Elasticity in Engineering Mechanics, 3rd EditionISBN: 9780470402559
656 pages
December 2010

Elasticity in Engineering Mechanics has been prized by many aspiring and practicing engineers as an easytonavigate guide to an area of engineering science that is fundamental to aeronautical, civil, and mechanical engineering, and to other branches of engineering. With its focus not only on elasticity theory, including nano and biomechanics, but also on concrete applications in real engineering situations, this acclaimed work is a core text in a spectrum of courses at both the undergraduate and graduate levels, and a superior reference for engineering professionals.
CHAPTER 1 INTRODUCTORY CONCEPTS AND MATHEMATICS.
Part I Introduction.
11 Trends and Scopes.
12 Theory of Elasticity.
13 Numerical Stress Analysis.
14 General Solution of the Elasticity.
15 Experimental Stress Analysis.
16 Boundary Value Problems of Elasticity.
Part II Preliminary Concepts.
17 Brief Summary of Vector Algebra.
18 Scalar Point Functions.
19 Vector Fields.
110 Differentiation of Vectors.
111 Differentiation of a Scalar Field.
112 Differentiation of a Vector Field.
113 Curl of a Vector Field.
114 Eulerian Continuity Equation for Fluids.
115 Divergence Theorem.
116 Divergence Theorem in Two Dimensions.
117 Line and Surface Integrals (Application of Scalar Product).
118 Stokes's Theorem.
119 Exact Differential.
120 Orthogonal Curvilinear Coordiantes in ThreeDimensional Space.
121 Expression for Differential Length in Orthogonal Curvilinear Coordinates.
122 Gradient and Laplacian in Orthogonal Curvilinear Coordinates.
Part III Elements of Tensor Algebra.
123 Index Notation: Summation Convention.
124 Transformation of Tensors under Rotation of Rectangular Cartesian Coordinate System.
125 Symmetric and Antisymmetric Parts of a Tensor.
126 Symbols dij and ijk (the Kronecker Delta and the Alternating Tensor).
127 Homogeneous Quadratic Forms.
128 Elementary Matrix Algebra.
129 Some Topics in the Calculus of Variations.
CHAPTER 2 THEORY OF DEFORMATION.
21 Deformable, Continuous Media.
22 RigidBody Displacements.
23 Deformation of a Continuous Region. Material Variables. Spatial Variables.
24 Restrictions on Continuous Deformation of a Deformable Medium.
25 Gradient of the Displacement Vector. Tensor Quantity.
26 Extension of an Infinitesimal Line Element.
27 Physical Significance of ii. Strain Definitions.
28 Final Direction of Line Element. Definition of Shearing Strain. Physical Significance of ij(i ? j).
29 Tensor Character of aß. Strain Tensor.
210 Reciprocal Ellipsoid. Principal Strains. Strain Invariants.
211 Determination of Principal Strains. Principal Axes.
212 Determination of Strain Invariants. Volumetric Strain.
213 Rotation of a Volume Element. Relation to Displacement Gradients.
214 Homogeneous Deformation.
215 Theory of Small Strains and Small Angles of Rotation.
216 Compatibility Conditions of the Classical Theory of Small Displacements.
217 Additional Conditions Imposed by Continuity.
218 Kinematics of Deformable Media.
Appendix 2A Strain–Displacement Relations in Orthogonal Curvilinear Coordinates.
Appendix 2B Derivation of Strain–Displacement Relations for Special Coordinates by Cartesian Methods.
Appendix 2C Strain–Displacement Relations in General Coordinates.
CHAPTER 3 THEORY OF STRESS.
31 Definition of Stress.
32 Stress Notation.
33 Summation of Moments. Stress at a Point. Stress on an Oblique Plane.
34 Tensor Character of Stress. Transformation of Stress Components under Rotation of Coordinate Axes.
35 Principal Stresses. Stress Invariants. Extreme Values.
36 Mean and Deviator Stress Tensors. Octahedral Stress.
37 Approximations of Plane Stress. Mohr's Circles in Two and Three Dimensions.
38 Differential Equations of Motion of a Deformable Body Relative to Spatial Coordinates.
Appendix 3A Differential Equations of Equilibrium in Curvilinear Spatial Coordinates.
Appendix 3B Equations of Equilibrium Including Couple Stress and Body Couple.
Appendix 3C Reduction of Differential Equations of Motion for SmallDisplacement Theory.
CHAPTER 4 THREEDIMENSIONAL EQUATIONS OF ELASTICITY.
41 Elastic and Nonelastic Response of a Solid.
42 Intrinsic Energy Density Function (Adiabatic Process).
43 Relation of Stress Components to Strain Energy Density Function.
44 Generalized Hooke's Law.
45 Isotropic Media. Homogeneous Media.
46 Strain Energy Density for Elastic Isotropic Medium.
47 Special States of Stress.
48 Equations of Thermoelasticity.
49 Differential Equation of Heat Conduction.
410 Elementary Approach to ThermalStress Problem in One and Two Variables.
411 Stress–Strain–Temperature Relations.
412 Thermoelastic Equations in Terms of Displacement.
413 Spherically Symmetrical Stress Distribution (The Sphere).
414 Thermoelastic Compatibility Equations in Terms of Components of Stress and Temperature. Beltrami–Michell Relations.
415 Boundary Conditions.
416 Uniqueness Theorem for Equilibrium Problem of Elasticity.
417 Equations of Elasticity in Terms of Displacement Components.
418 Elementary ThreeDimensional Problems of Elasticity. SemiInverse Method.
419 Torsion of Shaft with Constant Circular Cross Section.
420 Energy Principles in Elasticity.
421 Principle of Virtual Work.
422 Principle of Virtual Stress (Castigliano's Theorem).
423 Mixed Virtual Stress–Virtual Strain Principles (Reissner’s Theorem).
Appendix 4A Application of the Principle of Virtual Work to a Deformable Medium (Navier–Stokes Equations).
