Elasticity

Tensor, Dyadic, and Engineering Approaches

By: PEI CHI CHOU

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Paperback | 17 January 1992

At a Glance

Paperback
320 Pages

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New edition

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20.9 x 13.6 x 1.91

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Written for advanced undergraduates and beginning graduate students, this exceptionally clear text treats both the engineering and mathematical aspects of elasticity. It is especially useful because it offers the theory of linear elasticity from three standpoints: engineering, Cartesian tensor, and vector-dyadic. In this way the student receives a more complete picture and a more thorough understanding of engineering elasticity. Prerequisites are a working knowledge of statics and strength of materials plus calculus and vector analysis. The first part of the book treats the theory of elasticity by the most elementary approach, emphasizing physical significance and using engineering notations. It gives engineering students a clear, basic understanding of linear elasticity. The latter part of the text, after Cartesian tensor and dyadic notations are introduced, gives a more general treatment of elasticity. Most of the equations of the earlier chapters are repeated in Cartesian tensor notation and again in vector-dyadic notation. By having access to this threefold approach in one book, beginning students will benefit from cross-referencing, which makes the learning process easier.Another helpful feature of this text is the charts and tables showing the logical relationships among the equations - especially useful in elasticity, where the mathematical chain from definition and concept to application is often long. Understanding of the theory is further reinforced by extensive problems at the end of each chapter.

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Non-Fiction Science Physics Classical Mathematics Dynamics & Statics Engineering & Technology Mechanical Engineering & Materials Materials Science Mechanics of Solids Technology in General Nanotechnology Civil Engineering

Preface
Introduction
Analysis of Stress	p. 1
Introduction	p. 1
Body Forces, Surface Forces, and Stresses	p. 2
Uniform State of Stress (Two-Dimensional)	p. 6
Principal Stresses	p. 9
Mohr's Circle of Stress	p. 11
State of Stress at a Point	p. 15
Differential Equations of Equilibrium	p. 17
Three-Dimensional State of Stress at a Point	p. 21
Summary	p. 28
Problems	p. 28
Strain and Displacement	p. 34
Introduction	p. 34
Strain-Displacement Relations	p. 35
Compatibility Equations	p. 39
State of Strain at a Point	p. 42
General Displacements	p. 45
Principle of Superposition	p. 48
Summary	p. 49
Problems	p. 49
Stress Strain Relations	p. 53
Introduction	p. 53
Generalized Hooke's Law	p. 54
Bulk Modulus of Elasticity	p. 60
Summary	p. 62
Problems	p. 62
Formulation of Problems in Elasticity	p. 65
Introduction	p. 65
Boundary Conditions	p. 66
Governing Equations in Plane Strain Problems	p. 69
Governing Equations in Three-Dimensional Problems	p. 75
Principal of Superposition	p. 79
Uniqueness of Elasticity Solutions	p. 82
Saint-Venant's Principle	p. 84
Summary	p. 85
Problems	p. 85
Two-Dimensional Problems	p. 89
Introduction	p. 89
Plane Stress Problems	p. 89
Approximate Character of Plane Stress Equations	p. 93
Polar Coordinates in Two-Dimensional Problems	p. 98
Axisymmetric Plane Problems	p. 105
The Semi-Inverse Method	p. 108
Problems	p. 111
Torsion of Cylindrical Bars	p. 115
General Solution of the Problem	p. 115
Solutions Derived from Equations of Boundaries	p. 123
Membrane (Soap Film) Analogy	p. 127
Multiply Connected Cross Sections	p. 132
Solution by Means of Separation of Variables	p. 136
Problems	p. 141
Energy Methods	p. 145
Introduction	p. 145
Strain Energy	p. 145
Variable Stress Distribution and Body Forces	p. 149
Principle of Virtual Work and the Theorem of Minimum Potential Energy	p. 151
Illustrative Problems	p. 157
Rayleigh-Ritz Method	p. 163
Problems	p. 166
Cartesian Tensor Notation	p. 170
Introduction	p. 170
Indicial Notation and Vector Transformations	p. 171
Higher-Order Tensors	p. 176
Gradient of a Vector	p. 179
The Kronecker Delta	p. 180
Tensor Contraction	p. 182
The Alternating Tensor	p. 182
The Theorem of Gauss	p. 186
Problems	p. 188
The Stress Tensor	p. 190
State of Stress at a Point	p. 190
Principal Axes of the Stress Tensor	p. 193
Equations of Equilibrium	p. 196
The Stress Ellipsoid	p. 199
Body Moment and Couple Stress	p. 200
Problems	p. 202
Strain, Displacement, and the Governing Equations of Elasticity	p. 204
Introduction	p. 204
Displacement and Strain	p. 204
Generalized Hooke's Law	p. 207
Equations of Compatibility	p. 212
Governing Equations in Terms of Displacement	p. 218
Strain Energy	p. 219
Governing Equations of Elasticity	p. 219
Problems	p. 223
Vector and Dyadic Notation in Elasticity	p. 225
Introduction	p. 225
Review of Basic Notations and Relations in Vector Analysis	p. 227
Dyadic Notation	p. 229
Vector Representation of Stress on a Plane	p. 233
Equations of Transformation of Stress	p. 235
Equations of Equilibrium	p. 238
Displacement and Strain	p. 238
Generalized Hooke's Law and Navier's Equation	p. 239
Equations of Compatibility	p. 240
Strain Energy	p. 242
Governing Equations of Elasticity	p. 243
Problems	p. 243
Orthogonal Curvilinear Coordinates	p. 245
Introduction	p. 245
Scale Factors	p. 245
Derivatives of the Unit Vectors	p. 250
Vector Operators	p. 252
Dyadic Notation and Dyadic Operators	p. 256
Governing Equations of Elasticity in Dyadic Notation	p. 257
Summary of Vector and Dyadic Operators in Cylindrical and Spherical Coordinates	p. 260
Problems	p. 264
Displacement Functions and Stress Functions	p. 266
Introduction	p. 266
Displacement Functions	p. 267
The Galerkin Vector	p. 272
The Solution of Papkovich-Neuber	p. 274
Stress Functions	p. 277
Problems	p. 282
References	p. 283
Index	p. 285
Table of Contents provided by Blackwell. All Rights Reserved.

Elasticity

Tensor, Dyadic, and Engineering Approaches

At a Glance

Paperback

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