| Lecture 1 |
Introduction to Scalar, Vector, Tensor, 3D Euclidean Vector Space, Kronecker Delta |
| Lecture 2 |
Permutation Symbol, Vector Cross Product, Scalar Triple Product, Tensor Product, Special Tensors |
| Lecture 3 |
Higher Order Tensors, Unit Tensor, Transpose and Trace of a Tensor, Symmetric and Skew-symmetric Tensor |
| Lecture 4 |
Spherical and Deviatoric Tensors, Orthogonal Tensors, Invariants, Eigenvalues and Eigenvectors of a Tensor |
| Lecture 5 |
Tensor Transformations, Isotropic Tensors |
| Lecture 6 |
Tensor Functions, Tensor Calculus |
| Lecture 7 |
Integral Theorms, Problems |
Quiz-1 |
Fall 2021
|
| Lecture 8 |
Analysis of Strain, Displacement Gradient Tensor |
| Lecture 9 |
Strain Tensor and Rotation Tensor, Deformation of an Area Element |
| Lecture 10.1 |
Strain Transformation |
| Lecture 10.2 |
Principal Strains, Strain Compatibility |
| Lecture 11 |
Analysis of Stress |
| Lecture 12 |
Traction Vector |
| Lecture 13 |
Stress Components, Normal and Shear Stresses, Stress Transformation, Principal Stresses |
| Lecture 14 |
State of Stress, Equilibrium Equations |
| Lecture 15 |
Constitutive Model, Material Behaviour |
| Lecture 16 |
Homogneous and Heterogeneous Materials, Isotropic and Anisotropic Materials |
Quiz-2 |
Fall 2021
|
| Lecture 17 |
Hooke's Law for Linear Elastic Material, Thermoelastic Constitutive Relations |
| Lecture 18 |
Strain Energy |
| Lecture 19 |
Clapeyron's Theorem, Betti/Rayleigh Reciprocal Theorem |
| Lecture 20 |
Boundary Value Problem Formulation |
| Lecture 21 |
Stress Formulation, Displacement Formulation |
| Lecture 22 |
Principle of Superposition, Saint Venant's Principle |
| Lecture 23 |
Direct Method, Inverse Method, Semi-Inverse Method |
| Lecture 24 |
2 Dimensional Elasticity Formulations: Plane Strain, Plane Stress |
| Lecture 25 |
Airy Stress Function Approach |
Quiz-3 |
Fall 2021
|
| Lecture 26 |
2D Polar Formulation, Problems in Rectangular Coordinates |
| Lecture 27 |
2D Problems in Linear Elasticity |
| Lecture 28 |
Problem: Cantilever Beam With End Load |
| Lecture 29 |
2D Problems in Linear Elasticity |
| Lecture 30 |
Generalised Solution in Polar Coordinates |
| Lecture 31 |
Problem: Thick Cylinder with Uniform Pressure |
| Lecture 32 |
Problem: Infinite Domain with Pressurized Hole |
| Lecture 33 |
Wedge Problems |
| Lecture 34 |
Flamant Problem |
Quiz-4 |
Fall 2021
|
| Lecture 35 |
Problem: Half Space Under a Surface Concentrated Moment |
| Lecture 36 |
Curved Beams Problem |
| Lecture 37 |
Torsion of Elastic Cylinders- 1 |
| Lecture 38 |
Torsion of Elastic Cylinders- 2 |
| Lecture 39 |
Membrane Analogy |
End-term Examination |
Fall 2021
|