Numerical analysis and simulations of quasistatic frictionless contact problems

• Autorzy: José Ramon Fernández García , Weimin Han , Meir Shillor , Mircea Sofonea
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

finite element method (FEM); normalcompliance; quasistatic contact; viscoplasticity; numerical approximation; Signorini condition; variational inequality; error estimate

• Wydawca: University of Zielona Gora Press
• Czasopismo: International Journal of Applied Mathematics and Computer Science
• Rocznik: 2001
• Tom: 11
• Numer: 1
• Strony: 205-222

Daty

wydano

2001

otrzymano

2000-09-01

poprawiono

2001-01-01

Twórcy

autor

José Ramon Fernández García

• Departamento de Matematica Aplicada, Universidade de Santiago de Compostela, 15706 Santiago de Compostela, Spain

autor

Weimin Han

• Department of Mathematics, University of Iowa, Iowa City, IA 52242, USA

autor

Meir Shillor

• Department of Mathematics and Statistics, Oakland University, Rochester, MI 48309, USA

autor

Mircea Sofonea

• Laboratoire de Theorie des Systemes, University of Perpignan, 52, Avenue de Villeneuve, 66860 Perpignan, France

Bibliografia

• Ciarlet P.G. (1978): The Finite Element Method for Elliptic Problems. - Amsterdam: North Holland.
• Chen J., Han W. and Sofonea M. (1999a): Numerical analysis of a class of evolution systems arising in viscoplasticity. - (preprint).
• Chen J., Han W. and Sofonea M. (1999b): Numerical analysis of a contact problem in rate-type elastic-viscoplasticity. - (preprint).
• Cristescu N. and Suliciu I. (1982): Viscoplasticity. - Bucharest: Martinus Nijhoff Publishers, Editura Tehnica.
• Duvaut G. and Lions J.L. (1976): Inequalities in Mechanics and Physics. - Berlin: Springer Verlag.
• 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..
• 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.
• 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.
• Hlaváček I., Haslinger J., Necăs J. and Lovíšek J. (1988): Solution of Variational Inequalities in Mechanics. - New York: Springer-Verlag.
• Ionescu I.R. and Sofonea M. (1993): Functional and Numerical Methods in Viscoplasticity. - Oxford: Oxford University Press.
• Kikuchi N. and Oden J.T. (1988): Contact Problems in Elasticity: A Study of Variational Inequalities and Finite Element Methods. - Philadelphia: SIAM.
• Raous M., Jean M. and Moreau J.J. (Eds.) (1995): Contact Mechanics. - New York: Plenum Press.
• Shillor M. (Ed.) (1998): Recent advances in contact mechanics. - Math. Computer Model., Vol.28, No.4-8.
• Sofonea M. (1997): On a contact problem for elastic-viscoplastic bodies. - Nonlin. Anal., Vol.29, No.9, pp.1037-1050.