ME 223: Solid Mechanics and Strength of Materials (S1/M)
R. Ganesh
August 2, 2023
R. Ganesh
Lecture 1
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About Me
At IIT Bombay since March 2021
R. Ganesh
Lecture 1
2 / 13
About Me
At IIT Bombay since March 2021
Academic Background
Doctor of Philosophy, University of Minnesota, Minneapolis, USA.
Modeling of wave propagation in nonlinear mechanical metamaterials.
Master of Technology in Computational Science, Indian Institute of Science (IISc),
Bangalore.
Numerical modeling of free vibrations of rotating beams.
Bachelor of Engineering in Mechanical Engineering, Sathyabama University, Chennai.
Professional Experience
R&D Mechanical Engineer, Halliburton Energy Services.
Modeling of self-excited vibrations in drilling systems
Project Associate, Computational NanoEngineering Lab, Indian Institute of Science.
Finite element modeling of microsystems
R. Ganesh
Lecture 1
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Introduction
Question
A ball is dropped onto a horizontal surface from a height h. The coefficient of restitution is e.
What is the total distance travelled by the ball before it comes to a complete rest on the surface?
R. Ganesh
Lecture 1
3 / 13
Introduction
Question
A ball is dropped onto a horizontal surface from a height h. The coefficient of restitution is e.
What is the total distance travelled by the ball before it comes to a complete rest on the surface?
Underlying assumptions
R. Ganesh
Lecture 1
3 / 13
Introduction
Question
A ball is dropped onto a horizontal surface from a height h. The coefficient of restitution is e.
What is the total distance travelled by the ball before it comes to a complete rest on the surface?
Underlying assumptions
Ball is represented as a particle (point mass).
Coefficient of restitution represents a measure of energy lost as heat and sound upon collision.
No Air Drag
R. Ganesh
Lecture 1
3 / 13
Introduction
Question
A ball is dropped onto a horizontal surface from a height h. The coefficient of restitution is e.
What is the total distance travelled by the ball before it comes to a complete rest on the surface?
Underlying assumptions
Ball is represented as a particle (point mass).
Coefficient of restitution represents a measure of energy lost as heat and sound upon collision.
No Air Drag
Are these assumptions really true? [Link]
R. Ganesh
Lecture 1
3 / 13
Introduction
Question
A ball is dropped onto a horizontal surface from a height h. The coefficient of restitution is e.
What is the total distance travelled by the ball before it comes to a complete rest on the surface?
Underlying assumptions
Ball is represented as a particle (point mass).
Coefficient of restitution represents a measure of energy lost as heat and sound upon collision.
No Air Drag
Are these assumptions really true? [Link]
Are these assumptions acceptable?
R. Ganesh
Lecture 1
3 / 13
Introduction
Question
A ball is dropped onto a horizontal surface from a height h. The coefficient of restitution is e.
What is the total distance travelled by the ball before it comes to a complete rest on the surface?
Underlying assumptions
Ball is represented as a particle (point mass).
Coefficient of restitution represents a measure of energy lost as heat and sound upon collision.
No Air Drag
Are these assumptions really true? [Link]
Are these assumptions acceptable?
Basketball official requirement [Rules]
“Be inflated to an air pressure such that, when it is dropped onto the floor
from a height of approximately 1, 800 mm measured from the underside of the
ball, it shall rebound to a height of between 1, 035 and 1, 085 mm, measured
to the underside of the ball”
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Lecture 1
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Introduction
Other examples of Collision
Packing Material: Link
Crash test for vehicles: Link 1; Link 2
R. Ganesh
Lecture 1
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Introduction
Other examples of Collision
Packing Material: Link
Crash test for vehicles: Link 1; Link 2
Objective
Understand behavior and develop rational rules for design
R. Ganesh
Lecture 1
4 / 13
Introduction
Other examples of Collision
Packing Material: Link
Crash test for vehicles: Link 1; Link 2
Objective
Understand behavior and develop rational rules for design
Solid Mechanics and Strength of Materials
Study the science/mechanics of “motion” of deformable bodies subjected to external loads.
R. Ganesh
Lecture 1
4 / 13
Introduction
Other examples of Collision
Packing Material: Link
Crash test for vehicles: Link 1; Link 2
Objective
Understand behavior and develop rational rules for design
Solid Mechanics and Strength of Materials
Study the science/mechanics of “motion” of deformable bodies subjected to external loads.
Motion: Rigid Body motion (position/velocity/acceleration) + Deformation (relative
motion between particles in the body)
Neglect rigid body motion by considering systems with constraints.
