Theories of thermoelasticity. In the static uncoupled thermoelasticity, thermal effects on a body are restricted to strains due to a steady-state temperature distribution. As a more general the- ory of thermoelasticity, considering the transient heat conduction equation leads to time-dependent temperature distributions which can be used to obtain the transient thermal stresses. Such problems are called quasi-static uncoupled thermoelasticity problems. Alternatively, if external thermo-mechanical loads applied to the body vary adequately rapidly with the time so that inertia effects are excited, the inertia terms must be taken into account in the equations of motion. This theory is known as the dynamic uncoupled thermoelasticity. It is obvious that in all these theories, the temperature field is independently obtained from the heat conduction equation, while the displacement and stress fields are assumed to be dependent of the temper- ature. When a structure is exposed to high-speed thermo-mechanical loads, the theories of uncoupled thermoelasticity may not provide entirely true physical behaviors. To avoid this drawback, interactions of the mechanical state of the elastic body on the temperature filed may be also simulated using the theories of coupled thermoelas- ticity. In these theories, the time derivatives of strain appear in the heat conduction equation so as to lead to the coupling between elasticity and energy equations. Ac- cordingly, to find the solution for temperature and displacement fields and finally stresses, these coupled equations must be solved concurrently. The thermoelasticity equations with the coupling effect was introduced by Xxxxxxx [27] in 1837, for the first time, and then 120 years later, Biot [10], in 1956, presented the theory of classical thermoelasticity based on the principles of the irreversible thermodynamics. A history of thermoelasticity can be further found in the text- books [11, 41]. Thus, under thermo-mechanical shock loading, the inertia and coupling effects can play important role in the thermoelastic behavior of a body. However, it has been shown that the coupling term may be more effective on the temperature and stress distributions than the inertia term in such situations (see [11, 41]). Applications of the coupled thermoelasticity in advanced structural design problems have attracted the attention of many researchers during the second half of the last century. These applications can range from aerospace structures to fast-burst reac- tors,...
