Classical and Generalized Models of Elastic Rods  book cover
1st Edition

Classical and Generalized Models of Elastic Rods

ISBN 9781420086492
Published November 14, 2008 by Chapman and Hall/CRC
380 Pages 3 B/W Illustrations

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Book Description

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


Saint-Venant’s Problem


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


Deformation of Nonhomogeneous Cylinders


Plane Strain Problem: Auxiliary Plane Strain Problems

Extension and Bending of Nonhomogeneous Cylinders



Elastic Cylinders Composed of Different Nonhomogeneous and Isotropic Materials

Piecewise Homogeneous Cylinders


Anisotropic Bodies


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


Answers to Selected Problems



Exercises appear at the end of each chapter.

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