Chapter
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
2.2 Geometric Construction of Small Deformation Theory
2.3 Strain Transformation
2.5 Spherical and Deviatoric Strains
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
3.5 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
5.4 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
6.2 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
Chapter 7. Two-Dimensional Formulation
7.3 Generalized Plane Stress
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
9.2 Extension 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
9.9 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
11.3 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
Chapter 14. Nonhomogeneous Elasticity
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
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
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 D Review of Mechanics of Materials
Elasticity
：Theory, Applications, and Numerics
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