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Numerical approximation of dynamic deformationsof a thermoviscoelastic rod against an elastic obstacle

Published online by Cambridge University Press:  15 August 2004

Maria I.M. Copetti
Maria I.M. Copetti*
Affiliation:
Laboratório de Análise Numérica e Astrofísica, Departamento de Matemática, Universidade Federal de Santa Maria, 97119-900 Santa Maria, RS, Brazil. mimc@lana.ccne.ufsm.br.
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Abstract

In this paper we consider a hyperbolic-parabolic problem that models the longitudinal deformations of a thermoviscoelastic rod supported unilaterally by an elastic obstacle. The existence and uniqueness of a strong solution is shown. A finite element approximation is proposed and its convergence is proved. Numerical experiments are reported.

Keywords

Thermoviscoelasticitydynamic contact problemfinite element approximationnumerical simulations.

Information

Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 38 , Issue 4 , July 2004, pp. 691 - 706
Copyright
© EDP Sciences, SMAI, 2004

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References

D.E. Carlson, Linear thermoelasticity, in Handbuch der physik, C. Truesdell Ed., VIa/2 (1972) 297–345.
Copetti, M.I.M., A one-dimensional thermoelastic problem with unilateral constraint. Math. Comp. Simul. 59 (2002) 361–376. CrossRef
Copetti, M.I.M. and French, D.A., Numerical solution of a thermoviscoelastic contact problem by a penalty method. SIAM J. Numer. Anal. 41 (2003) 1487–1504. CrossRef
W.A. Day, Heat conduction with linear thermoelasticity. Springer, New York (1985).
Eck, C., Existence of solutions to a thermo-viscoelastic contact problem with Coulomb friction. Math. Mod. Meth. Appl. Sci. 12 (2002) 1491–1511. CrossRef
Eck, C. and Jarušek, J., The solvability of a coupled thermoviscoelastic contact problem with small Coulomb friction and linearized growth of frictional heat. Math. Meth. Appl. Sci. 22 (1999) 1221–1234. 3.0.CO;2-M>CrossRef
Elliott, C.M. and Qi, T., A dynamic contact problem in thermoelasticity. Nonlinear Anal. 23 (1994) 883–898. CrossRef
S. Jiang and R. Racke, Evolution equations in thermoelasticity. Chapman & Hall/ CRC (2000).
Kim, J.U., A one-dimensional dynamic contact problem in linear viscoelasticity. Math. Meth. Appl. Sci. 13 (1990) 55–79. CrossRef
Kuttler, K.L. and Shillor, M., A dynamic contact problem in one-dimensional thermoviscoelasticity. Nonlinear World 2 (1995) 355–385.
Schatzman, M. and Bercovier, M., Numerical approximation of a wave equation with unilateral constraints. Math. Comp. 53 (1989) 55–79. CrossRef