Modeling Nonlinear Problems in the Mechanics of Strings and Rods [electronic resource] : The Role of the Balance Laws /
By: O'Reilly, Oliver M [author.].
Contributor(s): SpringerLink (Online service).
Series: Interaction of Mechanics and Mathematics: Publisher: Cham : Springer International Publishing : Imprint: Springer, 2017Edition: 1st ed. 2017.Description: XX, 425 p. 147 illus., 137 illus. in color. | Binding - Card Paper |.Content type: text Media type: computer Carrier type: online resourceISBN: 9783319505985.Subject(s): Mechanical Engineering
| Dynamical Systems and Ergodic Theory | Solid Mechanics | Applications of Nonlinear Dynamics and Chaos TheoryDDC classification: 515.39 | 515.48 Online resources: Click here to access eBook in Springer Nature platform. (Within Campus only.)
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Springer Nature eBookSummary: 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.
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