Applied Elasticity (ME40605/ME60401), Autumn 2020

Mechanical Engineering Department, Indian Institute of Technology Kharagpur

Instructor:

Dr Jeevanjyoti Chakraborty (JC)

Email: jeevan@mech.iitkgp.ac.in; jeevanjyoti4@gmail.com


Policies and Guidelines:

All policies and guidelines regarding attendance, grades, assignment submission, absence from exams are laid out in detail in the Policies and Guidelines tab.


Learning Resources

Topics Problem Sheets

Mathematical Preliminaries:
Notes
Recorded Notes


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
PS 1

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
PS 2

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]

PS3

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]
PS4

Boundary conditions:

Recorded Notes
[L33]
None

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:


Lecture videos

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

  • Example Problem using Airy Stress Function Approach:   [L42], [L43]
PS5

2D Elasticity … contd. (Using Jupyter Notebook)

Jupyter Notebook files with detailed explanations:


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:


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]



Textbook

The textbook for this course is Elasticity by Martin H. Saad. (Preferably, the third edition but other editions are fine.)