Spatial Behavior in the Strongly Elliptic Anisotropic Thermoelastic Materials

Abstract

In the present article we consider a prismatic semi-infinite cylinder occupied by an anisotropic homogeneous compressible linear thermoelastic material having an elasticity tensor that is strongly elliptic. The cylinder is subjected to zero body force and heat supply, zero displacement–temperature variation on the lateral boundary and pointwise specified displacement–temperature variation over the base. The main purpose of this contribution is to examine how certain measures of the displacement–temperature variation evolve with respect to the axial variable, provided that the strong ellipticity of the elasticity tensor is assumed. To this end, some appropriate measures are associated with the displacement–temperature variation and then an appropriate second-order differential inequality is established under the strong ellipticity condition on the elasticity tensor. The results are specialized for transversely isotropic and rhombic systems of elastic materials.