Mathematical Preliminaries:
Notes
Recorded Notes

• Vector Representations:   [L1]

• Dot Product Representations:   [L2]

• Dyadic Product:   [L3] (Upto 9:06 of L3)

• Contraction:   [Starting at 9:06 of L3] and [L4]

• Coordinate Transformations:   [L5] and [L6]

Live Sessions:

• Sep. 1 (Tuesday): 12 noon to 1 PM
• Sep. 3 (Thursday): 5 PM to 6 PM
• Sep. 5 (Saturday): 9 AM to 10:30 AM

Kinematics:
Notes
Recorded Notes

(The following pre-recorded lectures are common with the Mechanics of Solids course.)

• Deformation:   [L7]

• Displacement:   [L8]

• Quantification of deformation: [L9]

• Strain:   [L10],   [L11],   [L12],   [L13]

• Rigid-Body Rotation:   [L14]

• Principal Strains and Principal Axes of Strain:   [L15]

• Strain Compatibility:   [L16]

Live Sessions:

• Sep. 8 (Tuesday): 12 noon to 1 PM
• Sep. 10 (Thursday): 5 PM to 6 PM (no attendance)
• Sep. 12 (Saturday): 9 AM to 10:30 AM

Stress:

Notes
Recorded Notes

(The following pre-recorded lectures are again common with the Mechanics of Solids course.)

• Traction:   [L17]

• Connection between Traction Vector and Stress:
  • Balance of Linear Momentum:   [L18]
  • Balance of Linear Momentum Applied to a Tetrahedron:   [L19], [L20]

• Cauchy’s Formula:   [L21]

• Cauchy’s Equations of Motion and Stress Equilibrium Equations:   [L22]

• Normal and Shear Components of Traction:   [L23]

• Principal Stresses:   [L24]

• State of Stress Referred to Principal Directions:   [L25]

• Octahedral Stress:   [L26]

• Mean and Deviatoric Stress:   [L27]

Material Behaviour:

Notes
Recorded Notes

• Need for Material Behaviour Relations:   [L28]

• Minor Symmetry:   [L29]

• Voigt Notation:   [L30]

• Major Symmetry:   [L31]

• Linear, Elastic, Isotropic Behaviour:   [L32]

Boundary conditions:

2D Elasticity:

Notes
Recorded Notes

• Plane Stress:   [L34], [L35]
• Plane Strain:   [L36], [L37]
• Polynomial Solutions:   [L38]
• Principle of Superposition and St. Venant’s Princple:   [L39]

2D Elasticity … contd.: (Using Jupyter Notebook)

Jupyter Notebook files:

• Introduction to Jupyter Notebook and Sympy
  
• Jupyter Notebook file demonstrated in [L43]
  

Lecture videos

• Introduction to Jupyter Notebook and SymPy:   [L40], [L41],

• Example Problem using Airy Stress Function Approach:   [L42], [L43]

2D Elasticity … contd. (Using Jupyter Notebook)

Jupyter Notebook files with detailed explanations:

• Biharmonic eqn. & Stresses in Polar coord.
• Axisymmetric Problems - Thick-walled Pressure Vessel
• Pure Bending of a Curved Bar
• Curved Bar under Horizontal Load

Lecture videos:

• Biharmonic eqn & Stresses in polar coordinates:   [L44]

• Solution of Problems in polar coordinates
  • Pressure vessels   [L45]
  • Curved bar: pure bending   [L46]
  • Curved bar: horizontal load   [Covered during Oct. 19 Live Session; Session recording available on MS Teams]

2D Elasticity … contd.: (Using Jupyter Notebook)

Jupyter Notebook files with detailed explanations:

• Plate with circular hole
  
• Flamant problem
  Displacement soln for curved bar under pure bending

Lecture videos:

• Solution of Problems in polar coordinates … contd.
  • Plate with circular hole   [L47]
  • Flamant problem   [L48]
• Finding displacements
  • Displacements for curved bar under pure bending problem   [Covered during Oct. 20 Live Session; Session recording available on MS Teams]

3D Elasticity:

Recorded Notes

Lecture videos:

• Introduction and connections with 2D elasticity:   [L49]
• Helmholtz displacement potential:   [L50]
• Lame’s strain potential:   [L51]
• Galerkin potential:   [L52]
• Papkovich-Neuber representation:   [L53], [L54]

3D Elasticity … contd.:

• Kelvin’s problem

Recorded Notes

Lecture videos:

• Mathematical precursor to Kelvin’s problem:   [L55]
• Kelvin’s problem:   [L56]