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1999 | 26 | 4 | 415-435
Tytuł artykułu

Analysis and numerical approximation of an elastic frictional contact problem with normal compliance

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
We consider the problem of frictional contact between an elastic body and an obstacle. The elastic constitutive law is assumed to be nonlinear. The contact is modeled with normal compliance and the associated version of Coulomb's law of dry friction. We present two alternative yet equivalent weak formulations of the problem, and establish existence and uniqueness results for both formulations using arguments of elliptic variational inequalities and fixed point theory. Moreover, we show the continuous dependence of the solution on the contact conditions. We also study the finite element approximations of the problem and derive error estimates. Finally, we introduce an iterative method to solve the resulting finite element system.
Rocznik
Tom
26
Numer
4
Strony
415-435
Opis fizyczny
Daty
wydano
1999
otrzymano
1998-12-17
Twórcy
autor
  • Department of Mathematics, University of Iowa, Iowa City, IA 52242, USA
  • Laboratoire de Théorie des Systèmes, Université de Perpignan, 52 Avenue de Villeneuve, 66 860 Perpignan, France
Bibliografia
  • [1] K. T. Andrews, A. Klarbring, M. Shillor and S. Wright, A dynamic thermoviscoelastic body in frictional contact with a rigid obstacle, Eur. J. Appl. Math., to appear.
  • [2] C P. G. Ciarlet, The Finite Element Method for Elliptic Problems, North-Holland, Amsterdam, 1978.
  • [3] M. Cocu, Existence of solutions of Signorini problems with friction, Int. J. Engrg. Sci. 22 (1984), 567-581.
  • [4] M. Cocu, Unilateral contact problems with friction for an elastoviscoplastic material with internal state variable, in: Proc. Contact Mechanics Int. Symp., A. Curnier (ed.), PPUR, 1992, 207-216.
  • [5] D G. Duvaut, Loi de frottement non locale, J. Méc. Théor. Appl., Special issue 1982, 73-78.
  • [6] G. Duvaut and J. L. Lions, Inequalities in Mechanics and Physics, Springer, Berlin, 1976.
  • [7] H W. Han, On the numerical approximation of a frictional contact problem with normal compliance, Numer. Funct. Anal. Optim. 17 (1996), 307-321.
  • [8] I. R. Ionescu and M. Sofonea, Functional and Numerical Methods in Viscoplasticity, Oxford Univ. Press, Oxford, 1993.
  • [9] N. Kikuchi and J. T. Oden, Contact Problems in Elasticity: A Study of Variational Inequalities and Finite Element Methods, SIAM, Philadelphia, 1988.
  • [10] A. Klarbring, A. Mikelič and M. Shillor, Frictional contact problems with normal compliance, Int. J. Engrg. Sci. 26 (1988), 811-832.
  • [11] J. A. C. Martins and J. T. Oden, Existence and uniqueness results for dynamic contact problems with nonlinear normal and friction interface laws, Nonlinear Anal. 11 (1987), 407-428.
  • [12] J. Nečas and I. Hlaváček, Mathematical Theory of Elastic and Elastoplastic Bodies$:$ An Introduction, Elsevier, Amsterdam, 1981.
  • [13] P P. D. Panagiotopoulos, Inequality Problems in Mechanics and Applications, Birkhäuser, Basel, 1985.
  • [14] M. Rochdi, M. Shillor and M. Sofonea, A quasistatic viscoelastic contact problem with normal compliance and friction, J. Elasticity 51 (1998), 105-126.
  • [15] M. Shillor and M. Sofonea, A quasistatic viscoelastic contact problem with friction, Int. J. Engrg. Sci., to appear.
  • [16] S N. Strömberg, Continuum Thermodynamics of Contact$,$ Friction and Wear, Ph.D. Thesis, Linköping University, 1995.
  • [17] N. Strömberg, L. Johansson and A. Klarbring, Derivation and analysis of a generalized standard model for contact friction and wear, Int. J. Solids Structures 33 (1996), 1817-1836.
  • [18] Z E. Zeidler, Nonlinear Functional Analysis and its Applications. IV$:$ Applications to Mathematical Physics, Springer, New York, 1988.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-zmv26i4p415bwm
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