Bifurcation and Buckling in Structures

Bifurcation and Buckling in Structures describes the theory and analysis of bifurcation and buckling in structures. Emphasis is placed on a general procedure for solving nonlinear governing equations and an analysis procedure related to thefinite-element method. Simple structural examples using trusses, columns, and frames illustrate the principles. Part I presents fundamental issues such as the general mathematical framework for bifurcation and buckling, procedures for the buckling load/mode analyses, and numerical analysis procedures to trace the solution curves and switch to bifurcation solutions. Advanced topics include asymptotic theory of bifurcation and bifurcation theory of symmetric systems. Part II deals with buckling of perfect and imperfect structures. An overview of the member buckling of columns and beams is provided, followed by the buckling analysis of truss and frame structures. The worst and random imperfections are studied as advanced topics. An extensive review of the history of buckling is presented. This text is ideal for advanced undergraduate and graduate students in engineering and applied mathematics. To assist readers, problems are listed at the end of each chapter, and their answers are given at the end of the book. Kiyohiro Ikeda is Professor Emeritus at Tohoku University, Japan. Kazuo Murota is a Project Professor at the Institute of Statistical Mathematics, Japan, as well as Professor Emeritus at the University of Tokyo, Kyoto University, and Tokyo Metropolitan University, Japan.

Part 1. Bifurcation in Structures 1. Introduction to Buckling and Bifurcation 2. Analysis of Buckling Load and Mode 3. Numerical Analysis I: Path Tracing 4. Numerical Analysis II: Branch Switching 5. Bifurcation Theory I: Basics 6. Bifurcation Theory II: Symmetric Structures Part 2. Buckling of Structures 7. Member Buckling of Columns and Beams 8. Structural Buckling I: Truss 9. Structural Buckling II: Frame 10. Advanced Topics on Imperfect Systems 11. History of Imperfect Buckling Appendix A. Answers to Problems

Kiyohiro Ikeda is Professor Emeritus at Tohoku University, Japan. His research interests include the application of bifurcation theory to bifurcation and buckling in structures and materials, as well as the theoretical and numerical analysis of structures with initial imperfections. Kazuo Murota is a Project Professor at the Institute of Statistical Mathematics, Japan, as well as Professor Emeritus at the University of Tokyo, Kyoto University, and Tokyo Metropolitan University, Japan. His research interests include bifurcation theory, discrete optimization, and numerical analysis.