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Stability Theory Of Elastic Rods


Stability Theory Of Elastic Rods
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Stability Theory Of Elastic Rods


Stability Theory Of Elastic Rods
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Author : Teodor Atanackovic
language : en
Publisher: World Scientific
Release Date : 1997-01-16

Stability Theory Of Elastic Rods written by Teodor Atanackovic and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997-01-16 with Technology & Engineering categories.


This book treats stability problems of equilibrium states of elastic rods. Euler energy and dynamical methods of stability analysis are introduced and stability criteria for each method is developed. Stability analysis is accompanied by a number of classical conservative and non-conservative, two- and three-dimensional problems. Some problems are treated by all three methods. Many generalized versions of known problems are presented (heavy vertical rod, rotating rod, Greenhill's problem, Beck's column, Pflüger's rod, strongest column, etc.). The generalizations consist in using either a generalized form of constitutive equations or a more general form of loading, or both. Special attention is paid to the influence of shear stresses and axis compressibility on the value of the critical load. Variational methods are applied to obtain estimates of the critical load and maximal deflection in the post-critical state, in a selected number of examples.



Stability Theory Of Elastic Rods


Stability Theory Of Elastic Rods
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Author : Teodor M. Atanackovic
language : en
Publisher: World Scientific
Release Date : 1997

Stability Theory Of Elastic Rods written by Teodor M. Atanackovic and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997 with Technology & Engineering categories.


This book treats stability problems of equilibrium states of elastic rods. Euler energy and dynamical methods of stability analysis are introduced and stability criteria for each method is developed. Stability analysis is accompanied by a number of classical conservative and non-conservative, two- and three-dimensional problems. Some problems are treated by all three methods. Many generalized versions of known problems are presented (heavy vertical rod, rotating rod, Greenhill's problem, Beck's column, Pflger's rod, strongest column, etc.). The generalizations consist in using either a generalized form of constitutive equations or a more general form of loading, or both. Special attention is paid to the influence of shear stresses and axis compressibility on the value of the critical load. Variational methods are applied to obtain estimates of the critical load and maximal deflection in the post-critical state, in a selected number of examples.



Linear Theories Of Elasticity And Thermoelasticity


Linear Theories Of Elasticity And Thermoelasticity
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Author : Clifford Truesdell
language : en
Publisher: Springer
Release Date : 2013-12-17

Linear Theories Of Elasticity And Thermoelasticity written by Clifford Truesdell and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-12-17 with Technology & Engineering categories.




Dynamics And Control Of Advanced Structures And Machines


Dynamics And Control Of Advanced Structures And Machines
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Author : Hans Irschik
language : en
Publisher: Springer
Release Date : 2016-11-11

Dynamics And Control Of Advanced Structures And Machines written by Hans Irschik and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-11-11 with Technology & Engineering categories.


The papers in this volume present and discuss the frontiers in the mechanics of controlled machines and structures. They are based on papers presented at the International Workshop on Advanced Dynamics and Model Based Control of Structures and Machines held in Vienna in September 2015. The workshop continues a series of international workshops held in Linz (2008) and St. Petersburg (2010).



Modeling Nonlinear Problems In The Mechanics Of Strings And Rods


Modeling Nonlinear Problems In The Mechanics Of Strings And Rods
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Author : Oliver M. O'Reilly
language : en
Publisher: Springer
Release Date : 2018-07-21

Modeling Nonlinear Problems In The Mechanics Of Strings And Rods written by Oliver M. O'Reilly and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-07-21 with Mathematics categories.


This book presents theories of deformable elastic strings and rods and their application to broad classes of problems. Readers will gain insights into the formulation and analysis of models for mechanical and biological systems. Emphasis is placed on how the balance laws interplay with constitutive relations to form a set of governing equations. For certain classes of problems, it is shown how a balance of material momentum can play a key role in forming the equations of motion. The first half of the book is devoted to the purely mechanical theory of a string and its applications. The second half of the book is devoted to rod theories, including Euler’s theory of the elastica, Kirchhoff ’s theory of an elastic rod, and a range of Cosserat rod theories. A variety of classic and recent applications of these rod theories are examined. Two supplemental chapters, the first on continuum mechanics of three-dimensional continua and the second on methods from variational calculus, are included to provide relevant background for students. This book is suited for graduate-level courses on the dynamics of nonlinearly elastic rods and strings.



Multiparameter Stability Theory With Mechanical Applications


Multiparameter Stability Theory With Mechanical Applications
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Author : Alexander P. Seyranian
language : en
Publisher: World Scientific
Release Date : 2003

Multiparameter Stability Theory With Mechanical Applications written by Alexander P. Seyranian and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003 with Technology & Engineering categories.


This book deals with fundamental problems, concepts, and methods ofmultiparameter stability theory with applications in mechanics. Itpresents recent achievements and knowledge of bifurcation theory, sensitivity analysis of stability characteristics, general aspects ofnonconservative stability problems, analysis of singularities ofboundaries for the stability domains, stability analysis ofmultiparameter linear periodic systems, and optimization of structuresunder stability constraints



A Primer On The Kinematics Of Discrete Elastic Rods


A Primer On The Kinematics Of Discrete Elastic Rods
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Author : M. Khalid Jawed
language : en
Publisher: Springer
Release Date : 2018-05-04

A Primer On The Kinematics Of Discrete Elastic Rods written by M. Khalid Jawed and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-05-04 with Technology & Engineering categories.


