Contents
Chapter 1 Introduction
1.1 A brief historical development
1.2 Some concepts
1.3 Book contents
Chapter 2 Mathematical Preliminaries
2.1 Physical quantities and index notation
2.2 Summation convention and two special arrays
2.3 Tensor algebra
2.4 Tensor calculus
Chapter 3 Analysis of Stress
3.1 Review of elementary MoM
3.2 Motivation & definition
3.3 Traction vector and cauchy relation
3.4 Stress transformation
3.5 Principal stresses
Chapter 4 Constitutive Relations
4.1 Basic concepts
4.2 Engineering materials
4.3 Constitutive relations for isotropic material (2-D)
4.4 Constitutive relations for isotropic material (3-D)
4.5 Constitutive relations for anisotropic materials
4.6 Constitutive relations for thermoelasticity
Chapter 5 Strain Energy
5.1 Concepts and formulas
5.2 Strain energy density for isotropic materials in some basic modes
5.3 Strain energy for isotropic materials in common structures
5.4 Octahedral shear stress
5.5 Deviatoric stress
5.6 Complementary strain energy
Chapter 6 Linear Elasticity of Isotropic Materials
6.1 Concepts
6.2 Constitutive equations in 2-D elasticity
6.3 Strains and compatibility equations in 2-D elasticity
6.4 Equilibrium equations
6.5 Boundary conditions
Chapter 7 Stress Function Method in 2-D Elasticity
7.1 Introduction to Airy stress function
7.2 Defining equation for Airy stress function
7.3 Solution techniques: inverse method
7.4 Solution techniques: semi-inverse approach
7.5 Solution techniques: Fourier methods
Chapter 8 Two-Dimensional Problems in Polar Coordinates
8.1 Polar coordinate formulation
8.2 Airy stress function in polar coordinates
8.3 General solutions in polar coordinates
Chapter 9 Failure Theories
9.1 Typical failure modes
9.2 Brittle and ductile failure
9.3 Introduction to linear elastic fracture mechanics
9.4 Introduction to fatigue
Chapter 10 Unsymmetric Bending and Curved Beams
10.1 Unsymmetric bending
10.2 Shear center
10.3 Curved beams
Chapter 11 Torsion of Prismatic Members
11.1 Reviews of MoM circular sections
11.2 St. Venant torsion theory
11.3 Prandtl stress function method
11.4 Prandtl's membrane analogy
Chapter 12 Energy Methods
12.1 Basic concepts for energy methods
12.2 Principles of virtual work and minimum total potential energy
12.3 Variational methods
Chapter 13 Advanced Topic I: Higher-Order Elasticity
13.1 Couple stress theory
13.2 A reformulated strain gradient elasticity theory
13.3 Simplified micromorphic theory
Chapter 14 Advanced Topic II: Magneto-Electro-Elastic Structure Theories
14.1 Theoretical framework
14.2 New MEE beam model incorporating foundation effect
14.3 New MEE microplate model
14.4 New FG-MEE composite beam model
Chapter 15 Advanced Topic III: Deformable Semiconductors
15.1 Field equations for piezoelectric semiconductor
15.2 Field equations for flexoelectric semiconductor
