
IS - 1
SP - 205
EP - 222
AB - A summary of recent results concerning the modelling as well as the variational and numerical analysis of frictionless contact problems for viscoplastic materials are presented. The contact is modelled with the Signorini or normal compliance conditions. Error estimates for the fully discrete numerical scheme are described, and numerical simulations based on these schemes are reported.
LA - eng
KW - finite element method (FEM); normalcompliance; quasistatic contact; viscoplasticity; numerical approximation; Signorini condition; variational inequality; error estimate; normal compliance condition; finite element method; frictionless contact
UR - http://eudml.org/doc/207500
ER -

References

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  1. Ciarlet P.G. (1978): The Finite Element Method for Elliptic Problems. - Amsterdam: North Holland. Zbl0383.65058
  2. Chen J., Han W. and Sofonea M. (1999a): Numerical analysis of a class of evolution systems arising in viscoplasticity. - (preprint). 
  3. Chen J., Han W. and Sofonea M. (1999b): Numerical analysis of a contact problem in rate-type elastic-viscoplasticity. - (preprint). 
  4. Cristescu N. and Suliciu I. (1982): Viscoplasticity. - Bucharest: Martinus Nijhoff Publishers, Editura Tehnica. 
  5. Duvaut G. and Lions J.L. (1976): Inequalities in Mechanics and Physics. - Berlin: Springer Verlag. Zbl0331.35002
  6. Fernández-García J., Sofonea M. and Viaño J.M. (1999): Numerical approach of a frictionless contact problem for elastic-viscoplastic materials with normal compliance. - to appear in Numer. Math.. Zbl1143.65391
  7. Fernández-García J., Han W., Shillor M. and Sofonea M. (2000): Recent advances on variational and numerical analysis in contact mechanics. - Proc. MTNS 2000, Perpignan, France, 2000, published on CD-ROM. 
  8. Fichera G. (1964): Problemi elastostatici con vincoli unilaterali. II. Problema di Signorini con ambique condizioni al contorno. - Mem. Accad. Naz. Lincei, S.VIII, Vol.VII, Sez.I, 5, pp.91-140. Zbl0146.21204
  9. Hlaváček I., Haslinger J., Necăs J. and Lovíšek J. (1988): Solution of Variational Inequalities in Mechanics. - New York: Springer-Verlag. Zbl0654.73019
  10. Ionescu I.R. and Sofonea M. (1993): Functional and Numerical Methods in Viscoplasticity. - Oxford: Oxford University Press. Zbl0787.73005
  11. Kikuchi N. and Oden J.T. (1988): Contact Problems in Elasticity: A Study of Variational Inequalities and Finite Element Methods. - Philadelphia: SIAM. Zbl0685.73002
  12. Raous M., Jean M. and Moreau J.J. (Eds.) (1995): Contact Mechanics. - New York: Plenum Press. 
  13. Shillor M. (Ed.) (1998): Recent advances in contact mechanics. - Math. Computer Model., Vol.28, No.4-8. 
  14. Sofonea M. (1997): On a contact problem for elastic-viscoplastic bodies. - Nonlin. Anal., Vol.29, No.9, pp.1037-1050. Zbl0918.73098

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