Classical and Generalized Models of Elastic Rods

Note: Supplemental materials are not guaranteed with Rental or Used book purchases.

ISBN: 9781420086492 | 1420086499
Cover: Hardcover
Copyright: 11/14/2008

Rent

(Recommended)

$139.05

Term

Due

Price

Semester

May 29

$139.05

Quarter

May 4

$132.10

Short Term

Apr 4

$125.15

*This item is part of an exclusive publisher rental program and requires an additional convenience fee. This fee will be reflected in the shopping bag.
Buy New

Usually Ships in 3-5 Business Days

$178.02
eBook

Available Instantly

Online: 180 Days

Downloadable: 180 Days

*To support the delivery of the digital material to you, a digital delivery fee of $3.99 will be charged on each digital item.

$161.70*

Reflecting new developments in the study of Saint-Venant's problem, Classical and Generalized Models of Elastic Rodsfocuses 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.

Preface	p. ix
Saint-Venant's Problem	p. 1
Preliminaries	p. 1
Formulation of Saint-Venant's Problem	p. 3
Saint-Venant's Solutions	p. 6
Extension	p. 6
Bending by Terminal Couples	p. 7
Torsion	p. 9
Flexure	p. 13
Unified Treatment	p. 16
Plane Deformation	p. 21
Statement of Problem	p. 21
Uniqueness Results	p. 23
Airy Function	p. 24
Complex Potentials	p. 26
Properties of Solutions to Saint-Venant's Problem	p. 34
New Method of Solving Saint-Venant's Problem	p. 35
Minimum Energy Characterizations of Solutions	p. 41
Truesdell's Problem	p. 44
Saint-Venant's Principle	p. 48
Exercises	p. 56
Theory of Loaded Cylinders	p. 59
Problems of Almansi and Michell	p. 59
Almansi-Michell Problem	p. 60
Almansi Problem	p. 64
Characterization of Solutions	p. 66
Direct Method	p. 71
Applications	p. 78
Deformation of a Circular Cylinder Subject to Uniform Load	p. 78
Thermoelastic Deformation of Cylinders	p. 80
Plane Temperature Field	p. 80
Exercises	p. 82
Deformation of Nonhomogeneous Cylinders	p. 83
Preliminaries	p. 83
Plane Strain Problem: Auxiliary Plane Strain Problems	p. 84
Basic Equations	p. 84
Airy Function	p. 86
Auxiliary Plane Strain Problems	p. 86
Extension and Bending of Nonhomogeneous Cylinders	p. 88
Torsion	p. 90
Flexure	p. 93
Elastic Cylinders Composed of Different Nonhomogeneous and Isotropic Materials	p. 94
Auxiliary Plane Strain Problems	p. 95
Extension and Bending	p. 97
Torsion and Flexure	p. 99
Uniformly Loaded Cylinders	p. 102
Almansi Problem	p. 106
Piecewise Homogeneous Cylinders	p. 109
Alternative Form of Auxiliary Plane Strain Problems	p. 110
Extension and Bending of Piecewise Homogeneous Cylinders	p. 112
Torsion and Flexure	p. 113
Applications	p. 114
Nonhomogeneous Cylinders with Constant Poisson's Ratio	p. 114
Deformation of a Nonhomogeneous Circular Cylinder	p. 116
Extension, Bending, and Torsion of Nonhomogeneous Tube	p. 117
Flexure of Hollow Cylinder	p. 119
Plane Strain of Nonhomogeneous Tube	p. 121
Special Solutions of Plane Strain Problem	p. 124
Exercises	p. 126
Anisotropic Bodies	p. 127
Preliminaries	p. 127
Generalized Plane Strain Problem	p. 128
Extension, Bending, and Torsion	p. 130
Flexure of Anisotropic Cylinders	p. 133
Minimum Energy Characterizations of Solutions	p. 136
Global Strain Measures	p. 138
Problem of Loaded Cylinders	p. 140
Orthotropic Bodies	p. 144
Extension, Bending, and Torsion of Orthotropic Cylinders	p. 146
Flexure	p. 150
Uniformly Loaded Cylinders	p. 152
Plane Strain Problem of Orthotropic Bodies	p. 154
Galerkin Representation	p. 155
Fundamental Solutions	p. 156
Somigliana Relations	p. 160
Existence Results	p. 162
Deformation of Elastic Cylinders Composed of Nonhomogeneous and Anisotropic Materials	p. 168
Generalized Plane Strain Problem for Composed Cylinders	p. 169
Extension, Bending by Terminal Couples, and Torsion	p. 170
Flexure	p. 173
Cylinders Composed of Different Orthotropic Materials	p. 175
Plane Strain Problem	p. 176
Extension and Bending of Composed Cylinders	p. 177
Flexure and Torsion	p. 179
Exercises	p. 182
Cosserat Elastic Continua	p. 183
Basic Equations	p. 183
Plane Strain	p. 187
Polar Coordinates	p. 188
Solution of Field Equations	p. 189
Fundamental Solutions	p. 190
Somigliana Relations	p. 194
Existence Theorems	p. 196
Saint-Venant's Problem for Cosserat Cylinders	p. 202
Preliminaries	p. 203
Extension, Bending, and Torsion	p. 206
Flexure	p. 212
Minimum Principles	p. 218
Global Strain Measures	p. 220
Theory of Loaded Cosserat Cylinders	p. 223
Exercises	p. 229
Nonhmogeneous Cosserat Cylinders	p. 231
Plane Strain Problems	p. 231
Saint-Venant's Problem	p. 232
Extension and Bending of Cosserat Cylinders	p. 233
Torsion	p. 234
Flexure	p. 236
Problems of Almansi and Michell	p. 238
Uniformly Loaded Cylinders	p. 238
Almansi's Problem	p. 244
Anisotropic Cosserat Cylinders	p. 246
Generalized Plane Strain	p. 247
Extension, Bending, and Torsion	p. 249
Flexure	p. 250
Uniformly Loaded Cylinders	p. 253
Recurrence Process	p. 256
Cylinders Composed of Different Elastic Materials	p. 258
Plane Strain Problems	p. 258
Extension and Bending	p. 260
Torsion	p. 261
Flexure	p. 263
Problem of Loaded Cylinders	p. 265
Exercises	p. 274
Porous Elastic Bodies	p. 275
Basic Equations	p. 275
Plane Strain	p. 277
Nonhomogeneous Bodies	p. 278
Homogeneous and Isotropic Materials	p. 280
Stress around a Hole	p. 284
Extension, Bending, and Torsion of Porous Elastic Cylinders	p. 285
Cylinders Composed of Different Porous Materials	p. 288
Auxiliary Plane Strain Problems	p. 288
Solution of the Problem	p. 290
Applications	p. 291
Deformation of Porous Elastic Tube	p. 291
Extension and Bending of Porous Circular Cylinder	p. 293
Exercises	p. 303
Answers to Selected Problems	p. 305
Bibliography	p. 347
Index	p. 371
Table of Contents provided by Ingram. All Rights Reserved.

FREE SHIPPING

Rent More, Save More! Use code: BBRENTAL

5% off 1 book, 7% off 2 books, 10% off 3+ books

Classical and Generalized Models of Elastic Rods

Summary

Table of Contents

Supplemental Materials