Chapter 1 Introduction 1.1 Introduction to Elasticity 1.1.1 Definition and Development History of Elasticity 1.1.2 Introduction to the Finite Element Method (FEM) 1.2 Relationship Between Elasticity and Other Branches of Solid Mechanics 1.3 Several Basic Concepts in Elasticity 1.4 Fundamental Assumptions in Elasticity 1.5 Chapter Summary Exercises References Chapter 2 Basic Theory of Spatial Problems in Elasticity 2.1 Stress State of a Point in an Elastic Body 2.2 Principal Stresses and Principal Stress Directions 2.2.1 Principal Stresses, Maximum and Minimum Principal Stresses 2.2.2 Principal Stress Directions 2.2.3 Maximum and Minimum Principal Shear Stresses 2.3 Basic Equations of Spatial Problems 2.3.1 Differential Equations of Equilibrium 2.3.2 Geometrical Equations 2.3.3 Physical Equations 2.4 Boundary Conditions 2.5 Basic Equations of Axisymmetric Problems 2.6 Chapter Summary Exercises References Chapter 3 Theory of Plane Problems 3.1 Plane Stress and Plane Strain 3.2 Basic Equations in Plane Problems 3.3 Stress at a Point in Plane Problems 3.4 Boundary Conditions and Saint-Venant's Principle 3.5 Solution of Plane Problems in Terms of Displacements 3.6 Solution of Plane Problems in Terms of Stresses 3.7 Case of Constant Body Force and Stress Function 3.8 Chapter Summary Exercises References Chapter 4 Solution of Plane Problems in Cartesian Coordinates 4.1 Inverse Method 4.1.1 Polynomial Solution with Inverse Method 4.1.2 Stress Solution of a Rectangular Beam Subjected to Pure Bending 4.1.3 Displacement Solution of a Rectangular Beam Subjected to Pure Bending 4.2 Semi-inverse Method 4.2.1 Solution of a Simply Supported Beam subjected to a Uniformly Distributed Load 4.2.2 Solution of a Wedge Subjected to Gravity and Liquid Pressure 4.3 Chapter Summary Exercises References Chapter 5 Solution of Plane Problems in Polar Coordinates 5.1 Differential Equations of Equilibrium in Polar Coordinates 5.2 Geometrical and Physical Equations in Polar Coordinates
5.3 Coordinate Transformation of Stress Components 5.4 Stress Function and Consistency Equation in Polar Coordinates 5.5 Stresses and Displacements of Axisymmetric Problems 5.6 A Circular Ring or Cylinder Subjected to Uniform Pressures 5.7 A Tunnel Subjected to Uniform Pressure 5.8 Stress Concentration of a Circular Hole 5.9 An Elastic Wedge Subjected to External Loads 5.10 A Semi-infinite Plane Subjected to a Concentrated Normal Load 5.11 A Semi-infinite Plane Subjected to a Uniformly Distributed Load 5.12 Chapter Summary Exercises References Chapter 6 Solution of Spatial Problems 6.1 Solution of Spatial Problems in Terms of Displacements 6.2 Semi-infinite Body Subjected to Gravity and Uniform Pressure 6.3 Semi-infinite Body Subjected to a Concentrated Normal Load 6.4 Solution of Spatial Problems in Terms of Stresses 6.5 Pure Bending of a Straight Bar 6.6 Torsion of a Prismatic Bar 6.7 Membrane Analogy for Torsion 6.8 Chapter Summary Exercises References Chapter 7 Bending of Thin Plates 7.1 Basic Concepts and Assumptions 7.2 Differential Equations of Deflection 7.3 Internal Forces on the Cross-section of a Thin Plate 7.4 Boundary Conditions and Equivalent Shear Forces to Torsional Moments 7.5 Navier's Solution by Double Trigonometric Series 7.6 Levy's Solution by Single Trigonometric Series 7.7 Bending of a Circular Thin Plate 7.8 Axisymmetric Bending of a Circular Thin Plate 7.9 Chapter Summary Exercises References Chapter 8 Variation in Elasticity 8.1 Introduction to Variational Methods 8.2 Displacement Variational Method 8.3 Stress Variational Method 8.4 Chapter Summary Exercises References Chapter 9 Finite Element Method of Plane Problems 9.1 Introduction 9.2 Matrix Representations of Basic Quantities and Basic Equations 9.3 Solution Steps of the Finite Element Method 9.4 Elemental Displacement Model and Convergence of Solution 9.5 Elemental Strain Matrix and Stress Matrix 9.6 Elemental Nodal Force Matrix and Stiffness Matrix 9.7 Elemental Nodal Load Matrix
9.8 Global Analysis of Structure 9.9 Solution Steps and Element Meshing 9.10 MATLAB Programming Example 9.11 Analysis of Calculated Results 9.12 Derivation of Basic Equations of FEM from the Variational Principle 9.13 Chapter Summary Exercises References Chapter 10 Introduction to Finite Element Software and a Solution Example 10.1 Introduction 10.2 Overview of Finite Element Software 10.3 Basic Operation Method of ABAQUS 10.4 Finite Element Solution Procedure and ABAQUS Analysis Workflow 10.5 Analysis of a Plane-Stress Problem Using ABAQUS 10.6 Chapter Summary Exercises References
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