ELASTICITY IN ENGINEERING MECHANICS -- CONTENTS -- Preface -- CHAPTER 1 INTRODUCTORY CONCEPTS AND MATHEMATICS -- Part I Introduction -- 1-1 Trends and Scopes -- 1-2 Theory of Elasticity -- 1-3 Numerical Stress Analysis -- 1-4 General Solution of the Elasticity Problem -- 1-5 Experimental Stress Analysis -- 1-6 Boundary Value Problems of Elasticity -- Part II Preliminary Concepts -- 1-7 Brief Summary of Vector Algebra -- 1-8 Scalar Point Functions -- 1-9 Vector Fields -- 1-10 Differentiation of Vectors -- 1-11 Differentiation of a Scalar Field -- 1-12 Differentiation of a Vector Field -- 1-13 Curl of a Vector Field -- 1-14 Eulerian Continuity Equation for Fluids -- 1-15 Divergence Theorem -- 1-16 Divergence Theorem in Two Dimensions -- 1-17 Line and Surface Integrals (Application of Scalar Product) -- 1-18 Stokes's Theorem -- 1-19 Exact Differential -- 1-20 Orthogonal Curvilinear Coordiantes in Three-Dimensional Space -- 1-21 Expression for Differential Length in Orthogonal Curvilinear Coordinates -- 1-22 Gradient and Laplacian in Orthogonal Curvilinear Coordinates -- Part III Elements of Tensor Algebra -- 1-23 Index Notation: Summation Convention -- 1-24 Transformation of Tensors under Rotation of Rectangular Cartesian Coordinate System -- 1-25 Symmetric and Antisymmetric Parts of a Tensor -- 1-26 Symbols δij and ijk (the Kronecker Delta and the Alternating Tensor) -- 1-27 Homogeneous Quadratic Forms -- 1-28 Elementary Matrix Algebra -- 1-29 Some Topics in the Calculus of Variations -- References -- Bibliography -- CHAPTER 2 THEORY OF DEFORMATION -- 2-1 Deformable, Continuous Media -- 2-2 Rigid-Body Displacements -- 2-3 Deformation of a Continuous Region. Material Variables. Spatial Variables -- 2-4 Restrictions on Continuous Deformation of a Deformable Medium -- Problem Set 2-4 -- 2-5 Gradient of the Displacement Vector. Tensor Quantity.

2-6 Extension of an Infinitesimal Line Element -- Problem Set 2-6 -- 2-7 Physical Significance of ii. Strain Definitions -- 2-8 Final Direction of Line Element. Definition of Shearing Strain. Physical Significance of ij(i = j) -- Problem Set 2-8 -- 2-9 Tensor Character of aß. Strain Tensor -- 2-10 Reciprocal Ellipsoid. Principal Strains. Strain Invariants -- 2-11 Determination of Principal Strains. Principal Axes -- Problem Set 2-11 -- 2-12 Determination of Strain Invariants. Volumetric Strain -- 2-13 Rotation of a Volume Element. Relation to Displacement Gradients -- Problem Set 2-13 -- 2-14 Homogeneous Deformation -- 2-15 Theory of Small Strains and Small Angles of Rotation -- Problem Set 2-15 -- 2-16 Compatibility Conditions of the Classical Theory of Small Displacements -- Problem Set 2-16 -- 2-17 Additional Conditions Imposed by Continuity -- 2-18 Kinematics of Deformable Media -- Problem Set 2-18 -- Appendix 2A Strain-Displacement Relations in Orthogonal Curvilinear Coordinates -- 2A-1 Geometrical Preliminaries -- 2A-2 Strain-Displacement Relations -- Appendix 2B Derivation of Strain-Displacement Relations for Special Coordinates by Cartesian Methods -- 2B-1 Cylindrical Coordinates -- 2B-2 Oblique Straight-Line Coordinates -- Appendix 2C Strain-Displacement Relations in General Coordinates -- 2C-1 Euclidean Metric Tensor -- 2C-2 Strain Tensors -- References -- Bibliography -- CHAPTER 3 THEORY OF STRESS -- 3-1 Definition of Stress -- 3-2 Stress Notation -- 3-3 Summation of Moments. Stress at a Point. Stress on an Oblique Plane -- Problem Set 3-3 -- 3-4 Tensor Character of Stress. Transformation of Stress Components under Rotation of Coordinate Axes -- Problem Set 3-4 -- 3-5 Principal Stresses. Stress Invariants. Extreme Values -- Problem Set 3-5 -- 3-6 Mean and Deviator Stress Tensors. Octahedral Stress -- Problem Set 3-6.

