Imperfect Bifurcation in Structures and Materials Engineering Use of Group-Theoretic Bifurcation Theory

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.

Introduction to Bifurcation Behavior * Critical Point and Local Behavior * Imperfection Sensitivity Laws * Critical Initial Imperfections (I) * Stochasticity of Initial Imperfections (I) * Experimentally-observed Bifurcation Diagrams * Group-theoretic Bifurcation Theory * Bifurcation Behavior of Dn-equivariant Systems * Critical Initial Imperfections (II) * Stochasticity of Initial Imperfections (II) * Description of Bifurcation Behaviors * Bifurcation of Cylindrical Sand Specimens * Echelon-mode Formation * Bifurcation of Steel Specimens * Miscellaneous Aspects of Bifurcation Phenomena * References * Index

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.