Course Contents and Assessment

S. No. Description Download link
1 Course contents Syllabus
2 Grading methodology Assessment Criteria

Lectures Schedule, Topics and Assignments/Papers

Lecture. No. Lecture Topic
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


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


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


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


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