Modeling Nonlinear Problems in the Mechanics of Strings and Rods
The Role of the Balance Laws
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Beschreibung
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.
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.
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 Includes supplementary material: sn.pub/extras
Autor*in
Oliver M. O'Reilly
Themen in »Modeling Nonlinear Problems in the Mechanics of Strings and Rods«
Dynamics of Rods and Strings Continuum Mechanics Eshelbian Mechanics Nonlinear Dynamics of Deformable One-dimensional Continua Nonlinear Problems
Stimmen zu »Modeling Nonlinear Problems in the Mechanics of Strings and Rods«
“This graduate-level textbook presents models of rods and strings obtained by using balance laws. … It will introduce students, especially those who are research-oriented, into modern theories. I believe that the book under review is an important addition to the subject, and I strongly recommend it to students and researchers in continuum mechanics, especially in the field of rods and strings.” (Teodor Atanacković, zbMATH 1370.74001, 2017)
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