Contents

Preface
1 Mathematical Preliminaries
 1.1 A vector and its representation: NPTEL link
 1.2 Dot-product, Cross-product and Tensor-product of two vectors: NPTEL link
 1.3 Second order tensors and their representation: NPTEL link
 1.4 Multiplying a second order tensor with a vector: dot product and tensor product: NPTEL link
 1.5 Multiplying two second order tensors: single-contraction, double-contraction and tensor product: NPTEL link
 1.6 Calculus of tensors: divergence and gradient
 1.7 Rotation tensor: NPTEL link
 1.8 Solved examples
 1.9 Objective questions to recall concepts
 1.10 Questions to practise
2 On Traction Vector, Stress Tensor and Stress Matrix
 2.1 Definition of traction vector: NPTEL link
 2.2 Relating traction on different planes at a point: NPTEL link
 2.3 Stress Tensor: NPTEL link
 2.4 Stress matrix as a representation of stress tensor: NPTEL link
 2.5 Transformation of Stress matrix: NPTEL link
 2.6 Solved examples
 2.7 Objective questions to recall concepts
 2.8 Questions to practise
3 Stress Equilibrium Equations
 3.1 Linear momentum balance: NPTEL link
 3.2 Angular momentum balance: NPTEL link
 3.3 Derivation of traction boundary condition: NPTEL link
 3.4 Solved examples
4 Maximizing Normal and Shear components of Traction
 4.1 Finding principal planes: NPTEL link
 4.2 Properties of Principal Planes: NPTEL link
 4.3 Maximizing shear component of traction: NPTEL link
 4.4 Mohr’s circle: NPTEL link
 4.5 Mohr’s stress plane: NPTEL link
 4.6 Stress invariants: NPTEL link
 4.7 Hydrostatic and deviatoric parts in stress tensor: NPTEL link
 4.8 Solved examples
5 On Strain Tensor and the associated Strain Matrix
 5.1 Longitudinal strain in a general body: NPTEL link
 5.2 Reference and deformed configurations: NPTEL link
 5.3 Relating line elements in reference and deformed configurations: NPTEL link
 5.4 Formula for longitudinal strain: NPTEL link
 5.5 Formula for shear strain: NPTEL link
 5.6 Formula for volumetric strain: NPTEL link
 5.7 Strain tensor: NPTEL link
 5.8 Local rotation tensor: NPTEL link
 5.9 Strain compatibility conditions: NPTEL link
 5.10 Similarity between stress and strain tensors: NPTEL link
 5.11 Solved examples
6 Stress - Strain relation
 6.1 Linear stress-strain relation: NPTEL link
 6.2 Independent components in stiffness tensor: NPTEL link
 6.3 Voigt Notation: NPTEL link
 6.4 Isotropic materials: NPTEL link
 6.5 On Young’s modulus, shear modulus and Poisson’s ratio: NPTEL link
 6.6 Isotropic thermoelasticity: NPTEL link
 6.7 Anisotropic materials: NPTEL link
 6.8 Inelastic behavior: NPTEL link
 6.9 Solved examples
7 Solving Axisymmetric Problems: Extension, Torsion and Inflation
 7.1 Cylindrical coordinate system: NPTEL link
 7.2 LMB Formulation:NPTEL link
 7.3 Strain matrix in cylindrical coordinate system: NPTEL link
 7.4 Relating stress and strain in cylindrical coordinate system: NPTEL link
 7.5 Extension, torsion and inflation of cylinders: NPTEL link
 7.6 Solving the simplified equations: NPTEL link
 7.7 Solved examples
8 Bending of Beams
 8.1 Pure bending of beams: NPTEL link
 8.2 Non-uniform bending of beams: NPTEL link
 8.3 Bending of unsymmetrical beams: NPTEL link
 8.4 Concept of shear center: NPTEL link
 8.5 Solved examples
9 Theory of Beams
 9.1 Motivation for beam theory: NPTEL link
 9.2 Euler-Bernouli Beam Theory: NPTEL link
 9.3 Timoshenko Beam Theory: NPTEL link
 9.4 Buckling of Beams: NPTEL link
 9.5 Solved examples
10 Energy Methods
 10.1 Linearity and superposition of elasticity equations: NPTEL link
 10.2 Energy stored in the body due to a applied force: NPTEL link
 10.3 Reciprocal relation: NPTEL link
 10.4 Generalized forces and generalized displacements: NPTEL link
 10.5 Castigliano’s First Theorem: NPTEL link
 10.6 Application of Castigliano’s theorem for solving beam problems: NPTEL link
 10.7 Solved examples
11 Theory of Failure
 11.1 Various theories of failure
 11.2 Solved examples