Deflection of Hyperstatic Thermoelastic Structures

In the classical theory of thermoelastic solids, the deflection of linearly elastic isotropic bodies as a result of applied thermal loads can be determined using Maisel's Integral Solution, a technique based on Betti's Reciprocal Theorem. It is a requirement of the technique that a solution to the isothermal equivalent linear elastic stress distribution problem is available. In the conventional structural analysis of linearly elastic structures, a particular adaptation of the virtual work method, known as the unit (dummy) load technique, may be used to obtain structure deflections. It has recently been shown that this technique can be adapted for the solution of hyperstatic structures where the hyperstatic stress distribution due to applied loading is not known. It will be shown that these approaches to deflection calculation are essentially equivalent, and that the application of either technique can considerably simplify deflection calculations for hyperstatic structures subject to temperature differentials.