Trefftz Method of Solving a 1D Coupled Thermoelasticity Problem for One- and Two-Layered Media

This paper discusses a 1D one-dimensional mathematical model for the thermoelasticity problem in two-layer plate. Basic equations dimensionless form contain both temperature and displacement. General solutions of homogeneous (displacement equations) are assumed to be linear combination Trefftz functions. Particular these then expressed with appropriately constructed sums derivatives general solutions. Next, inverse operators those appearing defined applied right-hand sides inhomogeneous equations. Thus, two systems functions obtained, satisfying strictly fully coupled system To determine unknown coefficients combinations, functional is that describes error meeting initial boundary conditions by approximate The minimization leads an solution under consideration. one layer plate graphically presented analyzed, illustrating possible application method. Our results show increasing number reduction differences between successive approximations.