7R52. Thermal Stresses. - N Noda (Dept of Mech Eng, Shizuoka Univ, Hamamatsu, Japan), RB Hetnarski (Dept of Mech Eng, Rochester Inst of Tech, Rochester NY, Japan). Y Tanigawa (Dept of Mech Syst Eng, Osaka Prefecture Univ, Sakai, Japan). Lastran Corp, Honeoye NY. 2000. 455 pp. ISBN 1-893000-01-X. \$70.00

Reviewed by P Puri (Dept of Math, Univ of New Orleans, 2000 Lakeshore Dr, New Orleans LA 70148).

The authors of this book are three eminent researchers who have made significant contributions to thermoelasticity. They have produced an excellent textbook. It is meant for senior undergraduates or graduate students. The reader is expected to be familiar with engineering mechanics and partial differential equations. Some use is made of Laplace transforms and special functions, in particular, the Bessel functions and the Legendre polynomials and functions. Appendices at the end of the book give adequate information on these topics. While the book is primarily meant as a textbook, it can also be useful to researchers as it contains the solutions to the basic problems in thermal stresses.

The language is clear and the illustrative examples are well chosen. They help the reader understand the processes of thermal stresses. For example, one of the illustrative examples is that of a clamped beam subjected to thermal expansion. This example explains very clearly how the thermal stresses are produced. Another illustrative example is the case of two horizontal bars of equal length, but different thermal expansion coefficients, with left ends clamped and right ends attached to a plate that can translate, but not rotate. When the bars are subjected to heating, one of them is subjected to stretching and the other to compression in addition to the thermal expansion. The stresses produced because of these effects are thoroughly analyzed. This reviewer presents these cases as a sample of the simple, but illustrative examples given throughout the book. A salient feature of the book is that most of the exercises have answers. This allows the book to be self instructional. The authors have been able to bring this book to the level of a beginning graduate student. They have successfully avoided notational obfuscation.

Chapter 1 is on thermal stresses in bars. The basic notion of stress and strain is presented. A number of solved examples are given to illustrate the theory. Chapter 2 discusses the thermal stresses in beams. This chapter starts with an exposition of stresses in beams due to mechanical loads, thereby explaining the concept of bending stress (normal stress) and bending moments. After this introductory section, thermal stresses in beams of different shapes and materials under various boundary and initial conditions are calculated.

Chapter 3 contains the derivation of the classical heat conduction equation based on Fourier’s law. The concepts of convection and radiation are explained. Solutions to several basic elementary problems are given. In Chapter 4, the governing equations of steady state thermoelasticity are developed. A general solution of Navier’s equations in terms of displacement functions and also in terms of Boussinesq-Papkovitch functions is derived. The analogy between the gradient of the temperature term in the thermoelastic equations and the body force term in the isothermal equations of elasticity is analyzed. Finally, the basic equations of thermoelasticity in terms of cylindrical and spherical coordinate systems and for multiply connected domains are derived. Chapter 5 is on plane problems in thermoelasticity. First, the notion of plane stress and plane strain is explained; then the governing equations for plane problems are derived. The governing equations are simplified by introducing the thermal stress function, and a general solution is presented. In the next section, the complex variable method is explained. In the last section, potential functions are introduced to obtain a general solution.

Chapter 6 contains solutions to the problems on thermal stresses in circular cylinders. The following techniques are discussed: The displacement technique, Thermal stress function, Thermoelastic potential, Complex variables, and the Dislocation method. A variety of problems are solved in order to explain these methods. Chapter 7 covers the determination of thermal stresses in spherical bodies. Starting with a simple one-dimensional example of thermal stresses in a spherical shell, the authors present solutions to problems of increasing complexity. Chapter 8 contains problems on thermal stresses in plates. A number of different boundary conditions and thermal loadings are considered. The problems of both theoretical and practical interest are solved.

Chapter 9 contains the analyses of thermal buckling of beams. In the process of buckling, small temperature variations can cause large effects, thereby causing instability. The final chapter is on thermodynamics as it relates to thermoelasticity. In the first section, the mathematical expression for the principle of energy conservation for thermoelasticity is derived. The second section is on the second law of thermodynamics. In this section, the reversible and irreversible processes, the cycle of Carnot, and the entropy are explained. In the next section, the Helmholtz free energy function, F, is introduced, and the Gibbs thermodynamic potential is expressed in terms of F, the stress and strain tensors. It is shown that the function, F, is independent of the spatial gradients of temperature. Entropy and stresses are expressed as gradients of F with respect to the temperature and the strain, respectively. Equations of heat conduction and the dynamical equations of thermoelasticity are derived in Section 4. The loss of energy due to mechanical expansion is taken into account, and the heat conduction equation contains the gradient of strain. Thus, the heat conduction equation and the dynamical equation of motion are coupled. A general solution of these equations is given. Section 5 is on variational theorems in thermoelasticity. Section 6 is on the uniqueness theorem, and the last section is on the reciprocal theorem. In this section, the use of the reciprocal theorem is made to solve a one-dimensional problem of thermal loading of a circular cylinder.

The authors have chosen, quite wisely, not to include the current developments in generalized thermoelasticity based on non-Fourier heat conduction laws. This subject has yet to reach maturity, and its inclusion would have increased the size and scope of the book excessively.

Thermal Stresses is strongly recommended as a textbook for a course in thermoelasticity, for libraries of universities at which engineering is taught, and for libraries of technical and research institutions. It is recommended for researchers as a source book for significant problems in thermoelasticity and their solutions under the classical regimes.