IST - Principles of Continuum Mechanics (2024)

Speakers and Syllabus

Detailed Syllabus:

 Name of the Speaker Number of Lectures Syllabus Prof. S. K. Tomar 6 Elasticity and Wave Propagation Basic concepts of theory of elasticity: stress, strain and their properties, Hooke’s law and its generalization, symmetry of stress tensor, equation of equilibrium and motion, compatibility conditions, Finite deformation; Waves in uniform elastic medium, Helmholtz decomposition of vector, body waves,boundary conditions, reflections/ refraction phenomena; Surface waves - Rayleigh, Love and stoneley. Prof. Peeyush Chandra 6 Fundamental PrinciplesEulerian and Lagrangian coordinate systems, stress-strain tensors and their properties, Polar Decomposition theorem, governing differential equations of continuum mechanics, conservation laws for the mass, linear momentum, angular momentum, energy, first and second laws of thermodynamics for a continuum, equations of state, boundary conditions, fundamental restrictions on constitutive laws. Prof. Gopal Chandra Shit 6 Computational Fluid Dynamics (CFD)  Need of CFD as tool, role in R&D, CFD Applications.  Concept of Finite Difference, Finite difference discretization, Convergence, Consistency, and Stability, Boundary conditions, CFD model formulation, Tridiagonal linear system of equations solver (TDMA/ Thomas Algorithm). Two time-level explicit scheme (Schmidt formula), Crank- Nicolson Implicit scheme and their von-Neumann stability analysis. Solution of one-dimensional wave equation using the Lax scheme, Lax-Wendroff Scheme and their von-Neumann stability analysis, CFL number.Second order wave equation using explicit method and its von- Neumann stability. Five point formula, Point-Gauss-Seidel and Line Gauss-Seidel method, Point and line Successive over/under relaxation method for Laplace and Poisson equations. Vorticity – Stream function formulation.MATALB program for Direct Numerical Solution of lid-driven cavity problem, Flow over a Backward-facing step problem. Graphical representation and validation of computational results. Basic concepts of the finite element methods for the solution of fluid dynamics problems. Dr S. C.Martha 6 Problems of Water Wave MechanicsSturm-Liouville problem, Boundary value problem for two- dimensional periodic water wave, eigenfunction solutions of linearized water wave boundary value problem, approximate solution of dispersion equation by Newton-Raphson method with MATLAB program.Least square method and its applications to water wave problems, energy balance equation using Green’s identity. Boundary element method (BEM), numerical implementation through MATLAB code, BEM applications to water wave problems.Fredholm integral equations of second kind and its numerical solution and MATLAB applications, integral equation method for solving a problem on wave mechanics. Dr Jitender Singh 6 Some Hydrodynamical ProblemsHydrodynamics of Rayleigh-Benard convection and Couette- Taylor problem, the mathematics of Boundary layer flows such as the stretching sheet problem.Numerical methods for hydrodynamic and the flow problems: Shooting method, the method of matrix exponentials, homotopy perturbation technique Dr Santanu Manna 6 Some Non-Elasticity ProblemsMohr’s circle diagram: principal stress & strain, Equations of deformation and equilibrium, combability etc.Concept of nonlocal elasticity: dynamic equation of motion, waves of dilatation and distortion, body wave & surface wave, concept of damping and meta-surface. Asymptotic analysis for elasticity problem, explicit models for surface waves, Bleustein-Gulyaev surface waves, comparison of asymptotic approach and analytical approach, hyperbolic- elliptic model of surface wave field.

Speakers:

1. Prof. S. K. Tomar, Professor, Department of Mathematics, Panjab University, Chandigarh (Presently: Vice Chancellor, J. C. Bose University of Science and Technology, YMCA, Faridabad, Haryana).
2. Prof. Peeyush Chandra (Rtd), Department of Mathematics, IIT Kanpur.
3. Prof. Gopal Chandra Shit, Professor, Department of Mathematics, Jadavpur University, Kolkata.
4. Dr. S. C. Martha, Associate Professor, Department of Mathematics, IIT Ropar.
5. Dr. Jitender Singh, Associate Professor, Department of Mathematics, Guru Nanak Dev University, Amritsar.
6. Dr. Santanu Manna, Associate Professor, Department of Mathematics, IIT Indore

Tutors:

1. