New Thermomechanical Reciprocity Relations With Application to Thermal Stress Analysisi

Based on the variational formulation of linear thermodynamics as developed previously by the writer, thermomechanical reciprocity relations are discussed which lead to new methods of analysis of thermal stresses. These reciprocity relations are quite different from the usual ones derived from the analogy of thermal loading with a combination of surface and body-force distribution. The results are applicable to stationary and transient temperatures in elastic and viscoelastic structures. The methods are entirely variational and do not require the evaluation of the temperature field. The stresses at one point are expressed directly in terms of any arbitrary distribution temperatures applied externally, including the effect of surface heat-transfer layer. The concepts and procedures are illustrated on a simple example. The relation is pointed out between the reciprocity property and the generalization of Castigliano’s principle to thermomechanics.