Imperfect Bifurcation In Structures And Materials
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Imperfect Bifurcation In Structures And Materials
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Author : Kiyohiro Ikeda
language : en
Publisher: Springer Nature
Release Date : 2019-09-25
Imperfect Bifurcation In Structures And Materials written by Kiyohiro Ikeda and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-09-25 with Science categories.
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.
Imperfect Bifurcation In Structures And Materials
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Author : Kiyohiro Ikeda
language : en
Publisher:
Release Date : 2014-01-15
Imperfect Bifurcation In Structures And Materials written by Kiyohiro Ikeda and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-01-15 with categories.
Bifurcation And Buckling In Structures
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Author : Kiyohiro Ikeda
language : en
Publisher: CRC Press
Release Date : 2021-12-30
Bifurcation And Buckling In Structures written by Kiyohiro Ikeda and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-12-30 with Mathematics categories.
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. 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.
Stability And Optimization Of Structures
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Author : Makoto Ohsaki
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-06-10
Stability And Optimization Of Structures written by Makoto Ohsaki and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-06-10 with Technology & Engineering categories.
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.
Resolution Of The Twentieth Century Conundrum In Elastic Stability
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Author : Isaac E Elishakoff
language : en
Publisher: World Scientific
Release Date : 2014-05-29
Resolution Of The Twentieth Century Conundrum In Elastic Stability written by Isaac E Elishakoff and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-05-29 with Technology & Engineering categories.
There have been stability theories developed for beams, plates and shells — the most significant elements in mechanical, aerospace, ocean and marine engineering. For beams and plates, the theoretical and experimental values of buckling loads are in close vicinity. However for thin shells, the experimental predictions do not conform with the theory, due to presence of small geometric imperfections that are deviations from the ideal shape.This fact has been referred to in the literature as ‘embarrassing’, ‘paradoxical’ and ‘perplexing’. Indeed, the popular adage, “In theory there is no difference between theory and practice. In practice there is”, very much applies to thin shells whose experimental buckling loads may constitute a small fraction of the theoretical prediction based on classical linear theory; because in practice, engineers use knockdown factors that are not theoretically substantiated.This book presents a uniform approach that tames this prima-donna-like and capricious behavior of structures that has been dubbed the ‘imperfection sensitivity’ — thus resolving the conundrum that has occupied the best minds of elastic stability throughout the twentieth century.
Local Bifurcations Center Manifolds And Normal Forms In Infinite Dimensional Dynamical Systems
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Author : Mariana Haragus
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-11-23
Local Bifurcations Center Manifolds And Normal Forms In Infinite Dimensional Dynamical Systems written by Mariana Haragus and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-11-23 with Mathematics categories.
An extension of different lectures given by the authors, Local Bifurcations, Center Manifolds, and Normal Forms in Infinite Dimensional Dynamical Systems provides the reader with a comprehensive overview of these topics. Starting with the simplest bifurcation problems arising for ordinary differential equations in one- and two-dimensions, this book describes several tools from the theory of infinite dimensional dynamical systems, allowing the reader to treat more complicated bifurcation problems, such as bifurcations arising in partial differential equations. Attention is restricted to the study of local bifurcations with a focus upon the center manifold reduction and the normal form theory; two methods that have been widely used during the last decades. Through use of step-by-step examples and exercises, a number of possible applications are illustrated, and allow the less familiar reader to use this reduction method by checking some clear assumptions. Written by recognised experts in the field of center manifold and normal form theory this book provides a much-needed graduate level text on bifurcation theory, center manifolds and normal form theory. It will appeal to graduate students and researchers working in dynamical system theory.
Bifurcation Theory Of Pattern Formation In Economic Geography
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Author : Kiyohiro Ikeda
language : en
Publisher: Springer Nature
Release Date : 2024-11-14
Bifurcation Theory Of Pattern Formation In Economic Geography written by Kiyohiro Ikeda and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-11-14 with Mathematics categories.
Dive into the fascinating world of economic agglomerations with this interdisciplinary study, which is perfect for readers in nonlinear mathematics, economic geography, and spatial economics. This book uniquely bridges these fields, employing group-theoretic bifurcation analysis in nonlinear mathematics to establish a robust theoretical foundation for economic geographers and mathematicians alike. Explore innovative models that describe the pattern formation in economic agglomerations through worker migration between regions. Delve into multi-regional formulations of classic economic geography models, applied to various spatial platforms such as line segments, racetracks, squares, and hexagonal lattices. This book, ideal for researchers and practitioners, offers cutting-edge insights and methodologies for understanding the complexities of spatial economic agglomerations.
Analysis And Control Of Complex Dynamical Systems
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Author : Kazuyuki Aihara
language : en
Publisher: Springer
Release Date : 2015-03-20
Analysis And Control Of Complex Dynamical Systems written by Kazuyuki Aihara and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-03-20 with Technology & Engineering categories.
This book is the first to report on theoretical breakthroughs on control of complex dynamical systems developed by collaborative researchers in the two fields of dynamical systems theory and control theory. As well, its basic point of view is of three kinds of complexity: bifurcation phenomena subject to model uncertainty, complex behavior including periodic/quasi-periodic orbits as well as chaotic orbits, and network complexity emerging from dynamical interactions between subsystems. Analysis and Control of Complex Dynamical Systems offers a valuable resource for mathematicians, physicists, and biophysicists, as well as for researchers in nonlinear science and control engineering, allowing them to develop a better fundamental understanding of the analysis and control synthesis of such complex systems.
Bifurcation Theory For Hexagonal Agglomeration In Economic Geography
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Author : Kiyohiro Ikeda
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-11-08
Bifurcation Theory For Hexagonal Agglomeration In Economic Geography written by Kiyohiro Ikeda and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-11-08 with Technology & Engineering categories.
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.
Singularities Bifurcations And Catastrophes
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Author : James Montaldi
language : en
Publisher: Cambridge University Press
Release Date : 2021-06-24
Singularities Bifurcations And Catastrophes written by James Montaldi and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-06-24 with Mathematics categories.
This textbook gives a contemporary account of singularity theory and its principal application, bifurcation theory.