Alternative Formulations: Reciprocal Relations

Synonyms

Alternative formulations; Linear theory; Reciprocal relations; Thermoelasticity

Overview

We give an alternative characterization of the solution to the mixed boundary–initial value problem of linear thermoelasticity in which the initial conditions are incorporated into the field equations. In the classical elasticity, such characterization was established by Ignaczak [8] (see also Gurtin [2, 3]).

We will use the alternative formulation of the mixed boundary–initial value problem in order to establish some reciprocal relations within the framework of linear theory of thermoelasticity for anisotropic and inhomogeneous materials. The reciprocal relation is derived for a body of volume region $B$ and surface $\partial B$ and represents an integral relation over $B$ and $\partial B$between body supplies, surface traction and surface flux, and displacements and temperature variations of two solutions of the mixed problem of the linear thermoelasticity, namely, a...