5R19. Imperfect Bifurcation in Structures and Materials: Engineering Use of Group-Theoretic Bifurcation Theory. Applied Mathematical Sciences, Vol 149. - K Ikeda (Dept of Civil Eng, Tohoku Univ, Aoba Sendai, 980-8579, Japan) and K Murota (Dept of Math Informatics, Univ of Tokyo, Tokyo, 113-0033, Japan). Springer-Verlag, New York. 2002. 411 pp. ISBN 0-387-95409-0. $69.95.
Reviewed by J Petrolito (Sch of Sci and Eng, La Trobe Univ, PO Box 199, Bendigo, Vic 3550, Australia).
Stability theory is of fundamental importance in structural engineering, and there is a large body of literature in the field. Much of the theory is directed toward the prediction of buckling or bifurcation loads for ideal structures. However, the role of imperfections is crucial for real structures, particularly for those that are sensitive to these effects. The current book is a graduate-level text that presents an overview of imperfections and the prediction of the initial post-buckling response of a system. The treatment is predominately analytical, rather than numerical. Hence, the problems treated are relatively simple since the analysis of most practical systems requires numerical techniques such as the finite element method.
The book is divided into three parts and 15 chapters. Each chapter includes a range of problems and a summary to consolidate the material. The theory is complemented by nearly 200 references from the field. The first chapter provides an overview of the problems that are considered in the book. This chapter, although brief, could be used as an upper-undergraduate level introduction to the field.
The first part of the book introduces the basic theory and derives the imperfection sensitivity laws for simple critical points. The theory is also linked to the classification system from chaos theory. The discussion includes procedures to identify critical imperfections and the role of probability theory for modeling random imperfections. Part 1 concludes with a chapter that links the theory to the behavior of real structures and materials. Two restrictions of the theory should be noted. Firstly, the loading is assumed to be described by one parameter only. Hence, the theory is not applicable to non-proportional loading, which occurs frequently in practice. Secondly, only the initial post-buckling response is considered. Other techniques need to be used if the complete load-deflection response of the system is required.
Part 2 extends the theory to the analysis of systems with multiple critical points. This is inherently more difficult and the mathematical demands on the reader increase considerably. In particular, extensive use is made of group theory. Although the basics of this theory are covered, readers will probably need to supplement this with material from standard texts in the field to provide an adequate background to follow this part. Part 3 is primarily focused on modeling bifurcation in materials, including both metals and soils. This part of the books also relies on group theory.
In summary, Imperfect Bifurcation in Structures and Materials provides an extensive range of material on the role of imperfections in stability theory. It would be suitable for a graduate-level course on the subject or as a reference to research workers in the field.