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1998 | 69 | 1 | 75-88
Tytuł artykułu

Analysis of a frictionless contact problem for elastic bodies

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EN
Abstrakty
EN
This paper deals with a nonlinear problem modelling the contact between an elastic body and a rigid foundation. The elastic constitutive law is assumed to be nonlinear and the contact is modelled by the well-known Signorini conditions. Two weak formulations of the model are presented and existence and uniqueness results are established using classical arguments of elliptic variational inequalities. Some equivalence results are presented and a strong convergence result involving a penalized problem is also proved.
Twórcy
autor
  • Institute of Mathematics, University of Setif, 19000 Setif, Algeria
autor
  • Department of Mathematics, University of Perpignan, 52 Avenue de Villeneuve, 66860 Perpignan, France
autor
  • Institute of Mathematics, University of Constantine, 25000 Constantine, Algeria
Bibliografia
  • [1] H. Brezis, Equations et inéquations non linéaires dans les espaces vectoriels en dualité, Ann. Inst. Fourier (Grenoble) 18 (1968), 115-175.
  • [2] M. Burguera and J. M. Via no, Numerical solving of frictionless contact problems in perfectly plastic bodies, Comput. Methods Appl. Mech. Engrg. 121 (1995), 303-322.
  • [3] S. Drabla, M. Rochdi and M. Sofonea, On a frictionless contact problem for elastic-viscoplastic materials with internal state variables, Math. Comput. Modelling 26 (1997), no. 12, 31-47.
  • [4] G. Duvaut et J. L. Lions, Les Inéquations en Mécanique et en Physique, Dunod, Paris, 1972.
  • [5] G. Fichera, Boundary value problem of elasticity with unilateral constraints, Encyclopedia of Physics, S. Flugge (ed.), Vol. VI a/2, Springer, Berlin, 1972.
  • [6] J. Haslinger and I. Hlaváček, Contact between elastic bodies. I. Continuous problem, Appl. Math. 25 (1980), 324-347.
  • [7] J. Haslinger and I. Hlaváček, Contact between elastic perfectly plastic bodies, Appl. Math. 27 (1982), 27-45.
  • [8] I. Hlaváček and J. Nečas, Mathematical Theory of Elastic and Elastoplastic Bodies: an Introduction, Elsevier, Amsterdam, 1981.
  • [9] I. Hlaváček and J. Nečas, Solution of Signorini's contact problem in the deformation theory of plasticity by secant modules method, Appl. Math. 28 (1983), 199-214.
  • [10] I. R. Ionescu and M. Sofonea, Functional and Numerical Methods in Viscoplasticity, Oxford Univ. Press, Oxford, 1993.
  • [11] N. Kikuchi and J. T. Oden, Theory of variational inequalities with application to problems of flow through porous media, Internat. J. Engrg. Sci. 18 (1980), 1173-1284.
  • [12] N. Kikuchi and J. T. Oden, Contact Problems in Elasticity, SIAM, Philadelphia, 1988.
  • [13] P. D. Panagiotopoulos, Inequality Problems in Mechanics and Applications, Birkhäuser, Basel, 1985.
  • [14] M. Rochdi and M. Sofonea, On frictionless contact between two elastic-viscoplastic bodies, Quart. J. Mech. Appl. Math. 50 (1997), 481-496.
  • [15] M. Sofonea, On a contact problem for elastic-viscoplastic bodies, Nonlinear Anal. 29 (1997), 1037-1050.
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Bibliografia
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