9R26. Linearized Theory of Elasticity. - WS Slaughter (Dept of Mech Eng, Univ of Pittsburgh, Pittsburgh PA 15261). Birkhauser Boston, Cambridge MA. 2002. 543 pp. ISBN 0-8176-4117-3. $79.95.
Reviewed by J Petrolito (Sch of Sci and Eng, La Trobe Univ, PO Box 199, Bendigo, Vic 3550, Australia).
This is a graduate-level text on elasticity theory that is aimed towards engineering students. There is a good balance between theory and practical applications, with the latter being particularly important for the stated audience. Elasticity theory is treated as a specialization of continuum mechanics rather than as an isolated theory. This approach acknowledges the basic concepts of continuum mechanics, without burdening the presentation with excessive generalities.
The book is divided into 11 chapters and an appendix. The first chapter contains a brief review of some very basic undergraduate theory on mechanics of solids. Although the author’s intention was to link this material with the elasticity theory presented in the remainder of the book, this chapter does not fit well within the book and could have been omitted without loss. In keeping with modern trends in the field, elasticity theory is predominately developed using direct tensor and cartesian tensor notation, and the second chapter provides a good introduction to these topics. The appendix describes the changes required when dealing with curvilinear coordinate systems.
Chapters 3–5 introduce the fundamental concepts of the theory, namely strain measures, stress measures and balance conditions, and constitutive relationships. The assumptions required to obtain the linear results from the nonlinear results are clearly described. This enables students to clearly understand the limitations of the linear results, rather than blindly using them in inappropriate situations. Chapter 6 summarizes the governing equations and discusses the basic issues associated with their solution, such as boundary conditions, uniqueness of the solution, and reciprocal theorems.
Chapters 7–9 use the theory to solve some typical two- and three-dimensional problems. The material in these chapters covers the usual range of topics normally found in elasticity books such as plane stress and place strain problems and torsion theory. However, the three-dimensional applications also include some unusual topics, namely dislocation surfaces and inclusion problems. These topics are useful in the fields of crystalline and composite materials and fracture mechanics.
Chapter 10 provides a brief discussion on energy theorems and the generation approximate solutions using the Rayleigh-Ritz method. The latter topic is of vital importance for obtaining solutions for practical problems, and the material could have been expanded to reflect this. The final chapter discusses the use of complex variable theory. This lengthy chapter derives general solutions of the governing equations and applies the theory to some important problems such as stress concentrations and cracks.
The book includes a good range of discussion and examples in each chapter to motivate and complement the theory, and problems are also included at the end of each chapter. This book is written in a clear style, and this makes it easy for students to assimilate the material. Hence, Linearized Theory of Elasticity can be recommended as a good example of a modern textbook in this field.