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2000 | 75 | 3 | 233-246
Tytuł artykułu

A viscoelastic contact problem with normal damped response and friction

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
We study an evolution problem which describes the quasistatic contact of a viscoelastic body with a foundation. We model the contact with normal damped response and a local friction law. We derive a variational formulation of the model and we establish the existence of a unique weak solution to the problem. The proof is based on monotone operators and fixed point arguments. We also establish the continuous dependence of the solution on the contact boundary conditions.
Rocznik
Tom
75
Numer
3
Strony
233-246
Opis fizyczny
Daty
wydano
2000
otrzymano
1999-09-27
poprawiono
2000-05-31
Twórcy
autor
  • Laboratoire de Théorie des Systèmes, Université de Perpignan, 52 Avenue de Villeneuve, 66860 Perpignan Cedex, France
  • Laboratoire de Mathématiques Appliquées, CNRS UMR 6620, Université Blaise Pascal (Clermont-Ferrand II), 63177 Aubière Cedex, France
autor
  • Laboratoire de Théorie des Systèmes, Université de Perpignan, 52 Avenue de Villeneuve, 66860 Perpignan Cedex, France
Bibliografia
  • [1] A. Amassad and M. Sofonea, Analysis of a quasistatic viscoplastic problem involving Tresca friction law, Discrete Cont. Dynam. Systems 4 (1998), 55-72.
  • [2] L.-E. Anderson, A quasistatic frictional problem with normal compliance, Nonlinear Anal. 16 (1991), 347-370.
  • [3] H. Brezis, Equations et inéquations non linéaires dans les espaces vectoriels en dualité, Ann. Inst. Fourier (Grenoble) 18 (1968), no. 1, 115-175.
  • [4] M. Cocu, E. Pratt and M. Raous, Formulation and approximation of quasistatic frictional contact, Internat. J. Engrg. Sci. 34 (1996), 783-798.
  • [5] G. Duvaut et J. L. Lions, Les Inéquations en Mécanique et en Physique, Dunod, Paris, 1972.
  • [6] R. Ionescu and M. Sofonea, Functional and Numerical Methods in Viscoplasticity, Oxford Univ. Press, Oxford, 1993.
  • [7] N. Kikuchi and J. T. Oden, Contact Problems in Elasticity: A Study of Variational Inequalities and Finite Element Methods, SIAM, Philadelphia, 1988.
  • [8] A. Klarbring, A. Mikelić and M. Shillor, The rigid punch problem with friction, Internat. J. Engrg. Sci. 29 (1991), 751-768.
  • [9] J. Nečas and I. Hlaváček, Mathematical Theory of Elastic and Elastoplastic Bodies: an Introduction, Elsevier, Amsterdam, 1981.
  • [10] P. D. Panagiotopoulos, Inequality Problems in Mechanics and Applications, Birkhäuser, Basel, 1985.
  • [11] M. Raous, M. Jean and J. J. Moreau, Contact Mechanics, Plenum Press, New York, 1995.
  • [12] M. Rochdi, M. Shillor and M. Sofonea, A quasistatic viscoelastic contact problem with normal compliance and friction, J. Elasticity 51 (1998), 105-126.
  • [13] M. Rochdi, M. Shillor and M. Sofonea, A quasistatic contact problem with directional friction and damped response, Appl. Anal. 68 (1998), 409-422.
  • [14] M. Rochdi, M. Shillor and M. Sofonea, Analysis of a quasistatic viscoelastic problem with friction and damage, Adv. Math. Sci. Appl. 10 (2000), 173-189.
  • [15] M. Sofonea and M. Shillor, Variational analysis of quasistatic viscoplastic contact problems with friction, Comm. Appl. Anal., to appear.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-apmv75z3p233bwm
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