Cover -- Frontmatter -- Half Title Page -- Title Page -- Copyright -- Preface -- Contents -- About the Author -- Part I: Foundations and Elementary Applications -- 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 -- References -- Exercises -- 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 -- References -- Exercises -- 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 and Deviatoric Stresses -- 3.6 Equilibrium Equations -- 3.7 Relations in Curvilinear Cylindrical and Spherical Coordinates -- References -- Exercises -- 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 -- References -- Exercises -- 5. Formulation and Solution Strategies -- 5.1 Review of Field Equations -- 5.2 Boundary Conditions and Fundamental Problem Clasifications -- 5.3 Stress Formulation -- 5.4 Displacement Formulation -- 5.5 Principle of Superposition -- 5.6 Saint-Venant's Principle -- 5.7 General Solution Strategies -- References -- Exercises -- 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 -- References -- Exercises -- 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 -- References -- Exercises -- 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 Polar Coordinate Solutions -- References -- Exercises -- 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 -- References -- Exercises -- Part II: Advanced Applications -- 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 -- References -- Exercises -- 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 -- References -- Exercises -- 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 -- References -- Exercises -- 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 -- References -- Exercises -- 14. Micromechanics Applications -- 14.1 Dislocation Modeling -- 14.2 Singular Stress States -- 14.3 Elasticity Theory with Distributed Cracks -- 14.4 Micropolar/Couple-Stress Elasticity -- 14.5 Elasticity Theory with Voids -- 14.6 Doublet Mechanics -- References -- Exercises -- 15. Numerical Finite and Boundary Element Methods -- 15.1 Basics of the Finite Element Method -- 15.2 Approximating Functions for Two-Dimensional Linear Triangular Elements -- 15.3 Virtual Work Formulation for Plane Elasticity -- 15.4 FEM Problem Application -- 15.5 FEM Code Applications -- 15.6 Boundary Element Formulation -- References -- Exercises -- Appendix A: Basic Field Equations in Cartesian, Cylindrical, and Spherical Coordinates -- Strain-Displacement Relations -- Equilibrium Equations -- Hooke's Law -- Equilibrium Equations in Terms of Displacements (Navier's Equations) -- Appendix B: Transformation of Field Variables Between Cartesian, Cylindrical, and Spherical Components -- Cylindrical Components from Cartesian.

Spherical Components from Cylindrical -- Spherical Components From Cartesian -- Appendix C: MATLAB Primer -- C.1 Getting Started -- C.2 Examples -- Reference -- Index.