9R9. Mechanics of Solids and Shells: Theories and Approximations. - G Wempner (Georgia Inst of Tech, Atlanta GA) and D Talaslidis (Aristotle Univ, Thessaloniki, Greece). CRC Press LLC, Boca Raton FL. 2003. 529 pp. ISBN 0-8493-9654-9. $119.95.
Reviewed by J Petrolito (Sch of Sci and Eng, La Trobe Univ, PO Box 199, Bendigo, Vic 3550, Australia).
This book can be considered a revised and updated edition of the first author’s book Mechanics of Solids with Applications to Thin Bodies, which was originally published in 1973. Readers who are familiar with this book will find that much of it has been retained, usually verbatim, in the book under review. The main differences are a slight rearrangement of the material, a new chapter on finite elements, and disappointedly, the deletion of the exercises. This latter change, which diminishes the usefulness of the book as a teaching text, is difficult to understand.
The book is suitable for senior undergraduate or postgraduate students and aims to provide a broad foundation of the fundamentals of stress analysis for solids. Much of the text makes significant use of general tensor analysis, and this is briefly covered in Chapters 1 and 2. The book uses component tensor notation, rather than direct ten-sor notation.
Chapters 3–5 cover the fundamentals of continuum mechanics. Chapter 3 discusses the geometry of deformation and the various notions of strain. It also covers the transformations and decompositions of the strain tensor, and the simplifications that can be used under certain conditions, such as for the case of small strains. Chapter 4 introduces the stress tensor and its properties. The two concepts are linked in a lengthy Chapter 5 on constitutive relationships, including elastic and plastic effects.
The energy principles of solid mechanics are discussed in Chapter 6. Virtual work is used as a starting point for deriving the various variational principles and their applications. This chapter also includes a brief discussion on stability theory. Chapter 7 simplifies the general formulation to linear behavior, and discusses some representative problems in two-dimensions. These include plane stress and plane strain problems, stress concentration and torsion theory.
Chapter 8 develops the differential geometry of a surface theory, and this acts as a prelude to Chapter 9 on shell theory. The latter chapter provides a concise presentation of the theory and the role of approximations. The development is continued in Chapter 10, which introduces the Kirchhoff-Love constraint and its implications. The final chapter provides a brief introduction to the finite element method.
Judged on its own merits, Mechanics of Solids and Shells: Theories and Approximations is a useful introduction to the field, and it can also serve as a reference for practicing engineers and researchers in the area. As mentioned previously, the lack of exercises makes it more difficult to use as a teaching text, and it would need to be supplemented if used in this role.