Galerkin Finite Element Displacement Formulation of Coupled Thermoelasticity Spherical Problems

Abstract

When the time rate of change of the thermomechanical forces in a continuum is high enough to produce stress wave, the solution must be sought through the simultaneous consideration of the first law of thermodynamics and the equations of thermoelasticity. The general finite element formulation of coupled thermoelasticity along with a general discussion for inclusion of mechanical and thermal boundary conditions is presented. The case is then considered for a spherical symmetry and the governing coupled thermoelastic equations are reduced for a thick sphere. Based on the Galerkin method, a Kantrovich approximation is applied to the displacement and temperature field and the finite element formulation of the problem is obtained.