UK Nonlinear News, November 2002


Imperfect Bifurcation in Structures and Materials

Kiyohiro Ikeda and Kazuo Murota

Reviewed by David Wagg

This book is a comprehensive treatment of the static bifurcation problems found in (mainly civil/structural) engineering applications. The focus is the effect of initial imperfection on bifurcation behaviour and a group theoretic approach is used to extend the analysis from simple structural elements to structures with more complex geometry including soils.

After an introductory chapter, the book is divided into three main parts. The first part deals with imperfect behaviour at simple critical points. This starts with a chapter on critical points and local behaviour which covers Liapunov-Schmidt reduction and classification of critical points. Following this are chapters on imperfection sensitivity laws (such as the Koiter two-thirds power law), critical initial imperfections and random initial imperfections. The final chapter in this part of the book looks at how to relate the perfect theoretical system to experimental observations by, for example, reconstructing the perfect system from a series of imperfect paths.

The second part of the book deals with imperfect bifurcation of symmetric systems and the first two chapters introduce the group theoretic approach to analysing static bifurcation problems. This approach is dependent on the inherent symmetries to be found in many structures. The examples covered in this part of the book can generally be modelled using the dihedral and cyclic groups. Subsequent chapters on critical initial imperfection, random initial imperfection and description of bifurcation behaviour use dome structures and soils as illustrative examples.

The final part of the book is on "modelling of bifurcation phenomena" with two chapters on soil specimens, one on steel and a final chapter covering miscellaneous bifurcation phenomena. This part tackles more complex systems which have both imperfection and uncertainty. Experimental results from cylindrical sand specimens are analysed and a detailed chapter on echelon-mode formation in both sand/soil is presented. As with part 2 strong use of the inherent symmetries in the systems are used to exploit the group theoretic approach where possible.

The style of the book is difficult to fault. The text is well written and regularly interspersed with illustrative examples. The mathematical formalism is kept to a minimum and the 194 figures (many of which show experimental results/photos) break up the text and make this a highly readable and informative book. The authors have also gone to the trouble of making chapter one and overview of the topics covered in the whole book. In summary a comprehensive treatment of the subject which is very well put together and of interest to all researchers working in this area: recommended.

UK Nonlinear News thanks Springer-Verlag for providing a review copy of this book.

A listing of books reviewed in UK Nonlinear News is available.


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