3-7 Approximations of Plane Stress. Mohr's Circles in Two and Three Dimensions -- Problem Set 3-7 -- 3-8 Differential Equations of Motion of a Deformable Body Relative to Spatial Coordinates -- Problem Set 3-8 -- Appendix 3A Differential Equations of Equilibrium in Curvilinear Spatial Coordinates -- 3A-1 Differential Equations of Equilibrium in Orthogonal Curvilinear Spatial Coordinates -- 3A-2 Specialization of Equations of Equilibrium -- 3A-3 Differential Equations of Equilibrium in General Spatial Coordinates -- Appendix 3B Equations of Equilibrium Including Couple Stress and Body Couple -- Appendix 3C Reduction of Differential Equations of Motion for Small-Displacement Theory -- 3C-1 Material Derivative. Material Derivative of a Volume Integral -- 3C-2 Differential Equations of Equilibrium Relative to Material Coordinates -- References -- Bibliography -- CHAPTER 4 THREE-DIMENSIONAL EQUATIONS OF ELASTICITY -- 4-1 Elastic and Nonelastic Response of a Solid -- 4-2 Intrinsic Energy Density Function (Adiabatic Process) -- 4-3 Relation of Stress Components to Strain Energy Density Function -- Problem Set 4-3 -- 4-4 Generalized Hooke's Law -- Problem Set 4-4 -- 4-5 Isotropic Media. Homogeneous Media -- 4-6 Strain Energy Density for Elastic Isotropic Medium -- Problem Set 4-6 -- 4-7 Special States of Stress -- Problem Set 4-7 -- 4-8 Equations of Thermoelasticity -- 4-9 Differential Equation of Heat Conduction -- 4-10 Elementary Approach to Thermal-Stress Problem in One and Two Variables Problem -- 4-11 Stress-Strain-Temperature Relations -- Problem Set 4-11 -- 4-12 Thermoelastic Equations in Terms of Displacement -- 4-13 Spherically Symmetrical Stress Distribution (The Sphere) -- Problem Set 4-13 -- 4-14 Thermoelastic Compatibility Equations in Terms of Components of Stress and Temperature. Beltrami-Michell Relations -- Problem Set 4-14.

4-15 Boundary Conditions -- Problem Set 4-15 -- 4-16 Uniqueness Theorem for Equilibrium Problem of Elasticity -- 4-17 Equations of Elasticity in Terms of Displacement Components -- Problem Set 4-17 -- 4-18 Elementary Three-Dimensional Problems of Elasticity. Semi-Inverse Method -- Problem Set 4-18 -- 4-19 Torsion of Shaft with Constant Circular Cross Section -- Problem Set 4-19 -- 4-20 Energy Principles in Elasticity -- 4-21 Principle of Virtual Work -- Problem Set 4-21 -- 4-22 Principle of Virtual Stress (Castigliano's Theorem) -- 4-23 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 -- 4B-1 Variable Stress-Strain Coefficients -- 4B-2 Higher-Order Relations -- 4B-3 Hypoelastic Formulations -- 4B-4 Summary -- Appendix 4C Micromorphic Theory -- 4C-1 Introduction -- 4C-2 Balance Laws of Micromorphic Theory -- 4C-3 Constitutive Equations of Micromorphic Elastic Solid -- Appendix 4D Atomistic Field Theory -- 4D-1 Introduction -- 4D-2 Phase-Space and Physical-Space Descriptions -- 4D-3 Definitions of Atomistic Quantities in Physical Space -- 4D-4 Conservation Equations -- References -- Bibliography -- CHAPTER 5 PLANE THEORY OF ELASTICITY IN RECTANGULAR CARTESIAN COORDINATES -- 5-1 Plane Strain -- Problem Set 5-1 -- 5-2 Generalized Plane Stress -- Problem Set 5-2 -- 5-3 Compatibility Equation in Terms of Stress Components -- Problem Set 5-3 -- 5-4 Airy Stress Function -- Problem Set 5-4 -- 5-5 Airy Stress Function in Terms of Harmonic Functions -- 5-6 Displacement Components for Plane Elasticity -- Problem Set 5-6 -- 5-7 Polynomial Solutions of Two-Dimensional Problems in Rectangular Cartesian Coordinates -- Problem Set 5-7.

5-8 Plane Elasticity in Terms of Displacement Components -- Problem Set 5-8 -- 5-9 Plane Elasticity Relative to Oblique Coordinate Axes -- Appendix 5A Plane Elasticity with Couple Stresses -- 5A-1 Introduction -- 5A-2 Equations of Equilibrium -- 5A-3 Deformation in Couple Stress Theory -- 5A-4 Equations of Compatibility -- 5A-5 Stress Functions for Plane Problems with Couple Stresses -- Appendix 5B Plane Theory of Elasticity in Terms of Complex Variables -- 5B-1 Airy Stress Function in Terms of Analytic Functions ψ(z) and χ(z) -- 5B-2 Displacement Components in Terms of Analytic Functions ψ(z) and χ(z) -- 5B-3 Stress Components in Terms of ψ(z) and χ(z) -- 5B-4 Expressions for Resultant Force and Resultant Moment -- 5B-5 Mathematical Form of Functions ψ(z) and χ(z) -- 5B-6 Plane Elasticity Boundary Value Problems in Complex Form -- 5B-7 Note on Conformal Transformation -- Problem Set 5B-7 -- 5B-8 Plane Elasticity Formulas in Terms of Curvilinear Coordinates -- 5B-9 Complex Variable Solution for Plane Region Bounded by Circle in the z Plane -- Problem Set 5B -- References -- Bibliography -- CHAPTER 6 PLANE ELASTICITY IN POLAR COORDINATES -- 6-1 Equilibrium Equations in Polar Coordinates -- 6-2 Stress Components in Terms of Airy Stress Function F = F(r, θ) -- 6-3 Strain-Displacement Relations in Polar Coordinates -- Problem Set 6-3 -- 6-4 Stress-Strain-Temperature Relations -- Problem Set 6-4 -- 6-5 Compatibility Equation for Plane Elasticity in Terms of Polar Coordinates -- Problem Set 6-5 -- 6-6 Axially Symmetric Problems -- Problem Set 6-6 -- 6-7 Plane Elasticity Equations in Terms of Displacement Components -- 6-8 Plane Theory of Thermoelasticity -- Problem Set 6-8 -- 6-9 Disk of Variable Thickness and Nonhomogeneous Anisotropic Material -- Problem Set 6-9 -- 6-10 Stress Concentration Problem of Circular Hole in Plate -- Problem Set 6-10.

6-11 Examples.