Bifurcation and Buckling in Structures

Science & Math

Murota, Kazuo

Ikeda, Kiyohiro

Mathematics

CRC-Press

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 the finite-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.&#12288; 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.&#12288; 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.

This book focuses on the optimization of a geometrically-nonlinear structure under stability constraint. It presents a deep insight into optimization-based and computer-assisted stability design of discrete structures. Coverage combines design sensitivity analysis developed in structural optimization and imperfection-sensitivity analysis developed in stability analysis.

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Ohsaki, Makoto

Reference

Springer

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Most physical systems lose or gain stability through bifurcation behavior. This book explains a series of experimentally found bifurcation phenomena by means of the methods of static bifurcation theory.

Bifurcation Theory of Pattern Formation in Economic Geography (Interdisciplinary Applied Mathematics, 61)

Takayama, Yuki

This book contributes to an understanding of how bifurcation theory adapts to the analysis of economic geography. It is easily accessible not only to mathematicians and economists, but also to upper-level undergraduate and graduate students who are interested in nonlinear mathematics. The self-organization of hexagonal agglomeration patterns of industrial regions was first predicted by the central place theory in economic geography based on investigations of southern Germany. The emergence of hexagonal agglomeration in economic geography models was envisaged by Krugman. In this book, after a brief introduction of central place theory and new economic geography, the missing link between them is discovered by elucidating the mechanism of the evolution of bifurcating hexagonal patterns. Pattern formation by such bifurcation is a well-studied topic in nonlinear mathematics, and group-theoretic bifurcation analysis is a well-developed theoretical tool. A finite hexagonal lattice is used to express uniformly distributed places, and the symmetry of this lattice is expressed by a finite group. Several mathematical methodologies indispensable for tackling the present problem are gathered in a self-contained manner. The existence of hexagonal distributions is verified by group-theoretic bifurcation analysis, first by applying the so-called equivariant branching lemma and next by solving the bifurcation equation. This book offers a complete guide for the application of group-theoretic bifurcation analysis to economic agglomeration on the hexagonal lattice.

Bifurcation Theory for Hexagonal Agglomeration in Economic Geography

This book offers a theoretical foundation for the self-organization of hexagonal agglomeration patterns of industrial regions, surveying the bifurcations of economic geography models for a system of cities on a hexagonal lattice. Offers advice on application.

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Books by Ikeda, Kiyohiro

See the best price to sell, buy, or rent books by Ikeda, Kiyohiro. BookScouter helps to compare book prices from 25+ online bookstores and 30+ buyback vendors with a single search.

Bifurcation and Buckling in Structures

Bifurcation and Buckling in Structures

Stability and Optimization of Structures: Generalized Sensitivity Analysis (Mechanical Engineering Series)

Stability and Optimization of Structures: Generalized Sensitivity Analysis (Mechanical Engineering Series)

Imperfect Bifurcation in Structures and Materials: Engineering Use of Group-Theoretic Bifurcation Theory (Applied Mathematical Sciences, 149)

Imperfect Bifurcation in Structures and Materials: Engineering Use of Group-Theoretic Bifurcation Theory (Applied Mathematical Sciences, 149)

Imperfect Bifurcation in Structures and Materials: Engineering Use of Group-Theoretic Bifurcation Theory (Applied Mathematical Sciences, 149)

Bifurcation Theory of Pattern Formation in Economic Geography (Interdisciplinary Applied Mathematics, 61)

Bifurcation Theory for Hexagonal Agglomeration in Economic Geography

Bifurcation Theory for Hexagonal Agglomeration in Economic Geography