CHAPTER 1 BASIC ASSUMPTIONS AND MATHEMATICAL
PRELIMINARIES
1.1 Introduction
1.2 Basic Assumptions
1.3 Coordinate Systems and Transformations
1.4 Vector and Matrix Notations and Their Operations
1.5 Divergence Theorem
Problems/Tutorial Questions
CHAPTER 2 STRESSES
2.1 Stress and the Stress Tensor
2.2 Equilibrium Equations
2.3 Traction Boundary Conditions
2.4 Stresses on an Oblique Plane
2.5 Principal Stresses
2.6 Stationary and Octahedral Shear Stresses
2.7 Equilibrium Equations in Curvilinear Coordinates
Problems/Tutorial Questions
CHAPTER 3 STRAINS
3.1 Strains
3.2 Finite Deformations
3.3 Strains in a Given Direction and Principal Strains
3.4 Stationary Shear Strains
3.5 Compatibility
3.6 Kinematic and Compatibility Equations in Curvilinear Coordinates
3.7 Concluding Remarks
Problems/Tutorial Questions
CHAPTER 4 FORMULATION OF ELASTICITY PROBLEMS
4.1 Strain Energy Density Function
4.2 Generalised Hooke's Law
4.3 Initial Stresses and Initial Strains
4.4 Governing Equations and Boundary Conditions
4.5 General Solution Techniques
4.6 St.Venant's Principle
Problems/Tutorial Questions
CHAPTER5 TWO-DIMENSIONAL ELASTICITY
5.1 Plane Strain Problems
5.2 Plane Stress Problems
5.3 Similarities and Differences Between Plane Strain/Plane Stress Problems
5.4 Airy Stress Function and Polynomial Solutions
5.5 Polar Coordinates
5.6 Axisymmetric Stress Distributions
5.7 Rotating Discs
5.8 Stresses Around a Circular Hole in a Plate Subjected to Equal Biaxial Tension-Compression (Pure Shear in the 45°Direction)
5.9 Stress Concentration Around a Circular Hole in a Plate Subjected to Uniaxial Tension
5.10 Concluding Remarks
Problems/Tutorial Questions
CHAPTER 6 TORSION OF BARS
6.1 Torsion of Bars in Strength of Materials
6.2 Warping
6.3 Prandtl's Stress Function
6.4 Torque
6.5 Bars of Circular and Elliptical Cross-Sections
6.6 Thin-Walled Structures in Torsion
6.7 Analogies
Problems/Tutorial Questions
CHAPTER 7 BENDING OF BARS
7.1 Bending Theory in Strength of Materials
7.2 Elasticity Formulation of Bending of Bars
7.3 Stress Resultants and Shear Centre
7.4 Bending of a Bar of a Circular Cross-Section
7.5 Bending of a Bar of an Elliptical Cross-Section
7.6 Analogies
Problems/Tutorial Questions
CHAPTER 8 THE STATE SPACE METHOD OF 3D ELASTICITY
8.1 Concept of State and State Variables
8.2 Solution for a Linear Time-Invariant System
8．3 Calculation ofe[A]t
8．4 Solution of Linear Time-Variant System
8．5 State Variable Equation of Elasticity
8．6 Application ofState Space Method
8．7 Conclusions
Problems／Tutorial Questions
CHAPTER9 BENDINGOFPLA7ES
9．1 Love．KirchhoffHypotheses
9．2 TheDisplacementFields
9．3 Strains and Generalised Strains
9．4 Bending Momems
9．5 The Governing Equation
9．6 GeneralisedForces
9．7 Boundary Conditions
9。8 RectangularPlates
9．9 CircularPlates
Problems／Tutorial Questions
CHAPTER 10 ENERGYPRINCIPLES
10．1 Introduction
10．2 Work，Strain Energy and Strain Complementary Energy
10．3 Principle ofVirtualWork
10．4 Application ofthe Principle ofVirtual Work
10．5 The Reciprocal Law ofBetti
10．6 Principle ofMinimum Potential Energy
10．7 Principle ofVirtual Complememary Work
10.8 Principle of Minimum Complementary Energy
10.9 Castigliano's Theorems
10.10 Application of the Principles of Minimum Strain Energy
10.11 Rayleigh-Ritz Method
Problems/Tutorial Questions
CHAPTER 11 FINITE DIFFERENCE METHOD
11.1 Finite Difference Formulations
11.2 Relations of Difference and Differential Operators
11.3 Difference Pattern for Laplace and Bi-harmonic Operators
11.4 Case Study
11.5 Boundary Condition for Plane Problem Bi-harmonic Function
11.6 Irregular Boundary and Uneven Mesh Intervals
Problems/Tutorial Questions
CHAPTER 12. FINTTE ELEMENT METHOD
12.1 Introduction
12.2 Outline of FEM
12.3 Formulation of Displacement Model
12.4 Triangular Element
12.5 Nodal Force Vector
12.6 Rectangular Element
12.7 Transformation Matrix and Assembly of Structure Stiffness Matrix ~
12.8 Other Remarks
Problems/Tutorial Questions
CHAPTER 13 SPECIAL TOPICS FOR ELASTICITY
13.1 Thermal Elasticity
13.2 Propagation of Elastic Wave
13.3 Strength Theory, Crack and Fracture
Problems/Tutorial Questions
References