The Generalized Thermodynamical Beltrami – Michell Tensorial Equations for the general Thermodynamical State of the Hooke Body

Abstract

This paper concerns the mathematical linear model of the elastic, homogeneous and isotropic body, with no considerable structure and with infinitesimal elastic strains, subjected to Thermal effects, in the frame of coupled thermoelectrodynamics; discussed firstly by Hooke (in the isothermal case), and shortly called (H). In this paper, firstly we introduce the invariable tensorial traditional and Lame descriptions of the coupled dynamic, thermoelastic, homogeneous and isotropic Hooke body, which initial configuration forms a simply-connected region in the three dimensional euclidean manifold. The news of this paper consists in deriving the invariable tensorial, generalized Beltrami – Michell stress-temperature equations for the (H) thermoelastic body (in the more general case than the thermal stress state), which initial configuration forms a simply-connected region in the three dimensional euclidean manifold. Finally, we end the paper by suggesting the problem for discussing, in addition to another open problem.