Elasticity in Engineering Mechanics, 3/e (Hardcover)

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.

◾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 dij 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.

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.

◾2-5 Gradient of the Displacement Vector. Tensor Quantity.

◾2-6 Extension of an Infinitesimal Line Element.

◾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).

◾2-9 Tensor Character of aß. Strain Tensor.

◾2-10 Reciprocal Ellipsoid. Principal Strains. Strain Invariants.

◾2-11 Determination of Principal Strains. Principal Axes.

◾2-12 Determination of Strain Invariants. Volumetric Strain.

◾2-13 Rotation of a Volume Element. Relation to Displacement Gradients.

◾2-14 Homogeneous Deformation.

◾2-15 Theory of Small Strains and Small Angles of Rotation.

◾2-16 Compatibility Conditions of the Classical Theory of Small Displacements.

◾2-17 Additional Conditions Imposed by Continuity.

◾2-18 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.

◾3-1 Definition of Stress.

◾3-2 Stress Notation.

◾3-3 Summation of Moments. Stress at a Point. Stress on an Oblique Plane.

◾3-4 Tensor Character of Stress. Transformation of Stress Components under Rotation of Coordinate Axes.

◾3-5 Principal Stresses. Stress Invariants. Extreme Values.

◾3-6 Mean and Deviator Stress Tensors. Octahedral Stress.

◾3-7 Approximations of Plane Stress. Mohr's Circles in Two and Three Dimensions.

◾3-8 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 Small-Displacement Theory.

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.

◾4-4 Generalized Hooke's Law.

◾4-5 Isotropic Media. Homogeneous Media.

◾4-6 Strain Energy Density for Elastic Isotropic Medium.

◾4-7 Special States of Stress.

◾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.

◾4-11 Stress–Strain–Temperature Relations.

◾4-12 Thermoelastic Equations in Terms of Displacement.

◾4-13 Spherically Symmetrical Stress Distribution (The Sphere).

◾4-14 Thermoelastic Compatibility Equations in Terms of Components of Stress and Temperature. Beltrami–Michell Relations.

◾4-15 Boundary Conditions.

◾4-16 Uniqueness Theorem for Equilibrium Problem of Elasticity.

◾4-17 Equations of Elasticity in Terms of Displacement Components.

◾4-18 Elementary Three-Dimensional Problems of Elasticity. Semi-Inverse Method.

◾4-19 Torsion of Shaft with Constant Circular Cross Section.

◾4-20 Energy Principles in Elasticity.

◾4-21 Principle of Virtual Work.

◾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.

◾Appendix 4C Micromorphic Theory.

◾Appendix 4D Atomistic Field Theory.

CHAPTER 5 PLANE THEORY OF ELASTICITY IN RECTANGULAR CARTESIAN COORDINATES.

◾5-1 Plane Strain.

◾5-2 Generalized Plane Stress.

◾5-3 Compatibility Equation in Terms of Stress Components.

◾5-4 Airy Stress Function.

◾5-5 Airy Stress Function in Terms of Harmonic Functions.

◾5-6 Displacement Components for Plane Elasticity.

◾5-7 Polynomial Solutions of Two-Dimensional Problems in Rectangular Cartesian Coordinates.

◾5-8 Plane Elasticity in Terms of Displacement Components.

◾5-9 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.

◾6-1 Equilibrium Equations in Polar Coordinates.

◾6-2 Stress Components in Terms of Airy Stress Function F = F(r,0 ).

◾6-3 Strain–Displacement Relations in Polar Coordinates.

◾6-4 Stress–Strain–Temperature Relations.

◾6-5 Compatibility Equation for Plane Elasticity in Terms of Polar Coordinates.

◾6-6 Axially Symmetric Problems.

◾6-7 Plane Elasticity Equations in Terms of Displacement Components.

◾6-8 Plane Theory of Thermoelasticity.

◾6-9 Disk of Variable Thickness and Nonhomogeneous Anisotropic Material.

◾6-10 Stress Concentration Problem of Circular Hole in Plate.

◾6-11 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.

◾7-1 General Problem of Three-Dimensional Elastic Bars Subjected to Transverse End Loads.

◾7-2 Torsion of Prismatic Bars. Saint-Venant's Solution. Warping Function.

◾7-3 Prandtl Torsion Function.

◾7-4 A Method of Solution of the Torsion Problem: Elliptic Cross Section.

◾7-5 Remarks on Solutions of the Laplace Equation, v2F = 0.

◾7-6 Torsion of Bars with Tubular Cavities.

◾7-7 Transfer of Axis of Twist.

◾7-8 Shearing–Stress Component in Any Direction.

◾7-9 Solution of Torsion Problem by the Prandtl Membrane Analogy.

◾7-10 Solution by Method of Series. Rectangular Section.

◾7-11 Bending of a Bar Subjected to Transverse End Force.

◾7-12 Displacement of a Cantilever Beam Subjected to Transverse End Force.

◾7-13 Center of Shear.

◾7-14 Bending of a Bar with Elliptic Cross Section.

◾7-15 Bending of a Bar with Rectangular Cross Section.

◾Appendix 7A Analysis of Tapered Beams.

CHAPTER 8 GENERAL SOLUTIONS OF ELASTICITY.

◾8-1 Introduction.

◾8-2 Equilibrium Equations.

◾8-3 The Helmholtz Transformation.

◾8-4 The Galerkin (Papkovich) Vector.

◾8-5 Stress in Terms of the Galerkin Vector F.

◾8-6 The Galerkin Vector: A Solution of the Equilibrium Equations of Elasticity.

◾8-7 The Galerkin Vector kZ and Love's Strain Function for Solids of Revolution.

◾8-8 Kelvin's Problem: Single Force Applied in the Interior of an Infinitely Extended Solid.

◾8-9 The Twinned Gradient and Its Application to Determine the Effects of a Change of Poisson's Ratio.

◾8-10 Solutions of the Boussinesq and Cerruti Problems by the Twinned Gradient Method.

◾8-11 Additional Remarks on Three-Dimensional Stress Functions.

References.

Bibliography.

INDEX.