1 Introduction
 1.1 Basic Concepts in Mechanics
  1.1.1 What is force?
  1.1.2 What is stress?
  1.1.3 What is displacement?
  1.1.4 What is strain?
 1.2 Basic Equations in Mechanics
  1.2.1 Equilibrium equations
  1.2.2 Strain-Displacement relation
  1.2.3 Compatibility equation
  1.2.4 Constitutive relation
 1.3 Classification of the Response of Materials
  1.3.1 Non-dissipative response
  1.3.2 Dissipative response
 1.4 Solution to Boundary Value Problems
  1.4.1 Displacement method
  1.4.2 Stress method
  1.4.3 Semi-inverse method
 1.5 Summary
2 Mathematical Preliminaries
 2.1 Overview
 2.2 Algebra of vectors
 2.3 Algebra of second order tensors
  2.3.1 Orthogonal tensor
  2.3.2 Symmetric and skew tensors
  2.3.3 Projection tensor
  2.3.4 Spherical and deviatoric tensors
  2.3.5 Polar Decomposition theorem
 2.4 Algebra of fourth order tensors
  2.4.1 Alternate representation for tensors
 2.5 Eigenvalues, eigenvectors of tensors
  2.5.1 Square root theorem
 2.6 Transformation laws
  2.6.1 Vectorial transformation law
  2.6.2 Tensorial transformation law
  2.6.3 Isotropic tensors
 2.7 Scalar, vector, tensor functions
 2.8 Gradients and related operators
 2.9 Integral theorems
  2.9.1 Divergence theorem
  2.9.2 Stokes theorem
  2.9.3 Green’s theorem
 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
  3.5.1 Gradient of displacement
  3.5.2 Example
 3.6 Transformation of curves, surfaces and volume
  3.6.1 Transformation of curves
  3.6.2 Transformation of areas
  3.6.3 Transformation of volumes
 3.7 Properties of the deformation tensors
 3.8 Strain Tensors
 3.9 Normal and shear strain
  3.9.1 Normal strain
  3.9.2 Principal strain
  3.9.3 Shear strain
  3.9.4 Transformation of linearized strain tensor
 3.10 Homogeneous Motions
  3.10.1 Rigid body Motion
  3.10.2 Uniaxial or equi-biaxial motion
  3.10.3 Isochoric 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
  4.2.1 Cauchy stress theorem
  4.2.2 Components of Cauchy stress
 4.3 Normal and shear stresses
 4.4 Principal stresses and directions
  4.4.1 Maximum and minimum normal traction
  4.4.2 Maximum and minimum shear traction
 4.5 Stresses on a Octahedral plane
 4.6 Examples of state of stress
 4.7 Other stress measures
  4.7.1 Piola-Kirchhoff stress tensors
  4.7.2 Kirchhoff, Biot and Mandel 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
  5.4.1 Conservation of linear momentum
  5.4.2 Conservation of angular 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
  6.3.1 Restrictions due to objectivity
  6.3.2 Restrictions due to Material Symmetry
 6.4 Isotropic Hooke’s law
 6.5 Material parameters
  6.5.1 Young’s modulus and Poisson’s ratio
  6.5.2 Shear Modulus
  6.5.3 Bulk Modulus
 6.6 Restriction on material parameters
 6.7 Internally constraint materials
  6.7.1 Incompressible 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
  7.3.1 Displacement method
  7.3.2 Stress method
 7.4 Illustrative example
  7.4.1 Inflation of an annular cylinder
  7.4.2 Uniaxial tensile loading of a plate with a hole
 7.5 General results
  7.5.1 Uniqueness of solution
  7.5.2 Principle of superposition
 7.6 Summary
 7.7 Self-Evaluation
8 Bending of Prismatic Straight Beams
 8.1 Overview
 8.2 Symmetrical bending
  8.2.1 Strength of materials solution
  8.2.2 2D Elasticity solution
 8.3 Asymmetrical bending
 8.4 Shear center
  8.4.1 Illustrative examples
 8.5 Summary
 8.6 Self-Evaluation
9 End Torsion of Prismatic Bars
 9.1 Overview
 9.2 Twisting of thick walled closed section
  9.2.1 Circular bar
 9.3 Twisting of solid open section
  9.3.1 Solid elliptical section
  9.3.2 Solid rectangular section
  9.3.3 Thin rolled section
  9.3.4 Triangular cross section
 9.4 Twisting of hollow section
  9.4.1 Hollow elliptical section
  9.4.2 Thin walled tubes
 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
  10.3.1 Pure bending
  10.3.2 Curved cantilever beam under end load
 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