The solvability of a coupled thermoviscoelastic contact problem with small Coulomb friction and linearized growth of frictional heat
✍ Scribed by Christof Eck; Jiří Jarušek
- Publisher
- John Wiley and Sons
- Year
- 1999
- Tongue
- English
- Weight
- 151 KB
- Volume
- 22
- Category
- Article
- ISSN
- 0170-4214
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✦ Synopsis
A coupled thermoviscoelastic frictional contact problem is investigated. The contact is modelled by the Signorini condition for the displacement velocities and the friction by the Coulomb law. The heat generated by friction is described by a non-linear boundary condition with at most linear growth. The weak formulation of the problem consists of a variational inequality for the elasticity part and a variational equation for the heat conduction part. In order to prove the existence of a solution to this problem we "rst use an approximation of the Signorini condition by the penalty method. The existence of a solution for the approximate problem is shown using the "xed-point theorem of Schauder. This theorem is applied to the composition of the solution operator for the contact problem with given temperature "eld and the solution operator for the heat equation problem with known displacement "eld. To obtain this proof, the unique solvability of both problems is necessary. Due to this reason it is necessary to introduce the penalty method. While the penalized contact problem has a unique solution, this is not clear for the original contact problem. The solvability of the original frictional contact problem is veri"ed by an investigation of the limit for vanishing penalty parameter.