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2002 | 12 | 1 | 17-26
Tytuł artykułu

Dynamic contact problems with velocity conditions

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
We consider dynamic problems which describe frictional contact between a body and a foundation. The constitutive law is viscoelastic or elastic and the frictional contact is modelled by a general subdifferential condition on the velocity, including the normal damped responses. We derive weak formulations for the models and prove existence and uniqueness results. The proofs are based on the theory of second-order evolution variational inequalities. We show that the solutions of the viscoelastic problems converge to the solution of the corresponding elastic problem as the viscosity tensor tends to zero and when the frictional potential function converges to the corresponding function in the elastic problem.
Rocznik
Tom
12
Numer
1
Strony
17-26
Opis fizyczny
Daty
wydano
2002
otrzymano
2001-09-01
poprawiono
2002-01-01
Twórcy
autor
  • Laboratoire de Théorie des Systèmes, Université de Perpignan, 52 Avenue de Villeneuve, 66860 Perpignan Cedex, France
  • Laboratoire de Théorie des Systèmes, Université de Perpignan, 52 Avenue de Villeneuve, 66860 Perpignan Cedex, France
Bibliografia
  • Amassad A., Shillor M. and Sofonea M. (1999): Aquasistatic contact problem for an elastic perfectly plastic body with Tresca's friction. - Nonlin. Anal., Vol. 35, No. 1, pp. 95-109.
  • Andrews K.T., Shillor M. and Kuttler K.L. (1997a): On the dynamic behaviorof a thermoviscoelastic body in frictional contact. -Europ. J. Appl. Math., Vol. 8, No. 4, pp. 417-436.
  • Andrews K.T., Klarbring A., Shillor M. and Wright S. (1997b): A dynamic contact problem with friction and wear. -Int. J. Eng. Sci., Vol. 35, No. 14, pp. 1291-1309.
  • Awbi B., Essoufi El.H. and Sofonea M. (2000): A viscoelastic contact problem with normal damped response and friction. - Annales Polonici Mathematici, Vol. 75, No. 3, pp. 233-246.
  • Barbu V. (1976): Nonlinear Semigroups and Differential Equations in Banach Spaces. - Leyden: Editura Academiei, Bucharest-Noordhoff.
  • Chau O., Han W. and Sofonea M. (2001a): Analysis and approximation of a viscoelastic contact problem with slip dependent friction. - Dynam. Cont. Discr. Impuls. Syst., Series B: Vol. 8, No. 2, pp. 153-174.
  • Chau O., Motreanu D. and Sofonea M. (2001b): Quasistatic Frictional Problems for Elastic and Viscoelastic Materials. -Applications of Mathematics, (to appear).
  • Duvaut G. and Lions J. L. (1976): Inequalities in Mechanics and Physics - Berlin: Springer-Verlag.
  • Han W. and Sofonea M. (2000): Evolutionary variational inequalities arising in viscoelastic contact problems. - SIAMJ. Num. Anal., Vol. 38, No. 2, pp. 556-579.
  • Han W. and Sofonea M. (2001): Time-dependent variational inequalities for viscoelastic contact problems. - J. Comput. Appl. Math. (to appear).
  • Jaruv sek J. and Eck C. (1999): Dynamic contact problems with small Coulomb friction for viscoelastic bodies. Existence of solutions. -Math. Models Meth. Appl. Sci., Vol. 9, No. 1, pp. 11-34.
  • Kavian O. (1993): Introduction à la theorie des points critique set applications aux equations elliptiques. - Berlin: Springer.
  • Kuttler K. L. and Shillor M. (1999): Set-valued pseudomonotone maps and degenerate evolution inclusions -Comm. Contemp. Math., Vol. 1, No. 1, pp. 87-123.
  • Martins J.A.C. and Oden T.J. (1987), Existence and uniqueness results for dynamic contact problems with nonlinear normal and friction interface laws. - Nonlin. Anal., Vol. 11, No. 3, pp. 407-428.
  • Nečas J. and Hlavaček I. (1981): Mathematical Theory of Elastic and Elastoplastic Bodies: An Introduction. - Amsterdam: Elsevier.
  • Panagiotopoulos P.D. (1985), Inequality Problems in Mechanical and Applications. - Basel: Birkhauser.
  • Rochdi M. and Shillor M. (2001c), A dynamic thermoviscoelastic frictional contact problem with damped response (submitted).
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-amcv12i1p17bwm
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