Modeling nonlinear problems in the mechanics of strings and rods : the role of the balance laws /

Modeling nonlinear problems in the mechanics of strings and rods : the role of the balance laws /

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Bibliographic Details
Author / Creator:	O'Reilly, Oliver M., author.
Imprint:	Cham, Switzerland : Springer, 2017.
Description:	1 online resource (xx, 425 pages) : illustrations (some color)
Language:	English
Series:	Interaction of mechanics and mathematics, 1860-6245 Interaction of mechanics and mathematics series,
Subject:	Continuum mechanics. Deformations (Mechanics) -- Mathematical models. Nonlinear theories. Continuum mechanics. Deformations (Mechanics) -- Mathematical models. Nonlinear theories. Electronic book.
Format:	E-Resource Book
URL for this record:	http://pi.lib.uchicago.edu/1001/cat/bib/11272550

Hidden Bibliographic Details
ISBN:	9783319505985 331950598X 9783319505961 3319505963
Digital file characteristics:	text file PDF
Notes:	Includes bibliographical references and index. Online resource; title from PDF title page (SpringerLink, viewed March 13, 2017).
Summary:	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.
Other form:	Print version: O'Reilly, Oliver M. Modeling nonlinear problems in the mechanics of strings and rods. Cham, Switzerland : Springer, 2017 3319505963 9783319505961
Standard no.:	10.1007/978-3-319-50598-5 10.1007/978-3-319-50

Table of Contents:

Part 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.