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Modeling Nonlinear Problems in the Mechanics of Strings and Rods

The Role of the Balance Laws

  • Oliver M. O'Reilly
Textbook

Part of the Interaction of Mechanics and Mathematics book series (IMM)

Table of contents

  1. Front Matter
    Pages i-xx
  2. Mechanics of Strings

    1. Front Matter
      Pages 1-1
    2. Oliver M. O’Reilly
      Pages 3-47
    3. Oliver M. O’Reilly
      Pages 49-92
    4. Oliver M. O’Reilly
      Pages 93-118
  3. Mechanics of Rods

    1. Front Matter
      Pages 119-119
    2. Oliver M. O’Reilly
      Pages 187-268
    3. Oliver M. O’Reilly
      Pages 269-293
    4. Oliver M. O’Reilly
      Pages 295-341
  4. Background Material

    1. Front Matter
      Pages 343-343
    2. Oliver M. O’Reilly
      Pages 345-375
    3. Oliver M. O’Reilly
      Pages 377-391
  5. Back Matter
    Pages 393-425

About this book

Introduction

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.

Keywords

Dynamics of Rods and Strings Continuum Mechanics Eshelbian Mechanics Nonlinear Dynamics of Deformable One-dimensional Continua Nonlinear Problems

Authors and affiliations

  • Oliver M. O'Reilly
    • 1
  1. 1.Department of Mechanical EngineeringUniversity of California, BerkeleyBerkeleyUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-50598-5
  • Copyright Information Springer International Publishing AG 2017
  • Publisher Name Springer, Cham
  • eBook Packages Engineering
  • Print ISBN 978-3-319-50596-1
  • Online ISBN 978-3-319-50598-5
  • Series Print ISSN 1860-6245
  • Series Online ISSN 1860-6253
  • Buy this book on publisher's site
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