Analysis of a frictionless contact problem for elastic bodies

S. Drabla; M. Sofonea; B. Teniou

Annales Polonici Mathematici (1998)

  • Volume: 69, Issue: 1, page 75-88
  • ISSN: 0066-2216

Abstract

top
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.

How to cite

top

S. Drabla, M. Sofonea, and B. Teniou. "Analysis of a frictionless contact problem for elastic bodies." Annales Polonici Mathematici 69.1 (1998): 75-88. <http://eudml.org/doc/270553>.

@article{S1998,
abstract = {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.},
author = {S. Drabla, M. Sofonea, B. Teniou},
journal = {Annales Polonici Mathematici},
keywords = {frictionless contact; elastic body; variational inequality; monotone operator; penalized problem; rigid foundation; Signorini conditions; weak formulations; existence; uniqueness; elliptic variational inequalities; equivalence results; strong convergence},
language = {eng},
number = {1},
pages = {75-88},
title = {Analysis of a frictionless contact problem for elastic bodies},
url = {http://eudml.org/doc/270553},
volume = {69},
year = {1998},
}

TY - JOUR
AU - S. Drabla
AU - M. Sofonea
AU - B. Teniou
TI - Analysis of a frictionless contact problem for elastic bodies
JO - Annales Polonici Mathematici
PY - 1998
VL - 69
IS - 1
SP - 75
EP - 88
AB - 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.
LA - eng
KW - frictionless contact; elastic body; variational inequality; monotone operator; penalized problem; rigid foundation; Signorini conditions; weak formulations; existence; uniqueness; elliptic variational inequalities; equivalence results; strong convergence
UR - http://eudml.org/doc/270553
ER -

References

top
  1. [1] H. Brezis, Equations et inéquations non linéaires dans les espaces vectoriels en dualité, Ann. Inst. Fourier (Grenoble) 18 (1968), 115-175. Zbl0169.18602
  2. [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. Zbl0851.73055
  3. [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. Zbl1185.35278
  4. [4] G. Duvaut et J. L. Lions, Les Inéquations en Mécanique et en Physique, Dunod, Paris, 1972. Zbl0298.73001
  5. [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. [6] J. Haslinger and I. Hlaváček, Contact between elastic bodies. I. Continuous problem, Appl. Math. 25 (1980), 324-347. 
  7. [7] J. Haslinger and I. Hlaváček, Contact between elastic perfectly plastic bodies, Appl. Math. 27 (1982), 27-45. 
  8. [8] I. Hlaváček and J. Nečas, Mathematical Theory of Elastic and Elastoplastic Bodies: an Introduction, Elsevier, Amsterdam, 1981. Zbl0448.73009
  9. [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. Zbl0512.73097
  10. [10] I. R. Ionescu and M. Sofonea, Functional and Numerical Methods in Viscoplasticity, Oxford Univ. Press, Oxford, 1993. Zbl0787.73005
  11. [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. Zbl0444.76069
  12. [12] N. Kikuchi and J. T. Oden, Contact Problems in Elasticity, SIAM, Philadelphia, 1988. Zbl0685.73002
  13. [13] P. D. Panagiotopoulos, Inequality Problems in Mechanics and Applications, Birkhäuser, Basel, 1985. 
  14. [14] M. Rochdi and M. Sofonea, On frictionless contact between two elastic-viscoplastic bodies, Quart. J. Mech. Appl. Math. 50 (1997), 481-496. Zbl0886.73059
  15. [15] M. Sofonea, On a contact problem for elastic-viscoplastic bodies, Nonlinear Anal. 29 (1997), 1037-1050. Zbl0918.73098

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.