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.

Recent technology involves large-scale physical or engineering systems consisting of thousands of interconnected elementary units. This monograph illustrates how engineering problems can be solved using the recent results of combinatorial mathematics through appropriate mathematical modeling. The structural solvability of a system of linear or nonlinear equations as well as the structural controllability of a linear time-invariant dynamical system are treated by means of graphs and matroids. Special emphasis is laid on the importance of relevant physical observations to successful mathematical modelings. The reader will become acquainted with the concepts of matroid theory and its corresponding matroid theoretical approach. This book is of interest to graduate students and researchers.

Systems Analysis by Graphs and Matroids: Structural Solvability and Controllability (Algorithms and Combinatorics)

Springer, Verlag

Discrete Convex Analysis is a novel paradigm for discrete optimization that combines the ideas in continuous optimization (convex analysis) and combinatorial optimization (matroid/submodular function theory) to establish a unified theoretical framework for nonlinear discrete optimization. The study of this theory is expanding with the development of efficient algorithms and applications to a number of diverse disciplines like matrix theory, operations research, and economics. This self-contained book is designed to provide a novel insight into optimization on discrete structures and should reveal unexpected links among different disciplines. It is the first and only English-language monograph on the theory and applications of discrete convex analysis. Discrete Convex Analysis provides the information that professionals in optimization will need to "catch up" with this new theoretical development. It also presents an unexpected connection between matroid theory and mathematical economics and expounds a deeper connection between matrices and matroids than most standard textbooks.

Discrete Convex Analysis (Monographs on Discrete Mathematics and Applications, Series Number 10)

Society for Industrial and Applied Mathematics

This illustrated book provides a modern investigation into the bifurcation phenomena of physical and engineering problems. Systematic methods are used to examine experimental and computational data from numerous examples (soil, sand, kaolin, concrete, domes).

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

Reference

Springer

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.

Systems Analysis by Graphs and Matroids: Structural Solvability and Controllability (Algorithms and Combinatorics, 3)

Matrices and Matroids for Systems Analysis (Algorithms and Combinatorics, 20)

A matroid is an abstract mathematical structure that captures combinatorial properties of matrices. This book offers a unique introduction to matroid theory, emphasizing motivations from matrix theory and applications to systems analysis. This book serves also as a comprehensive presentation of the theory and application of mixed matrices, developed primarily by the present author in the 1990's. A mixed matrix is a convenient mathematical tool for systems analysis, compatible with the physical observation that "fixed constants" and "system parameters" are to be distinguished in the description of engineering systems. This book will be extremely useful to graduate students and researchers in engineering, mathematics and computer science. From the reviews: "…The book has been prepared very carefully, contains a lot of interesting results and is highly recommended for graduate and postgraduate students." András Recski, Mathematical Reviews Clippings 2000m:93006

Computers & Technology

Computer Science

This book offers a unique introduction to matroid theory, emphasizing motivations from matrix theory and applications to systems analysis. It serves also as a comprehensive presentation of the theory and application of mixed matrices.

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

Books by Murota, Kazuo

See the best price to sell, buy, or rent books by Murota, Kazuo. 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

Systems Analysis by Graphs and Matroids: Structural Solvability and Controllability (Algorithms and Combinatorics)

Discrete Convex Analysis (Monographs on Discrete Mathematics and Applications, Series Number 10)

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)

Systems Analysis by Graphs and Matroids: Structural Solvability and Controllability (Algorithms and Combinatorics, 3)

Matrices and Matroids for Systems Analysis (Algorithms and Combinatorics, 20)

Matrices and Matroids for Systems Analysis (Algorithms and Combinatorics, 20)