Contents
1 Introduction
 1.1 Basic Concepts in Mechanics
 1.2 Basic Equations in Mechanics
 1.3 Classification of the Response of Materials
 1.4 Solution to Boundary Value Problems
 1.5 Summary
2 Mathematical Preliminaries
 2.1 Overview
 2.2 Algebra of vectors
 2.3 Algebra of second order tensors
 2.4 Algebra of fourth order tensors
 2.5 Eigenvalues, eigenvectors of tensors
 2.6 Transformation laws
 2.7 Scalar, vector, tensor functions
 2.8 Gradients and related operators
 2.9 Integral theorems
 2.10 Summary
 2.11 Self-Evaluation
3 Kinematics
 3.1 Overview
 3.2 Body
 3.3 Deformation Gradient
 3.4 Lagrangian and Eulerian description
 3.5 Displacement, velocity and acceleration
 3.6 Transformation of curves, surfaces and volume
 3.7 Properties of the deformation tensors
 3.8 Strain Tensors
 3.9 Normal and shear strain
 3.10 Homogeneous Motions
 3.11 Compatibility condition
 3.12 Summary
 3.13 Self-Evaluation
4 Traction and Stress
 4.1 Overview
 4.2 Traction vectors and stress tensors
 4.3 Normal and shear stresses
 4.4 Principal stresses and directions
 4.5 Stresses on a Octahedral plane
 4.6 Examples of state of stress
 4.7 Other stress measures
 4.8 Summary
 4.9 Self-Evaluation
5 Balance Laws
 5.1 Overview
 5.2 System
 5.3 Conservation of Mass
 5.4 Conservation of momentum
 5.5 Summary
 5.6 Self-Evaluation
6 Constitutive Relations
 6.1 Overview
 6.2 Definition of elastic process
 6.3 Restrictions on constitutive relation
 6.4 Isotropic Hooke’s law
 6.5 Material parameters
 6.6 Restriction on material parameters
 6.7 Internally constraint materials
 6.8 Orthotropic Hooke’s law
 6.9 Summary
 6.10 Self-Evaluation
7 Boundary Value Problem: Formulation
 7.1 Overview
 7.2 Formulation of boundary value problem
 7.3 Techniques to solve boundary value problems
 7.4 Illustrative example
 7.5 General results
 7.6 Summary
 7.7 Self-Evaluation
8 Bending of Prismatic Straight Beams
 8.1 Overview
 8.2 Symmetrical bending
 8.3 Asymmetrical bending
 8.4 Shear center
 8.5 Summary
 8.6 Self-Evaluation
9 End Torsion of Prismatic Bars
 9.1 Overview
 9.2 Twisting of thick walled closed section
 9.3 Twisting of solid open section
 9.4 Twisting of hollow section
 9.5 Summary
 9.6 Self-Evaluation
10 Bending of Curved Beams
 10.1 Overview
 10.2 Winkler-Bach formula for curved beams
 10.3 2D Elasticity solution for curved beams
 10.4 Summary
 10.5 Self-Evaluation
11 Beam on Elastic Foundation
 11.1 Overview
 11.2 General formulation
 11.3 Example 1: Point load
 11.4 Example 2: Concentrated moment
 11.5 Example 3: Uniformly distributed load
 11.6 Summary
 11.7 Self-Evaluation
Bibliography