Appendix 4B Nonlinear Constitutive Relationships.
Appendix 4C Micromorphic Theory.
Appendix 4D Atomistic Field Theory.
CHAPTER 5 PLANE THEORY OF ELASTICITY IN RECTANGULAR CARTESIAN COORDINATES.
51 Plane Strain.
52 Generalized Plane Stress.
53 Compatibility Equation in Terms of Stress Components.
54 Airy Stress Function.
55 Airy Stress Function in Terms of Harmonic Functions.
56 Displacement Components for Plane Elasticity.
57 Polynomial Solutions of TwoDimensional Problems in Rectangular Cartesian Coordinates.
58 Plane Elasticity in Terms of Displacement Components.
59 Plane Elasticity Relative to Oblique Coordinate Axes.
Appendix 5A Plane Elasticity with Couple Stresses.
Appendix 5B Plane Theory of Elasticity in Terms of Complex Variables.
CHAPTER 6 PLANE ELASTICITY IN POLAR COORDINATES.
61 Equilibrium Equations in Polar Coordinates.
62 Stress Components in Terms of Airy Stress Function F = F(r,0 ).
63 Strain–Displacement Relations in Polar Coordinates.
64 Stress–Strain–Temperature Relations.
65 Compatibility Equation for Plane Elasticity in Terms of
Polar Coordinates.
66 Axially Symmetric Problems.
67 Plane Elasticity Equations in Terms of Displacement Components.
68 Plane Theory of Thermoelasticity.
69 Disk of Variable Thickness and Nonhomogeneous Anisotropic Material.
610 Stress Concentration Problem of Circular Hole in Plate.
611 Examples.
Appendix 6A Stress–Couple Theory of Stress Concentration Resulting from Circular Hole in Plate.
Appendix 6B Stress Distribution of a Diametrically Compressed Plane Disk.
CHAPTER 7 PRISMATIC BAR SUBJECTED TO END LOAD.
71 General Problem of ThreeDimensional Elastic Bars Subjected to Transverse End Loads.
72 Torsion of Prismatic Bars. SaintVenant's Solution. Warping Function.
73 Prandtl Torsion Function.
74 A Method of Solution of the Torsion Problem: Elliptic Cross Section.
75 Remarks on Solutions of the Laplace Equation, v2F = 0.
76 Torsion of Bars with Tubular Cavities.
77 Transfer of Axis of Twist.
78 Shearing–Stress Component in Any Direction.
79 Solution of Torsion Problem by the Prandtl Membrane Analogy.
710 Solution by Method of Series. Rectangular Section.
711 Bending of a Bar Subjected to Transverse End Force.
712 Displacement of a Cantilever Beam Subjected to Transverse End Force.
713 Center of Shear.
714 Bending of a Bar with Elliptic Cross Section.
715 Bending of a Bar with Rectangular Cross Section.
Appendix 7A Analysis of Tapered Beams.
CHAPTER 8 GENERAL SOLUTIONS OF ELASTICITY.
81 Introduction.
82 Equilibrium Equations.
83 The Helmholtz Transformation.
84 The Galerkin (Papkovich) Vector.
85 Stress in Terms of the Galerkin Vector F.
86 The Galerkin Vector: A Solution of the Equilibrium Equations of Elasticity.
87 The Galerkin Vector kZ and Love's Strain Function for Solids of Revolution.
88 Kelvin's Problem: Single Force Applied in the Interior of an Infinitely Extended Solid.
89 The Twinned Gradient and Its Application to Determine the Effects of a Change of Poisson's Ratio.
810 Solutions of the Boussinesq and Cerruti Problems by the Twinned Gradient Method.
811 Additional Remarks on ThreeDimensional Stress Functions.
References.
Bibliography.
INDEX.
Ken P. Chong, PhD, PE, Fellow of AAM, ASME, SEM, DistMASCE, is a Professor at The George Washington University and an associate at NIST. He has been an interim division director,engineering advisor, and director of the mechanics and materials for a total of twentyone years at the U.S. National Science Foundation. He has published over 200 refereed papers, and is the author or coauthor of twelve books including Intelligent Structures, Modeling and SimulationBased Life Cycle Engineering, and Materials for the New Millennium. He has taught at the Universities of Wyoming, Hong Kong, and Houston, in addition to being a visiting professor at MIT and University of Washington.
James D. Lee, PhD, PE, Fellow of ASME, is a Professor at The George Washington University teaching in the areas of continuum mechanics, nanomechanics, fracture mechanics, and finite element methods. He has been a researcher at General Tire and Rubber Company, NIST, and NASA, and has published over 100 journal papers and many conference papers. He also coauthored the book Meshless Methods in Solid Mechanics. He received the School of Engineering and Applied Science at GWU Distinguished Researcher Award.
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