Numerical treatment of contact problems with thermal effect

Anna Ochal; Michal Jureczka

doi:10.3934/dcdsb.2018027

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2018, Volume 23, Issue 1: 387-400. Doi: 10.3934/dcdsb.2018027

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Numerical treatment of contact problems with thermal effect

Anna Ochal^, and
Michal Jureczka

Jagiellonian University in Krakow, Faculty of Mathematics and Computer Science, Lojasiewicza 6, 30-348 Krakow, Poland

^* Corresponding author: Anna Ochal
^* Corresponding author: Anna Ochal

Received: December 2016

Revised: May 2017

Published: November 2017

The research was supported by the National Center Science of Poland under Maestro Advanced Project no DEC-2012/06/A/ST1/00262.

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Abstract

The paper deals with the formulation and the finite element approximation of a quasi-static thermoviscoelastic problem which describes frictional contact between a deformable body and a rigid foundation. The contact is modeled by normal damped response condition whereas the friction is described by the Coulomb law of dry friction. The weak formulation of the model consists of a coupled system of the variational inequality for the displacement and the parabolic equation for the temperature. The main aim of this paper is to present a fully discrete scheme for numerical approximation together with an error estimation of a solution to this problem. Finally, computational simulations are performed to illustrate the mathematical model.

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Mathematics Subject Classification: Primary: 65M60, 35Q79, 35K85; Secondary: 35Q74.

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Figure 1. Body's shape and temperature at t = 0:25

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Figure 2. Body's shape and temperature at t = 0:5

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Figure 3. Body's shape and temperature at t = 0:75

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Figure 4. Body's shape and temperature at t = 1

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