Deformation is implicitly tied to material behavior.
Other names: Mechanics of Deformable Bodies, Mechanics of Solids, Mechanics of Materials
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Lecture 1
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Modeling
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Modeling
R. Ganesh
Lecture 1
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Modeling
R. Ganesh
Lecture 1
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Modeling
Modeling Approximation
Phenomena well described by Newtonian Mechanics
Study of forces: body load, surface load, point loads, moment/couple
Study of deformation: small/large displacement/rotations
Constitutive law: Relationship between force and deformation:
Elastic/Viscoelastic/Plastic/...
R. Ganesh
Lecture 1
5 / 13
Modeling
Modeling Approximation
Phenomena well described by Newtonian Mechanics
Study of forces: body load, surface load, point loads, moment/couple
Study of deformation: small/large displacement/rotations
Constitutive law: Relationship between force and deformation:
Elastic/Viscoelastic/Plastic/...
“All Models are wrong, but some are useful” - George E. P. Box (Journal of American
Statistical Association, 1976)
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Lecture 1
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ME 223: Course details
Contents
Axially loaded 1D bars
Concept of stress, equilibrium equations, stress transformations, Mohr’s circle
Concept of strain, strain-displacement relationship
Constitutive equations, thermal stress/strain
Plane stress, Plane strain and Boundary Value Problems
Bending of beams
Torsion of shafts
Buckling
Theories of failure/Energy methods [Time permitting ...]
References
An Introduction to Mechanics of Solids: Stehen H. Crandall, Norman C. Dahl, Thomas J.
Lardner, M S Sivakumar
Engineering Mechanics of Solids: Egor P. Popov
Mechanics of Materials, Enhanced Edition: Barry J. Goodno, James N. Gere
Many other books: Check references on ASC
R. Ganesh
Lecture 1
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ME 223: Course details
Course Evaluation
Final Exam (40%)
Mid-semester Exam (25%)
Announced Quizzes (2) (20%)
Pop-up Quiz & Tutorials (15%) (Exact split to be decided during the semester)
Please adhere to the academic honor code [Link]
R. Ganesh
Lecture 1
7 / 13
ME 223: Course details
Course Evaluation
Final Exam (40%)
Mid-semester Exam (25%)
Announced Quizzes (2) (20%)
Pop-up Quiz & Tutorials (15%) (Exact split to be decided during the semester)
Please adhere to the academic honor code [Link]
Tutorials
Subset of tutorials will be assigned points (binary points; not graded).
Problem sheet to be solved in class, with the help of instructor and TAs.
Additional problems may be provided as homework (not graded).
Office Hours
R. Ganesh (Instructor): Every Wednesday, 1730-1830, (S25, Mechanical Engineering Dept.)
Arunav Choudhury, Mritunjay Hiremath, Sorab Khan: To be decided
Communication through Moodle (anonymous feedback). Contact via MS Teams/e-mail.
R. Ganesh
Lecture 1
7 / 13
ME 223: Course details
Course Evaluation
Final Exam (40%)
Mid-semester Exam (25%)
Announced Quizzes (2) (20%)
Pop-up Quiz & Tutorials (15%) (Exact split to be decided during the semester)
Please adhere to the academic honor code [Link]
Tutorials
Subset of tutorials will be assigned points (binary points; not graded).
Problem sheet to be solved in class, with the help of instructor and TAs.
Additional problems may be provided as homework (not graded).
Office Hours
R. Ganesh (Instructor): Every Wednesday, 1730-1830, (S25, Mechanical Engineering Dept.)
Arunav Choudhury, Mritunjay Hiremath, Sorab Khan: To be decided
Communication through Moodle (anonymous feedback). Contact via MS Teams/e-mail.
No DX grade in course
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Lecture 1
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Kirigami Metamaterials
Animation
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1D Analysis
[Isobe and Okumura, Scientific Reports, 2016]
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2D Analysis
[Yang et. al, Phys. Rev. Materials, 2018]
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Possible Extensions
[Celli et. al, Soft Matter, 2018]
[Widstrand et. al, EML, 2022]
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Drilling Vibrations
Vibrations
Axial Vibrations - Bit Bounce
Lateral Vibrations - Whirl
Torsional Vibrations - Stick-slip
Stick-Slip Oscillation [Animation]
[Julien Marck, 2015]
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Drilling system with only Torsional degree of freedom
Experimental Data
R. Ganesh
Numerical Data
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