On solvability and approximation of 1D models of coupled thermoelasticity

In this paper we briefly present the origin and some mathematical formulations of the “extended” model problem (for beam or plate strip) for quadruples of unknown functions U = {{u₁, u₂}, {ϑ₁, ϑ₂}} within the framework of the linearised theory of coupled thermoelasticity. Thus, we introduce a weak formulation of the model problem as well as semidiscrete (in time) and complete discrete (in time and space variables) formulations. According to a special, but still real, physical situation, we may split the extended model into two independent and simplified models representing stretching and bending of the beam. For the sake of brevity, we restrict ourselves here only to the bending effect, which is a more interesting case from a mathematical point of view.