Modeling nonlinear problems in the mechanics of strings and rods : the role of the balance laws
By: O'Reilly, Oliver M.
Series: Interaction of mechanics and mathematics. / edited by Lev Truskinovsky.Publisher: Switzerland Springer 2017Description: xx, 425p.ISBN: 9783319505961.Subject(s): Continuum mechanics | Nonlinear theoriesDDC classification: 531 | Or3m 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.Item type | Current location | Collection | Call number | Status | Date due | Barcode | Item holds |
---|---|---|---|---|---|---|---|
![]() |
PK Kelkar Library, IIT Kanpur | General Stacks | 531 Or3m (Browse shelf) | Available | A185202 |
Browsing PK Kelkar Library, IIT Kanpur Shelves , Collection code: General Stacks Close shelf browser
531 Oc39c Computational statics and dynamics | 531 Oc3c2 Computational statics and dynamics [2nd ed.] | 531 Op7 Optical methods for solid mechanics | 531 Or3m Modeling nonlinear problems in the mechanics of strings and rods | 531 OS3 MECHANICS | 531 P191c Classical mechanics | 531 P197c Continuum mechanics and thermodynamics of matter |
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.
There are no comments for this item.