Some results, following Gibbs and Murnaghan, on thegeneral thermodynamical properties of a continuous andisotropic medium are reviewed in Part I. These discussionslead to the formulation of various thermodynamic functionsfor a thermo-elastic solid in small strain. The expressionfor the free energy is useful, in particular, for approximate solutions of thermal stress problems involving either steady or transient heating. Also in Part I, a rather general condition is established under which the inertia effect due to transient thermal expansions may be neglected. Conditions under which temperature distributions may be calculated independently of stresses and strains are also given. Attention is given to the order of approximations involved in such simplifications.
The general results in Part I are applied to two problemsin Part II and Part III. The problem of thermal shock,a type of failure due to sudden heating or cooling, isstudied in Part II. The analytic results obtained thereare compared with the experimental results on thermal shockcarried out by N.A.C.A. investigators on circular ceramicand ceramal dics. The correlation between theory andexperiment is considered satisfactory.
Thermal stresses in thin cylindrical shells and platesare formulated and discussed in Part III. It is assumed thatthe temperature varies only across the thickness, and the Young's modulus may be an arbitrary function of temperature. A convention regarding the choice of the reference surface is introduced, by means of which the present theory becomes comparable to the ordinary theory of plates and shells. Methods based on similarity considerations are devised such that the resulting stresses and strains in a shell or plate caused by temperature gradient and external loads can be predicted by experimenting with a similar specimen at a uniform temperature. These considerations are motivated by the necessity to overcome the difficulties both in analyticcalculations and experimental measurements of stressesand strains at elevated temperatures, especially whentransient heating and complicated loads are involved. Sucha situation arises, for example, in the combustion chamberof a rocket engine, where stresses produced by supportingseats are often too complicated to compute by purelyanalytical methods.
