Approximation of Thermoelasticity Contact Problem With Nonmonotone Friction

Ivan Šestak; Bo>>ko S. Jovanović

doi:10.3879/j.issn.1000-0887.2010.01.008

Volume 31 Issue 1

Turn off MathJax

Article Contents

Article Navigation > Applied Mathematics and Mechanics > 2010 > 31(1): 71-80

Ivan Šestak, Bo>>ko S. Jovanović. Approximation of Thermoelasticity Contact Problem With Nonmonotone Friction[J]. Applied Mathematics and Mechanics, 2010, 31(1): 71-80. doi: 10.3879/j.issn.1000-0887.2010.01.008

Citation:

PDF( 539 KB)

Approximation of Thermoelasticity Contact Problem With Nonmonotone Friction

doi: 10.3879/j.issn.1000-0887.2010.01.008

Ivan Šestak¹,
Bo>>ko S. Jovanović²

University of Belgrade, Faculty of Mining and Geology, Du>>ina 7, 11000 Belgrade, Serbia;
University of Belgrade, Faculty of Mathematics, Studentski trg 16, 11000 Belgrade, Serbia

Received Date: 2009-03-29
Rev Recd Date: 2009-10-17
Publish Date: 2010-01-15

Abstract

Abstract

The formulation and approxmiation of a static thermoelasticity problem that described bilateral frictional contact between a deformable body and a rigid foundation was presented. The friction was in the form of nonmonotone and multivalued law. The coupling effect of the problem was neglected, therefore the thermic part of the problem was considered independently of the elasticity problem. For the displacement vector, a substationary problem for non-convex, locally Lipschitz continuous functional representing the total potential energy of the body was form ulated. All problems form ulated were approxmiated by the finite element method.
- static thermoelastic contact,
- nonmonotone multivalued friction,
- hemivariational inequality,
- substationary problem,
- finite element approxmiation

FullText(HTML)

References(19)

References

[1]	Panagiotopoulos P D.Inequality Problems in Mechanics and Applications: Convex and Nonconvex Energy Functions[M]. Boston, Basel, Stuttgart: Birkhuser, 1985.
[2]	Panagiotopoulos P D.Hemivariational Inequalities: Applications in Mechanics and Engineering[M]. Berlin, Heidelberg, New York: Springer, 1993.
[3]	Denkowski Z, Migórski S. A system of evolution hemivariational inequalities modeling thermoviscoelastic frictional contact[J].Nonlinear Analysis, 2005, 60(8): 1415-1441. doi: 10.1016/j.na.2004.11.004
[4]	Goeleven D, Motreanu D, Dumont Y,et al.Variational and Hemivariational Inequalities. Theory, Methods and Applications, Volume Ⅰ: Unilateral Analysis and Unilateral Mechanics[M]. Boston, Dordrecht, London: Kluwer, 2003.
[5]	Goeleven D, Motreanu D.Variational and Hemivariational Inequalities. Theory, Methods and Applications, Volume Ⅱ: Unilateral Problems[M]. Dordrecht, London: Kluwer, 2003.
[6]	Naniewicz Z, Panagiotopoulos P D.Mathematical Theory of Hemivariational Inequalities and Applications[M]. New York, Basel, Hong Kong: Marcel Dekker, 1995.
[7]	Haslinger J, Miettinen M, Panagiotopoulos P D.Finite Element Method for Hemivariational Inequalities. Nonconvex Optimization and Its Applications[M].Vol 35, Dordrecht: Kluwer, 1999.
[8]	Baniotopoulos C C, Haslinger J, Morávková Z. Mathematical modeling of delamination and nonmonotone friction problems by hemivariational inequalities[J].Appl Math, 2005, 50(1): 1-25. doi: 10.1007/s10492-005-0001-7
[9]	Miettinen M, Haslinger J. Approximation of nonmonotone multivalued differential inclusions[J].IMA J Numer Anal, 1995, 15(4): 475-503. doi: 10.1093/imanum/15.4.475
[10]	Miettinen M, Mkel M M, Haslinger J. On numerical solution of hemivariational inequalities by nonsmooth optimization methods[J].J Global Optimization, 1995, 6(4): 401-425. doi: 10.1007/BF01100086
[11]	Miettinen M, Haslinger J. Finite element approximation of vector-valued hemivariational problems[J].J Global Optimization, 1997, 10(1): 17-35. doi: 10.1023/A:1008234502169
[12]	Lukan L, Vlcˇek J. A bundle-Newton method for nonsmooth unconstrained minimization[J].Math Prog, 1998, 83(1/3): 373-391.
[13]	Baniotopoulos C C, Haslinger J, Morávková Z.Contact problems with nonmonotone friction: discretization and numerical realization[J].Comput Mech, 2007, 40(1): 157-165. doi: 10.1007/s00466-006-0092-3
[14]	Adams R S. Sobolev Spaces.Pure and Applied Mathematics[M].Vol 65.New York,London: Academic Press, 1975.
[15]	Kufner A, John O, Fucˇik S.Function Spaces[M]. Leyden: Noordhoff International Publishing and Prague: Academia, 1977.
[16]	Necˇas J.Les Méthodes Directes en Théorie des quations Elliptiques[M]. Paris: Masson, 1967.
[17]	Clarke F H.Optimization and Nonsmooth Analysis[M]. New York, Chichester, Brisbane, Toronto and Singapore: Wiley, 1983.
[18]	Ciarlet P G.The Finite Element Method for Elliptic Problems[M]. Amsterdam： North-Holland, 1978.
[19]	Glowinski R, Lions J L. Trémoliéres R.Numerical Analysis of Variational Inequalities. Series in Mathematics and Applications[M]. Vol 8. Amsterdam: North-Holland, 1981.