Classical and Generalized Models of Elastic Rods
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Features
- Contains results for inhomogeneous elastic bars that have not been included in similar books
- Presents a method to study the problem of elastic bars subjected to body forces and surface tractions on the lateral boundary
- Examines elastic bars made of Cosserat elastic materials
- Discusses the deformation of porous elastic cylinders
- Studies the deformation of cylinders composed of different materials
- Includes many exercises and examples that show how the methods discussed can solve engineering problems
Summary
Reflecting new developments in the study of Saint-Venant’s problem, Classical and Generalized Models of Elastic Rods focuses on the deformation of elastic cylinders for three models of continuum: classical elastic continuum, Cosserat elastic body, and porous elastic material.
The author presents a method to construct Saint-Venant’s solutions, minimum energy characterizations of these solutions, and a proof of Saint-Venant’s principle. He then discusses the deformation of nonhomogenous and isotropic cylinders as well as the problem of loaded anisotropic elastic cylinders. The book also deals with the deformation of cylinders within the linearized theory of homogeneous Cosserat elastic solids, the deformation of nonhomogeneous Cosserat cylinders, and the extension, bending, and torsion of porous elastic cylinders.
With numerous results not found in related texts, this book provides a unique, unified point of view in the theory of the deformation of elastic cylinders.
Table of Contents
Preface
Saint-Venant’s Problem
Preliminaries
Formulation of Saint-Venant’s Problem
Saint-Venant’s Solutions
Unified Treatment
Plane Deformation
Properties of the Solutions to Saint-Venant’s Problem
New Method of Solving Saint-Venant’s Problem
Minimum Energy Characterizations of Solutions
Truesdell’s Problem
Saint-Venant’s Principle
Theory of Loaded Cylinders
Problems of Almansi and Michell
Almansi–Michell Problem
Almansi Problem
Characterization of Solutions
Direct Method
Applications
Deformation of Nonhomogeneous Cylinders
Preliminaries
Plane Strain Problem: Auxiliary Plane Strain Problems
Extension and Bending of Nonhomogeneous Cylinders
Torsion
Flexure
Elastic Cylinders Composed of Different Nonhomogeneous and Isotropic Materials
Piecewise Homogeneous Cylinders
Applications
Anisotropic Bodies
Preliminaries
Generalized Plane Strain Problem
Extension, Bending, and Torsion
Flexure of Anisotropic Cylinders
Minimum Energy Characterizations of Solutions
Global Strain Measures
Problem of Loaded Cylinders
Orthotropic Bodies
Plane Strain Problem of Orthotropic Bodies
Deformation of Elastic Cylinders Composed of Nonhomogeneous and Anisotropic Materials
Cylinders Composed of Different Orthotropic Materials
Cosserat Elastic Continua
Basic Equations
Plane Strain
Saint-Venant’s Problem for Cosserat Cylinders
Minimum Principles
Global Strain Measures
Theory of Loaded Cosserat Cylinders
Nonhomogeneous Cosserat Cylinders
Plain Strain Problems
Saint-Venant’s Problem
Problems of Almansi and Michell
Anisotropic Cosserat Cylinders
Cylinders Composed of Different Elastic Materials
Porous Elastic Bodies
Basic Equations
Plane Strain
Extension, Bending, and Torsion of Porous Elastic Cylinders
Cylinders Composed of Different Porous Materials
Applications
Answers to Selected Problems
Bibliography
Index
Exercises appear at the end of each chapter.
