This book is discusses theories of deformable elastic strings and rods and their application to wide classes of problems. Readers will be able to formulate models for problems featuring one-dimensional continua that populate many interesting applications ranging from the human spine and gecko adhesion to columns and plant stems. 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 in dynamics of nonlinearly elastic rods and strings.
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Table of ContentsPart I Mechanics of Strings.- Mechanics of a String.- Applications of the Mechanics of a String.- Link, Writhe, and Twist.- Part II Mechanics of Rods.- Theory of the Elastica and a Selection of its Applications.- Kirchoff's Rod Theory.- Theory of an Elastic Rod with Extension and Shear.- Green and Naghdi's Rod Theory.- Part III Background Material.- A Rapid Review of Some Elements of Continuum Mechanics.- Variational Methods.