Imperfect Bifurcation in Structures and Materials Engineering Use of Group-Theoretic Bifurcation Theory - Ikeda, Kiyohiro; Murota, Kazuo; SpringerLink (Online service) (New York, NY : Springer New York, 2010)
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 (soil, sand, kaolin, concrete, domes). For mathematicians, static bifurcation theory for finite-dimensional systems, as well as its implications for practical problems, is illuminated by the numerous examples. Engineers may find this book, with its minimized mathematical formalism, to be a useful introduction to modern bifurcation theory. This second edition strengthens the theoretical backgrounds of group representation theory and its application, uses of block-diagonalization in bifurcation analysis, and includes up-to-date topics of the bifurcation analysis of diverse materials from rectangular parallelepiped sand specimens to honeycomb cellular solids. Reviews of first edition: "The present book gives a wide and deep description of imperfect bifurcation behaviour in engineering problems. $1! = (Bthe book offers a number of systematic methods based on contemporary mathematics. $1! = (BOn balance, the reviewed book is very useful as it develops a modern static imperfect bifurcation theory and fills the gap between mathematical theory and engineering practice." (Zentralblatt MATH, 2003) "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. ... 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." ( Applied Mechanics Reviews, 2003) "This book is a comprehensive treatment of the static bifurcation problems found in (mainly civil/structural) engineering applications.... The text is well written and regularly interspersed with illustrative examples. The mathematical formalism is kept to a minimum and the 194 figures break up the text and make this a highly readable and informative 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, 2002)s
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.
Keywords: Mathematics; Differentiable dynamical systems; Mechanical engineering; Mathematics; Dynamical Systems and Ergodic Theory; Structural Mechanics