Thermo-elastic plane deformations in doubly-connected domains with temperature and pressure which depend of the thermal conductivity

Abstract

We propose a new weak formulation for the plane problem of thermoelastic theory in multiply-connected domains. This permits to avoid the difficulties connected with the Cesaro-Volterra boundary conditions in the related elliptic boundary-value problem. In the second part we consider a nonlinear version of the problem assuming that the thermal conductivity depends not only on the temperature but also on the pressure. Recent studies reveals that this situation can occur in practice. A theorem of existence and uniqueness is proved for this problem.

Keywords

• Plane strain problem
• Doubly-connected domain
• Weak formulation
• Cesaro-Volterra boundary conditions
• Pressure dependence of thermal conductivity
• Existence and uniqueness of solutions