Swayam Central

# 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: 2794

### SUMMARY

 Course Status : Completed Course Type : Core Duration : 12 weeks Start Date : 29 Jul 2019 End Date : 18 Oct 2019 Exam Date : 16 Nov 2019 Category : Mechanical Engineering Level : Undergraduate

### COURSE LAYOUT

Week 1: Mathematical preliminaries and notation; Kinematics of deformation: rigid vs deforming solids; Lagrangian and Eulerian descriptions; Concept of Traction vector
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 at a point; Mohr’s circle
Week 4: Stress invariants; Octahedral Plane; Decomposition of stress tensor; Concept of strain and strain tensor; ongitudinal, shear and volumetric strains
Week 5: State of strain in simple cases; Strain compatibility condition; Local infinitesimal rotation; Linear stress-strain relation:isotropic and orthotropic cases; Relation between material constants
Week 6: Stress and strain matrices in cylindrical coordinate system; Equations of equilibrium in cylindrical coordinate system, Axisymmetric deformations: combined extension-torsion of a cylinder
Week 7: Belt friction, Review of particle dynamics, Circular motion
Week 8: Bending of beams having non-symmetrical cross-section; Shear center, Shear flow in thin and open cross-section beams
Week 9: Deflection of a beam: Euler Bernouli and Timoshenko beam models; Buckling of beams
Week 10: Reciprocal relations, Castigliano’s theorem, Deflection of straight and curved beams using energy method
Week 11: Various theories of failure and their application
Week 12: Brief introduction to plasticity, Yield surface

### BOOKS AND REFERENCES

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

### INSTRUCTOR BIO

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: 16 November 2019, 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 are being discontinued from July 2019 semester and will not be dispatched