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Textbook on Modeling Nonlinear Problems in the Mechanics of Strings and Rods
My latest textbook, O. M. O’Reilly, Modeling Nonlinear Problems in the Mechanics of Strings and Rods, has just been published by Springer Verlag. The electronic version of this book is available (for free if your university's library has a subscription) on this website:
This book outlines the development of a hierarchy of rod models for a variety of applications. The lowest members of this hierarchy are extensible elastic strings and inextensible strings. Other members include Euler’s theory of the elastica, Kirchhoff’s rod theory and a range of Cosserat (or directed) rod theories. The developments are illustrated using problems such as the chain fountain, hockled cables, the elastica arm scale, coupled stretching and twisting of DNA strands, classic problems on inextensible strings, adhesion of slender bodies, buckling of columns, and the linear vibration of beams.
The book is suited for graduate-level courses on the dynamics of rods and strings. Two supplemental chapters, one on continuum mechanics and the other on variational principles, are included.