This primer discusses a numerical formulation of the theory of an elastic rod, known as a discrete elastic rod, that was recently developed in a series of papers by Miklós Bergou et al. Their novel formulation of discrete elastic rods represents an exciting new method to simulate and analyze the behavior of slender bodies that can be modeled using an elastic rod. The formulation has been extensively employed in computer graphics and is highly cited. In the primer, we provide relevant background from both discrete and classical differential geometry so a reader familiar with classic rod theories can appreciate, comprehend, and use Bergou et al.’s computational efficient formulation of a nonlinear rod theory. The level of coverage is suitable for graduate students in mechanics and engineering sciences.



Mathematical Approaches To Biomolecular Structure And Dynamics


Mathematical Approaches To Biomolecular Structure And Dynamics
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Author : Jill P. Mesirov
language : en
Publisher: Springer Science & Business Media
Release Date : 1996-08-29

Mathematical Approaches To Biomolecular Structure And Dynamics written by Jill P. Mesirov 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 1996-08-29 with Science categories.


This IMA Volume in Mathematics and its Applications MATHEMATICAL APPROACHES TO BIOMOLECULAR STRUCTURE AND DYNAMICS is one of the two volumes based on the proceedings of the 1994 IMA Sum mer Program on "Molecular Biology" and comprises Weeks 3 and 4 of the four-week program. Weeks 1 and 2 appeared as Volume 81: Genetic Mapping and DNA Sequencing. We thank Jill P. Mesirov, Klaus Schulten, and De Witt Sumners for organizing Weeks 3 and 4 of the workshop and for editing the proceedings. We also take this opportunity to thank the National Institutes of Health (NIH) (National Center for Human Genome Research), the National Science Foundation (NSF) (Biological Instrumen tation and Resources), and the Department of Energy (DOE), whose fi nancial support made the summer program possible. A vner Friedman Robert Gulliver v PREFACE The revolutionary progress in molecular biology within the last 30 years opens the way to full understanding of the molecular structures and mech anisms of living organisms. Interdisciplinary research in mathematics and molecular biology is driven by ever growing experimental, theoretical and computational power. The mathematical sciences accompany and support much of the progress achieved by experiment and computation as well as provide insight into geometric and topological properties of biomolecular structure and processes. This volume consists of a representative sample of the papers presented during the last two weeks of the month-long Institute for Mathematics and Its Applications Summer 1994 Program in Molecular Biology.



Stability Bifurcation And Postcritical Behaviour Of Elastic Structures


Stability Bifurcation And Postcritical Behaviour Of Elastic Structures
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Author : M. Pignataro
language : en
Publisher: Elsevier
Release Date : 2013-10-22

Stability Bifurcation And Postcritical Behaviour Of Elastic Structures written by M. Pignataro and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-10-22 with Technology & Engineering categories.


A comprehensive and systematic analysis of elastic structural stability is presented in this volume. Traditional engineering buckling concepts are discussed in the framework of the Liapunov theory of stability by giving an extensive review of the Koiter approach. The perturbation method for both nonlinear algebraic and differential equations is discussed and adopted as the main tool for postbuckling analysis. The formulation of the buckling problem for the most common engineering structures - rods and frames, plates, shells, and thin-walled beams, is performed and the critical load evaluated for problems of interest. In many cases the postbuckling analysis up to the second order is presented. The use of the Ritz-Galerkin and of the finite element methods is examined as a tool for approximate bifurcation analysis. The volume will provide an up-to-date introduction for non-specialists in elastic stability theory and methods, and is intended for graduate and post-graduate students and researchers interested in nonlinear structural analysis problems. Basic prerequisites are kept to a minimum, a familiarity with elementary algebra and calculus is all that is required of readers to make use of this book.



Stability Of Structures


Stability Of Structures
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Author : Z. P. Ba?ant
language : en
Publisher: World Scientific
Release Date : 2010

Stability Of Structures written by Z. P. Ba?ant and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010 with Technology & Engineering categories.


A crucial element of structural and continuum mechanics, stability theory has limitless applications in civil, mechanical, aerospace, naval and nuclear engineering. This text of unparalleled scope presents a comprehensive exposition of the principles and applications of stability analysis. It has been proven as a text for introductory courses and various advanced courses for graduate students. It is also prized as an exhaustive reference for engineers and researchers. The authors' focus on understanding of the basic principles rather than excessive detailed solutions, and their treatment of each subject proceed from simple examples to general concepts and rigorous formulations. All the results are derived using as simple mathematics as possible. Numerous examples are given and 700 exercise problems help in attaining a firm grasp of this central aspect of solid mechanics. The book is an unabridged republication of the 1991 edition by Oxford University Press and the 2003 edition by Dover, updated with 18 pages of end notes.