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A one-dimensional quasi-static contact problem in linear thermoelasticity

Published online by Cambridge University Press:  26 September 2008

M. I. M. Copetti  and
C. M. Elliott
M. I. M. Copetti
Affiliation:
School of Mathematical and Physical Sciences, University of Sussex, Brighton BN1 9QH, UK Departamento de Matemática, Universidade Federal de Santa Maria, 97119 Santa Maria – RS, Brasil
C. M. Elliott
Affiliation:
School of Mathematical and Physical Sciences, University of Sussex, Brighton BN1 9QH, UK
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Abstract

The existence, uniqueness and regularity of the solution to a one-dimensional linear thermoelastic problem with unilateral contact of the Signorini type are established. A finite element approximation is described, and an error bound is derived. It is shown that if the time step is O(h2), then the error in L2 in the temperature and in L∞ in the displacement is O(h). Some numerical experiments are presented.

Type
Research Article
Information
European Journal of Applied Mathematics , Volume 4 , Issue 2 , June 1993 , pp. 151 - 174
Copyright
Copyright © Cambridge University Press 1993

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References

Boley, B. A. & Weiner, J. H. 1960 Theory of Thermal Stresses. Wiley.Google Scholar
Carlson, D. E. 1972 Linear thermoelasticity. In Truesdell, C., ed., Handbuch der Physik. Vol. VIa/2, 297–345.Google Scholar
DAY, W. A. 1985 Heat Conduction with Linear Thermoelasticity. Springer-Verlag.Google Scholar
Duvaut, G. 1980 Free boundary problem connected with thermoelasticity and unilateral contact. In Free Boundary Problems. Vol. II, Roma.Google Scholar
Duvaut, G. & Lions, J. L. 1972 Inéquations en thermoélasticité et magnétohydrodynamique. Arch. Rat. Mech. Anal., 46, 241–279.Google Scholar
Gilbert, R. P., Shi, P. & Shillor, M. 1990 A quasi-static contact problem in linear thermoelasticity. Rediconti di Matematica. (To appear.)Google Scholar
Shi, P. & Shillor, M. 1990 Uniqueness and stability of the solution to a thermoelastic contact problem. Euro. J. Appl. Math., 1 (4), 371–387.Google Scholar
Shi, P., Shillor, M. & Zou, X. 1990 Numerical solutions to one dimensional problems of thermoelastic contact. Preprint. Oakland University.CrossRefGoogle Scholar
ThomÉe, V. 1984 Galerkin finite element methods for parabolic problems. Vol. 1054 of Lecture Notes in Mathematics. Springer-Verlag.Google Scholar