Interaction of Mechanics and Mathematics

Modeling Nonlinear Problems in the Mechanics of Strings and Rods

The Role of the Balance Laws

Authors: O'Reilly, Oliver

  • Includes two appendices that review topics on continuum mechanics and variational methods
  • Separated into two parts on strings and rods for convenience of reading and learning
  • Contains many examples and illustrations throughout
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eBook $59.99
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  • ISBN 978-3-319-50598-5
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  • Immediate eBook download after purchase
Hardcover $79.99
price for USA
  • ISBN 978-3-319-50596-1
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
About this Textbook

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.

About the authors

Oliver M. O’Reilly is a professor in the Department of Mechanical Engineering at the University of California at Berkeley (UCB). He received his B.E. in Mechanical Engineering from the National University of Ireland, Galway (NUIG) in 1985. Subsequently, he received his M.S. and Ph.D. degrees in Theoretical and Applied Mechanics from Cornell University. At Cornell, he studied under Phil Holmes and Frank Moon. Prior to joining the faculty at UCB in 1992, he spent two years as a postdoctoral researcher at the Institut für Mechanik at ETH-Zürich under Jürg Dual.

O’Reilly’s interests span the fields of continuum mechanics and nonlinear dynamics. He has a broad range of specializations including Cosserat theories of deformable bodies, constrained rigid body dynamics, contact mechanics, linear and nonlinear vibrations, and linear and nonlinear dynamics of deformable bodies. He has applied these interests to a range of applications including soft robots, MEMS resonators, brake squeal, the dynamics of toys, motorcycle navigation, axially moving media, artificial and natural satellites, spinal kinematics, and vehicle collision dynamics. O’Reilly has coauthored over 90 archival journal articles, written three text books and is a co-inventor on two patents. He has also received several teaching awards including U.C. Berkeley's Distinguished Teaching Award in 1999, the Pi-Tau-Sigma Professor of the Year Award in 2003 and the Tau-Beta-Pi Outstanding Faculty of the Year Award in 2013.



Table of contents (9 chapters)

  • Mechanics of a String

    O’Reilly, Oliver M.

    Pages 3-47

  • Applications of the Mechanics of a String

    O’Reilly, Oliver M.

    Pages 49-92

  • Link, Writhe, and Twist

    O’Reilly, Oliver M.

    Pages 93-118

  • Theory of the Elastica and a Selection of Its Applications

    O’Reilly, Oliver M.

    Pages 121-185

  • Kirchhoff’s Rod Theory

    O’Reilly, Oliver M.

    Pages 187-268

Buy this book

eBook $59.99
price for USA (gross)
  • ISBN 978-3-319-50598-5
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $79.99
price for USA
  • ISBN 978-3-319-50596-1
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Modeling Nonlinear Problems in the Mechanics of Strings and Rods
Book Subtitle
The Role of the Balance Laws
Authors
Series Title
Interaction of Mechanics and Mathematics
Copyright
2017
Publisher
Springer International Publishing
Copyright Holder
Springer International Publishing AG
eBook ISBN
978-3-319-50598-5
DOI
10.1007/978-3-319-50598-5
Hardcover ISBN
978-3-319-50596-1
Series ISSN
1860-6245
Edition Number
1
Number of Pages
XX, 425
Number of Illustrations and Tables
10 b/w illustrations, 137 illustrations in colour
Topics