Numerical analysis of a quasi-static contact problem for a thermoviscoelastic beam |
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Authors: | M.I.M. CopettiJ.R. Ferná ndez |
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Affiliation: | a Laboratório de Análise Numérica e Astrofísica, Departamento de Matemática, Universidade Federal de Santa Maria, 97105-900, Santa Maria, RS, Brazilb Departamento de Matemática Aplicada I, Universidade de Vigo, Escola de Enxeñería de Telecomunicación, Campus As Lagoas Marcosende s/n, 36310 Vigo, Spain |
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Abstract: | In this paper we revisit a quasi-static contact problem of a thermoviscoelastic beam between two rigid obstacles which was recently studied in [1]. The variational problem leads to a coupled system, composed of an elliptic variational inequality for the vertical displacement and a linear variational equation for the temperature field. Then, its numerical resolution is considered, based on the finite element method to approximate the spatial variable and the implicit Euler scheme to discretize the time derivatives. Error estimates are proved from which, under adequate regularity conditions, the linear convergence is derived. Finally, some numerical simulations are presented to show the accuracy of the algorithm and the behavior of the solution. |
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Keywords: | Thermoviscoelastic beam Signorini contact conditions Error estimates Numerical simulations |
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