Solving thermoelasticity problems by means of Trefftz functions

Abstract

The paper presents a new method of approximate solving of the two- and three-dimensional thermoelasticity problems in a finite body. The method presented here can be used for solving direct and inverse problems as well. System of thermoelasticity equations is reduced to the system of wave equations where the temperature occurs as inhomogeneity in one of them. The thermal field is approximated by linear combination of heat polynomials (Trefftz functions for heat conduction equation). The system of wave equations is solved by means of wave polynomials (Trefftz functions for wave equation). Convergence of the T-functions method is proved. The procedure of solving direct and inverse thermoelasticity problems by means of Trefftz functions is tested on an example. Sensitiveness of the method according to data disturbance was checked.