Kontaktní problémy se zahrnutím vzniku a šíření tepla

Abstract

This thesis focuses mainly on the derivation of mathematical model of contact thermo-dynamics, which can be apply on numerical algorithm. We consider problem, where the thermal expansion affects displacement and vice versa where the displacement of solid influences temperature of the material. This happens especially on the contact boundary of each body, where we consider Coulomb friction, which depends on pressure on contact boundary. Firstly from physical equations we derive weak formulations and discretize them in space and time. We transform this equations into dual problem in Lagrange multipliers, which are more sutiable for numerical computation. In last part we describe the process of finding the numerical solution. At the end reader can see solution of problem based on process derived in this text.