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Applied Elasticity

By Prof. Soham Roychowdhury   |   IIT Bhubaneswar
Learners enrolled: 66
ABOUT THE COURSE:

This course focuses on the application of elasticity theory in various structural deformation problems. With a brief revisit to the theory of elasticity, the course explores the solution techniques for different solid mechanics problems using the field equations of elasticity for both stress based and displacement based approaches. Special emphasis is given for solving the structures with complex geometries described by both Cartesian and polar coordinates. The course is expected to be useful for the postgraduate course work as well as academic research.

INTENDED AUDIENCE: First year postgraduate students of Mechanical Systems Design/Machine Design/ Computational Solid Mechanics/Applied Mechanics specialization, and final year undergraduate students of Mechanical Engineering

PREREQUISITES: Solid Mechanics/Mechanics of Materials (UG level)
Summary
Course Status : Upcoming
Course Type : Core
Language for course content : English
Duration : 12 weeks
Category :
  • Mechanical Engineering
  • Advanced Mechanics
Credit Points : 3
Level : Postgraduate
Start Date : 21 Jul 2025
End Date : 10 Oct 2025
Enrollment Ends : 28 Jul 2025
Exam Registration Ends : 15 Aug 2025
Exam Date : 01 Nov 2025 IST
NCrF Level   : 4.5 — 8.0

Note: This exam date is subject to change based on seat availability. You can check final exam date on your hall ticket.


Page Visits



Course layout

Week 1:  Introduction and Mathematical Preliminaries: Tensor algebra and indicial notation, Transformation of tensors, Tensor calculus.

Week 2: Deformation and Strain: Lagrangian and Eulerian descriptions of deformation, Deformation gradient tensor, Green-Lagrange and Eulerian strain tensors, Infinitesimal strain tensor, Dilation, Strain compatibility equations.

Week 3: Stress Measures and Balance Laws: Surface traction vector, Cauchy stress tensor at a point, Cauchy stress formula, First and second Piola Kirchhoff stress tensors, Mass, momentum, angular momentum, and energy balance, Stress power.

 Week 4: Constitutive Relations: Generalized Hooke’s law for linear elastic solids, Concept of material symmetry, Elastic stiffness tensors for monoclinic, orthotropic, transversely isotropic and isotropic materials, Strain energy density function, Hyperelasticity.

 Week 5: Field Equations of Elasticity: Problem formulation using field equations of elasticity, Stress and displacement based solution techniques, Lame-Navier equations and Beltrami-Michell equations, Different elasticity theorems.

 Week 6: Stress Functions and Planar Elastic Problems: Stress functions, Plane stress formulation, Plane strain formulation, Anti-plane strain problems, Effect of body forces, Different forms of stress functions.

 Week 7: Planar Bending Problems: Stress functions for solving bending of straight beams, Pure bending problem, Beams subjected to concentrated and distributed transverse loading.

 Week 8: Torsional Problems: Torsion of prismatic shaft using Prandtl’s stress function, Solution for elliptical, triangular, and rectangular shafts, Torsion of hollow sections.

 Week 9: Problems in Polar Coordinates I: Field equations in polar coordinates, Stress functions in polar coordinate, General Michell solution, Axisymmetric problem solution, Bending of curved beams.

 Week 10: Problems in Polar Coordinates II: Semi-infinite domain problems involving elastic half space, quarter plane, and plane elastic wedge under different loading conditions.

 Week 11: Problems in Polar Coordinates III: Notch and crack problems, Rotating disc problems, Stress concentration around a hole within a plate subjected to tension.

 Week 12: Advanced Topics: Disk under diametrical compression, Plane elastic contact problem solution, Thermo-elastic deformation problems.


Books and references

  1. M. H. Sadd, Elasticity Theory, Applications, and Numerics, Elsevier 
  2. A. F. Bower, Applied Mechanics of Solids, CRC Press 
  3. S. Timoshenko, and J. N. Goodier, Theory of Elasticity, McGraw Hill 
  4. A. P. Boresi, K. P. Chong, and J. D. Lee, Elasticity in Engineering Mechanics, Wiley 
  5. W. S. Slaughter, The Linearized Theory of Elasticity, Springer 
  6. J. R. Barber, Elasticity, Kluwer Academic Publishers

Instructor bio

Prof. Soham Roychowdhury

IIT Bhubaneswar
Dr. Soham Roychowdhury is a faculty(Assistant Professor) at the School of Mechanical Sciences, IIT Bhubaneswar Since 2019. He obtained BE degree in Mechanical Engineering from IIEST Shibpur (formerly known as Bengal Engineering and Science University Shibpur) in 2012, followed by MTech degree in Mechanical Systems Design from IIT Kharagpur in 2014, and finally PhD degree from IIT Kharagpur 2019. He was awarded the Director’s Gold Medal and Dr. Shankar Dayal Sharma Memorial Gold Medal of IIT Kharagpur for MTech program, and Institute Silver Medal of BESU Shibpur for BE program. His research interest includes mechanics of inflatable structures, structural stability, computational solid mechanics, vibration of structures etc. He has taught different undergraduate and postgraduate course at IIT Bhubaneswar such as Theory of Machines-I, Theory of Machines-II, Applied Elasticity, Advanced Solid Mechanics, Dynamics and Control of Mechanical System, Vibration of Structures etc.

Course certificate

The course is free to enroll and learn from. But if you want a certificate, you have to register and write the proctored exam conducted by us in person at any of the designated exam centres.
The exam is optional for a fee of Rs 1000/- (Rupees one thousand only).
Date and Time of Exams: November 01, 2025 Morning session 9am to 12 noon; Afternoon Session 2pm to 5pm.
Registration url: Announcements will be made when the registration form is open for registrations.
The online registration form has to be filled and the certification exam fee needs to be paid. More details will be made available when the exam registration form is published. If there are any changes, it will be mentioned then.
Please check the form for more details on the cities where the exams will be held, the conditions you agree to when you fill the form etc.

CRITERIA TO GET A CERTIFICATE

Average assignment score = 25% of average of best 8 assignments out of the total 12 assignments given in the course.
Exam score = 75% of the proctored certification exam score out of 100

Final score = Average assignment score + Exam score

Please note that assignments encompass all types (including quizzes, programming tasks, and essay submissions) available in the specific week.

YOU WILL BE ELIGIBLE FOR A CERTIFICATE ONLY IF AVERAGE ASSIGNMENT SCORE >=10/25 AND EXAM SCORE >= 30/75. If one of the 2 criteria is not met, you will not get the certificate even if the Final score >= 40/100.

Certificate will have your name, photograph and the score in the final exam with the breakup.It will have the logos of NPTEL and IIT Kharagpur .It will be e-verifiable at nptel.ac.in/noc.

Only the e-certificate will be made available. Hard copies will not be dispatched.

Once again, thanks for your interest in our online courses and certification. Happy learning.

- NPTEL team


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