Front Cover -- Elasticity: Theory, Applications, and Numerics -- Copyright Page -- Contents -- Preface -- About the Author -- PART I: FOUNDATIONS AND ELEMENTARY APPLICATIONS -- Chapter 1. Mathematical Preliminaries -- 1.1 Scalar, Vector, Matrix, and Tensor Definitions -- 1.2 Index Notation -- 1.3 Kronecker Delta and Alternating Symbol -- 1.4 Coordinate Transformations -- 1.5 Cartesian Tensors -- 1.6 Principal Values and Directions for Symmetric Second-Order Tensors -- 1.7 Vector, Matrix, and Tensor Algebra -- 1.8 Calculus of Cartesian Tensors -- 1.9 Orthogonal Curvilinear Coordinates -- Chapter 2. Deformation: Displacements and Strains -- 2.1 General Deformations -- 2.2 Geometric Construction of Small Deformation Theory -- 2.3 Strain Transformation -- 2.4 Principal Strains -- 2.5 Spherical and Deviatoric Strains -- 2.6 Strain Compatibility -- 2.7 Curvilinear Cylindrical and Spherical Coordinates -- Chapter 3. Stress and Equilibrium -- 3.1 Body and Surface Forces -- 3.2 Traction Vector and Stress Tensor -- 3.3 Stress Transformation -- 3.4 Principal Stresses -- 3.5 Spherical, Deviatoric, Octahedral, and von Mises Stresses -- 3.6 Equilibrium Equations -- 3.7 Relations in Curvilinear Cylindrical and Spherical Coordinates -- Chapter 4. Material Behavior-Linear Elastic Solids -- 4.1 Material Characterization -- 4.2 Linear Elastic Materials-Hooke's Law -- 4.3 Physical Meaning of Elastic Moduli -- 4.4 Thermoelastic Constitutive Relations -- Chapter 5. Formulation and Solution Strategies -- 5.1 Review of Field Equations -- 5.2 Boundary Conditions and Fundamental Problem Classifications -- 5.3 Stress Formulation -- 5.4 Displacement Formulation -- 5.5 Principle of Superposition -- 5.6 Saint-Venant's Principle -- 5.7 General Solution Strategies -- Chapter 6. Strain Energy and Related Principles -- 6.1 Strain Energy.

6.2 Uniqueness of the Elasticity Boundary-Value Problem -- 6.3 Bounds on the Elastic Constants -- 6.4 Related Integral Theorems -- 6.5 Principle of Virtual Work -- 6.6 Principles of Minimum Potential and Complementary Energy -- 6.7 Rayleigh-Ritz Method -- Chapter 7. Two-Dimensional Formulation -- 7.1 Plane Strain -- 7.2 Plane Stress -- 7.3 Generalized Plane Stress -- 7.4 Antiplane Strain -- 7.5 Airy Stress Function -- 7.6 Polar Coordinate Formulation -- Chapter 8. Two-Dimensional Problem Solution -- 8.1 Cartesian Coordinate Solutions Using Polynomials -- 8.2 Cartesian Coordinate Solutions Using Fourier Methods -- 8.3 General Solutions in Polar Coordinates -- 8.4 Example Polar Coordinate Solutions -- Chapter 9. Extension, Torsion, and Flexure of Elastic Cylinders -- 9.1 General Formulation -- 9.2 Extension Formulation -- 9.3 Torsion Formulation -- 9.4 Torsion Solutions Derived from Boundary Equation -- 9.5 Torsion Solutions Using Fourier Methods -- 9.6 Torsion of Cylinders with Hollow Sections -- 9.7 Torsion of Circular Shafts of Variable Diameter -- 9.8 Flexure Formulation -- 9.9 Flexure Problems without Twist -- PART II: ADVANCED APPLICATIONS -- Chapter 10. Complex Variable Methods -- 10.1 Review of Complex Variable Theory -- 10.2 Complex Formulation of the Plane Elasticity Problem -- 10.3 Resultant Boundary Conditions -- 10.4 General Structure of the Complex Potentials -- 10.5 Circular Domain Examples -- 10.6 Plane and Half-Plane Problems -- 10.7 Applications Using the Method of Conformal Mapping -- 10.8 Applications to Fracture Mechanics -- 10.9 Westergaard Method for Crack Analysis -- Chapter 11. Anisotropic Elasticity -- 11.1 Basic Concepts -- 11.2 Material Symmetry -- 11.3 Restrictions on Elastic Moduli -- 11.4 Torsion of a Solid Possessing a Plane of Material Symmetry -- 11.5 Plane Deformation Problems.

11.6 Applications to Fracture Mechanics -- 11.7 Curvilinear Anisotropic Problems -- Chapter 12. Thermoelasticity -- 12.1 Heat Conduction and the Energy Equation -- 12.2 General Uncoupled Formulation -- 12.3 Two-Dimensional Formulation -- 12.4 Displacement Potential Solution -- 12.5 Stress Function Formulation -- 12.6 Polar Coordinate Formulation -- 12.7 Radially Symmetric Problems -- 12.8 Complex Variable Methods for Plane Problems -- Chapter 13. Displacement Potentials and Stress Functions -- 13.1 Helmholtz Displacement Vector Representation -- 13.2 Lamé's Strain Potential -- 13.3 Galerkin Vector Representation -- 13.4 Papkovich-Neuber Representation -- 13.5 Spherical Coordinate Formulations -- 13.6 Stress Functions -- Chapter 14. Nonhomogeneous Elasticity -- 14.1 Basic Concepts -- 14.2 Plane Problem of Hollow Cylindrical Domain under Uniform Pressure -- 14.3 Rotating Disk Problem -- 14.4 Point Force on the Free Surface of a Half-Space -- 14.5 Antiplane Strain Problems -- 14.6 Torsion Problem -- Chapter 15. Micromechanics Applications -- 15.1 Dislocation Modeling -- 15.2 Singular Stress States -- 15.3 Elasticity Theory with Distributed Cracks -- 15.4 Micropolar/Couple-Stress Elasticity -- 15.5 Elasticity Theory with Voids -- 15.6 Doublet Mechanics -- Chapter 16. Numerical Finite and Boundary Element Methods -- 16.1 Basics of the Finite Element Method -- 16.2 Approximating Functions for Two-Dimensional Linear Triangular Elements -- 16.3 Virtual Work Formulation for Plane Elasticity -- 16.4 FEM Problem Application -- 16.5 FEM Code Applications -- 16.6 Boundary Element Formulation -- Appendix A Basic Field Equations in Cartesian, Cylindrical, and Spherical Coordinates -- Appendix B Transformation of Field Variables Between Cartesian, Cylindrical, and Spherical Components -- Appendix C MATLAB Primer -- Appendix D Review of Mechanics of Materials.

Index.