Imperfect Bifurcation in Structures and Materials

This book provides a modern investigation into the bifurcation phenomena of physical and engineering problems. Systematic methods--based on asymptotic, probabilistic, and group-theoretic standpoints--are used to examine experimental and computational data from numerous examples (e.g., soil, sand, kaolin, concrete, domes, etc.). Engineers may find this book, with its minimized mathematical formalism, to be a useful introduction to modern bifurcation theory. For mathematicians, static bifurcation theory for finite dimensional systems, as well as its implications for practical problems, is illuminated by the numerous examples.

The ?rst edition of this book was published in 2002 for an audience of applied mathematicians and engineers. The response to the ?rst edition, represented by sev eral book reviews, has been most heartening. Accordingly, the second edition of this book maintains its major framework and serves as an expanded revision of our previous work. In the second edition, the theoretical backgrounds of group representation the ory are strengthened and made self contained, in response to a request of a book reviewer and students of the authors. Based on these strengthened backgrounds, a theory and a numerical procedure on block diagonalization are presented. Among a number of methodologies, block diagonalization analysis has come to be acknowl edged as a systematic and rigorous procedure for symmetry exploitation for the following two purposes: • Gain better insight into bifurcation behaviors via blockwise singularity detection. • Enhance the computational e?ciency and accuracy of the numerical analysis.

Exercises at the ends of chapters or sections Solutions to selected exercises in the book Detailed Illustrations

Auteur
Kiyohiro Ikeda is a Professor in the Department of Civil Engineering, Graduate School of Engineering at Tohoku University. Kazuo Murota is a Professor in the Department of Mathematical Informatics, Graduate School of Information Science and Technology at University of Tokyo.

Contenu
Overview of Book.- Imperfect Behavior at Simple Critical Points.- Critical Points and Local Behavior.- Imperfection Sensitivity Laws.- Worst Imperfection (I).- Random Imperfection (I).- Experimentally Observed Bifurcation Diagrams.- Imperfect Bifurcation of Symmetric Systems.- Group-Theoretic Bifurcation Theory.- Bifurcation Behavior of Dn-Equivariant Systems.- Worst Imperfection (II).- Random Imperfection (II).- Description and Computation of Bifurcation Behaviors.- Efficient Transformation for Block-Diagonalization.- Modeling of Bifurcation Phenomena.- Bifurcation of Cylindrical Sand Specimens.- Echelon-Mode Formation.- Bifurcation of Steel Specimens.- Flower Patterns on Honeycomb Structures.