Venue: Feynman Lecture Hall
Class Timings: Tuesdays & Thursdays from 11:30 AM - 1:00 PM
First Meeting: 8 August 2024
Course Syllabus:
Elasticity
- Continuum mechanics: Deformation gradient, polar decompositions, measures of strain, strain tensor
- Special cases: Small and large strain, large rotations, large displacements
- Constitutive laws: Stress-strain relations, Young’s modulus, Poisson ratio
- 1D problems: Bending of beams, energetics, Euler elastica, buckling, rod theory, contact forces
- Elastodynamics: Wave propagation, half-plane problems, solution strategies
- Energetics: Variational principles, energy functional, hyperelastic materials
- Overview: Continuum formulation, limitations, mathematical preliminaries
- Kinematics: Lagrangian and Eulerian perspectives, streamlines, streaklines, pathlines, stream function, vorticity, velocity gradients etc.
- Transport theorem: Stress tensor, symmetries, equilibrium, Reynolds transport theorem, conservation laws, Navier’s equation
- Navier-Stokes: Constitutive laws, NS equations, Scaling, Reynolds number
- Special cases: Unidirectional flows, Stokes 1st and 2nd problem, Lubrication
- Euler equations: Ideal flow, Boundary conditions, Bernoulli's equation, Potential flow, solution strategies, Ideas of boundary layers
- Stokes equations: Reduction, Properties, Flow past a sphere, Flow past a cylinder, Stokes paradox
- Hydrodynamic stability: Overview of stability analysis, Kelvin-Helmholtz, Rayleigh-Taylor instabilities.
Textbooks:
1. Landau and Lifshitz, Theory of elasticity (3rd edition)2. William S. Slaughter, The Linearized Theory of Elasticity (Springer)
3. Audoly and Pomeau, Elasticity and Geometry (Oxford)
4. D. J. Acheson, Elementary Fluid Dynamics (Oxford)
5. Kundu, Cohen, and Rowling, Fluid Mechanics (Academic Press)
6. S. Childress, An Introduction to Theoretical Fluid Mechanics (Courant)
7. Batchelor, An Introduction to Fluid Dynamics, (Cambridge)
Course Evaluation: Problem sets (40%), Class participation and notes (20%), Final Exam (40%)
Course Outcome:1. Students will learn about the theoretical formalism of elasticity theory and fluid dynamics.
2. They will also learn about practical applications of the theory to real life phenomena and to experiments.
3. Develop problem solving skills using different techniques, both analytic and numerical
- Teacher: Brato Chakrabarti
Credit Score: 4