Elasticity: (Dover Books on Physics)

Table of Contents:
Preface Part I Review of Mathematical Notation and Continuum Mechanics Basic Equations of the Linear Theory of Elasticity 1 Vectors and Tensors 1. Notation 2. Vectors 3. Transformation Relations 3.1 Scalars 3.2 Vectors 3.3 Properties of the transformation matrix 4. Second Order Tensors 5. Higher Order Tensors 6. Dual Vector of an Antisymetric Tensor 7. Eigenvalue Problem 8. Isotropic Tensors 9. Tensor Fields 10. Integral Theorems 11. Classification of Vector Fields 2. Kinematics 1. Introduction 2. Spatial and Material Coordinates 3. Velocity and Material Time Derivative 4. Volume Elements 5. Reynold's Transport Theorem 6. Displacement Vector 7. Compatibility Equation 8. Infinitesimal Strain Tensor in Curvilinear Coordinates 9. Spherical and Deviatroic Strain Tensors 3. Stress 1. Introduction 2. Stress Tractions 3. Stress Tensor in the Material Sense 4. Properties of the Stress Tensor 4. Basic Equations of Continuum Mechanics 1. Introduction 2. Conservation of Mass 3. Cauchy's Equations of Motion 4. Considerations of Angular Momentum 5. Energy Conservation Equation 5. Linear Elasticity 1. Introduction 2. Geranlized Hooke's Law 3. Summary of the Equations of Isotropic Elasticity 4. Boundary Conditions 5. Uniqueness and Superposition 6. Saint-Venant's Principle 7. Displacement Formulation 8. Thermoelasticity Part II Two-Dimensional Elasticity 6 General Theory of Plane Elasticity 1. Introduction 2. Plane Deformation or Plane Strain 3. Plane Stress 4. Biharmonic Solutions 7 Problems in Cartesian Coordinates 1. Introduction 2. Mathematical Preliminaries 3. Polynomial Solutions 3.1 Uniaxial tension 3.2 Simply supported beam under pure moments 3.3 Beam bent by its own weight 4. Fourier Series Solutions 4.1 Beam subjected to sinusoidal load 5. Fourier Analysis 5.1 Fourier trigonometric series 6. General Fourier Solution of Elasticity Problem 6.1 Case 4-odd in x and even in y 6.2 Displacement solution using Marguerre function 7. Multiple Fourier Analysis 8. Problems Involving Infinite or Semi-Infinite Dimensions 8.1 Infinite strip loaded by uniform pressure 8.2 Fourier transform solutions 8.3 Solution of the infinite strip problem using integral transforms 8.4 Semi-infinite strip problems 8.5 Solution for the half-plane 9. Saint-Venant Boundary Region in Elastic Strips 10. Nonorthogonal Boundary Function Expansions 10.1 Point-matching 10.2 Least squares 10.3 Iterative improvements to point-matching techniques 11. Plane Elasticity Problems Using Nonorthogonal Functions 11.1 Examples requring functions nonorthogonal on the boundaries 8 Problems in Polor Coordinates 1. Introduction 2. Axially Symmetric Problems 2.1 Lame problem 2.2 Pure bending of a curved beam 2.3 Rotational dislocation 3. Solution of Axisymmetric Problems Using the Navier Equation 4. Michell Solution 5. Examples Using the Michell Solution 5.1 Interior problem-stresses distributed around the edge of a disk 5.2 Exterior problem-infinite plane with circular hole 5.3 Annulus problem 5.4 Symmetry conditions 6. General Solutions Not Involving Orthogonal Functions 7. Wedge Problem 7.1 Wedge under uniform side load 7.2 Stress singularities at the tip of a wedge (M.L. williams solution) 7.3 Truncated semi-infinite wedge 8. Special Problems Using the Flamant Solution 8.1 Concentrated load in hole in infinite plate 9 Complex Variable Solutions 1. Introduction 2. Complex Variables 3. Complex Stress Formulation 4. Polar Coordinates 5. Interior Problem 6. Conformal Transformations 10 Finite Difference and Finite Element Methods 1. Introduction 2. Finite Element Method 3. Displacement Functions 4. Stresses and Strains 5. Nodal Force-Displacement Relations 6. Analysis of a Structure 7. Facet Stiffness Matrix 8. Local and Global Coordinates 9. Finite Element Example 10. Finite Difference Methods 11 Energy Theorems and Variational Techniques 1. Introduction 2. Calculus of Variations 3. Strain Energy Methods 4. Theorem of Stationary Potential Energy 5. Rayleigh-Ritz Method 6. Energy Method for Problems Involving Multiply Connected Domains Part III Three-Dimensional Elasticity 12 Saint-Venant Tension and Bending Theory 1. Torsion of Circular Cylinder 2. Non-Circular Section 3. Uniqueness of Saint-Venant Torsion Problem 4. Semi-Inverse Approach-Problems of Saint-Venant 5. Torsion of Rectangular Bars Using Fourier Anaylsis 6. Prandtl Stress Functions 7. Solution of a Hollow Cylinder 8. Solution by Use of Orthogonal Series 9. Polar Coordinates 10. Nonorthogonal Functions on Boundary 11. Complex Variable Solutions of Torsion Problems 12. Membrane Anaogy for Torsion 13. Torsion of Circular Shafts of Variable Diameter 14. Saint-Venant Approximation for Circular Cylinders 15. Flexure of Beams by Transverse End Loads 16. Flexure of a Circular Beam Under a Load Py Through the Centroid 13 Navier Equation and the Galerkin Vector 1. Solution of the Navier Equation in Three-Dimensional Elastostatics 2. Stress Functions 3. The Galerkin Vector 4. Equivalent Galerkin Vector 5. Mathematical Notes on the Galerkin Vector 6. Love's Strain Function 7. Long Solid Cylinders Axisymmetrically Loaded 8. Infinite Cylinder or Hole in an Elastic Body 9. Thick Axisymmetrically Loaded Plate 10. Axisymmetrically Loaded Plate with a Hole 11. Hankel Transform Methods 12. Axisymmetric Problem of a Half Space 13. Boussinesq Problem 14. Contact Problems 15. Short Cylinders-Multiple Fourier-Bessel Series Analysis 16. End-Loading on a Semi-Infinite Cylinder 17. Axisymmetric Torsion 18. Asymmetric Loadings 14 Papkovich-Neuber Solution 1. Introduction 2. Concentrated Force in the Infinite Solid 3. Concentrated Load Not at the Origin 4. Other Special Singular Solutions 5. Concentrated Load Tangential to the Surface of the Half Space-Cerruti's Problem 6. Concentrated Loads at the Tip of an Elastic Cone 7. Symmetrically Loaded Spheres 8. Spherical Harmonics 9. The Internal Problem 10. Interior Problem with Body Forces 11. Gravitating Sphere 12. Rotating Sphere 13. The External Problem 14. Stress Concentration Due to a Spherical Cavity 15. Hollow Sphere 16. End Effects in a Truncated Semi-Infinited Cone 17. General Solution of Non-Axismmetric Problems by 6. Complex Variable Formulae 7. Bessel Functions 8. Hankel Transform 9. Legendre Functions

About the Author :
A founding member of the American Society of Biomechanics, Robert William Soutas-Little is Professor Emeritus in the Department of Mechanical Engineering and the Department of Materials Science and Mechanics at Michigan State University.