Introduction to Linear Elasticity

1. Introduction and Mathematical Preliminaries.- 1.1 Scope.- 1.2 Vector Algebra.- 1.3 Scalar and Vector Fields.- 1.4 Indicial Notation.- 1.5 Coordinate Rotation.- 1.6 Cartesian Tensors.- 1.7 Algebra of Cartesian Tensors.- 1.8 Operational Tensors.- 1.9 Computational Examples.- Exercises.- References.- 2. Traction, Stress and Equilibrium.- 2.1 Introduction.- 2.2 State of Stress.- 2.3 Equilibrium.- 2.4 Principal Stress.- 2.5 Stresses in Principal Coordinates.- 2.6 Properties and Special States of Stress.- Exercises.- References.- 3. Deformations.- 3.1 Introduction.- 3.2 Strain.- 3.3 Physical Interpretation of Strain Tensor.- 3.4 Principal Strains.- 3.5 Volume and Shape Changes.- 3.6 Compatibility.- 3.7 Computational Example.- Exercises.- References.- 4. Material Behavior.- 4.1 Introduction.- 4.2 Uniaxial Behavior.- 4.3 Generalized Hooke's Law.- 4.4 Thermal Strains.- 4.5 Physical Data.- Exercises.- References.- 5. Formulation, Uniqueness and Solution Strategies.- 5.1 Introduction.- 5.2 Displacement Formulation.- 5.3 Force Formulation.- 5.4 Other Formulations.- 5.5 Uniqueness.- 5.6 Membrane Equation.- 5.7 Solution Strategies.- Exercises.- References.- 6. Extension, Bending and Torsion.- 6.1 Introduction.- 6.2 Prismatic Bar under Axial Loading.- 6.3 Cantilever Beam under End Loading.- 6.4 Torsion.- Exercises.- References.- 7. Two-Dimensional Elasticity.- 7.1 Introduction.- 7.2 Plane Stress Equations.- 7.3 Plane Strain Equations.- 7.4 Cylindrical Coordinates.- 7.5 Thick-Walled Cylinder or Disk.- 7.6 Sheet with Small Circular Hole.- 7.7 Curved Beam.- 7.8 Rotational Dislocation.- 7.9 Narrow, Simply Supported Beam.- 7.10 Semi-Infinite Plate with a Concentrated Load.- Exercises.- References.- 8. Bending of Thin Plates.- 8.1 Introduction.- 8.2 Assumptions.- 8.3 Formulation.- 8.4Solutions.- 8.5 Commentary.- Exercises.- References.- 9. Time-Dependent Effects.- 9.1 Introduction.- 9.2 Vibrations in an Infinite Elastic Medium.- 9.3 Free Vibration.- 9.4 Uniform Rotation of a Beam.- Exercises.- References.- 10. Energy Principles.- 10.1 Introduction.- 10.2 Conservation of Energy.- 10.3 Strain Energy.- 10.4 Work of External Loading.- 10.5 Principle of Virtual Work.- 10.6 Variational Principles.- 10.7 Direction Variational Methods.- Exercises.- References.- 11. Strength and Failure Criteria.- 11.1 Introduction.- 11.2 Isotropic Materials.- 11.3 Yield Surfaces.- 11.4 Anisotropic Materials.- 11.5 Failure of Structures.- Exercises.- References.- 12. Something New.