Classical and Generalized Models of Elastic Rods 1st Edition by Iesan ISBN 1420086502 9781420086508

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Product details:

ISBN 10: 1420086502

ISBN 13: 9781420086508

Author:  D. Iesan 

Classical and Generalized Models of Elastic Rods 1st Edition: 

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.

 

Classical and Generalized Models of Elastic Rods 1st Edition Table of contents:

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

Porous Elastic Bodies

• Basic Equations
• Plane Strain
• Extension, Bending, and Torsion of Porous Elastic Cylinders
• Cylinders Composed of Different Porous Materials
• Applications

 

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