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About this book

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.

Table of Contents

Frontmatter

Mechanics of Strings

Frontmatter

2017 | OriginalPaper | Chapter

Chapter 1. Mechanics of a String

Oliver M. O’Reilly

2017 | OriginalPaper | Chapter

Chapter 2. Applications of the Mechanics of a String

Oliver M. O’Reilly

2017 | OriginalPaper | Chapter

Chapter 3. Link, Writhe, and Twist

Oliver M. O’Reilly

Mechanics of Rods

Frontmatter

2017 | OriginalPaper | Chapter

Chapter 4. Theory of the Elastica and a Selection of Its Applications

Oliver M. O’Reilly

2017 | OriginalPaper | Chapter

Chapter 5. Kirchhoff’s Rod Theory

Oliver M. O’Reilly

2017 | OriginalPaper | Chapter

Chapter 6. Theory of an Elastic Rod with Extension and Shear

Oliver M. O’Reilly

2017 | OriginalPaper | Chapter

Chapter 7. Green and Naghdi’s Rod Theory

Oliver M. O’Reilly

Background Material

Frontmatter

2017 | OriginalPaper | Chapter

Chapter 8. A Rapid Review of Some Elements of Continuum Mechanics

Oliver M. O’Reilly

2017 | OriginalPaper | Chapter

Chapter 9. Variational Methods

Oliver M. O’Reilly

Backmatter

Additional information

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