# Solid Mechanics

By Prof. Ajeet Kumar   |   IIT Delhi
This is the first course where deformation of solid bodies and the underlying concepts are introduced to undergraduate students. The course begins by building foundation of the concepts of stress and strain in three-dimensional deformable bodies. It further uses these concepts to study extension, torsion and bending of beams. The one-dimensional theory of beams are also introduced. We also discuss various theories of failure which are critical for design of machine elements in industry.

INTENDED AUDIENCE: Any Interested Learners
PREREQUISITES:         1st year Engineering Mechanics

Learners enrolled: 2464

### SUMMARY

 Course Status : Ongoing Course Type : Core Duration : 12 weeks Start Date : 14 Sep 2020 End Date : 04 Dec 2020 Exam Date : 19 Dec 2020 Enrollment Ends : 25 Sep 2020 Category : Mechanical Engineering Advanced Mechanics Level : Undergraduate

### COURSE LAYOUT

Week 1: Mathematical preliminaries and notation; Concept of Traction vector; Concept of Stress tensor
Week 2: Stress tensor and its representation in Cartesian coordinate system; Transformation of stress matrix; Equations of equilibrium; Symmetry of stress tensor
Week 3: State of stress in simple cases; Principal stress components and principal planes; Maximizing shear component of traction; Mohr’s circle
Week 4: Stress invariants; Octahedral Plane; Decomposition of stress tensor; Concept of strain and strain tensor
Week 5: Longitudinal, shear and volumetric strains; Local infinitesimal rotation; Strain compatibility condition
Week 6: Linear stress-strain relation for isotropic bodies; Relation between material constants
Week 7: Stress and strain matrices in cylindrical coordinate system; Equations of equilibrium in cylindrical coordinate system
Week 8: Axisymmetric deformations: combined extension-torsion-inflation of a cylinder
Week 9: Bending of beams having symmetrical and non-symmetrical cross-section
Week 10: Shear center, Shear flow in thin and open cross-section beams; Euler Bernouli and Timoshenko beam theories; beam buckling
Week 11: Energy methods, Reciprocal relations, Castigliano’s theorem, Deflection of straight and curved beams using energy method
Week 12: Various theories of failure and their application

### BOOKS AND REFERENCES

Advanced Mechanics of Solids (LS Srinath) Stength of Materials, Parts I & II (S. Timoshenko)

### Prof. Ajeet Kumar

IIT Delhi
Prof. Ajeet Kumar is currently working as an Associate Professor in the Department of Applied Mechanics at IIT Delhi. He received his PhD from the Department of Theoretical & Applied Mechanics at Cornell University. He primarily works in the field of solid mechanics. His key topics of research are: Theory of continuum and nano rods, Finite deformation elastoplasticity, Computational Mechanics, Molecular modeling, Fluid-structure interaction, etc. To known more about him, please visit his webpage: http://web.iitd.ac.in/~ajeetk/

### 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: 19 December 2020 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

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 Madras .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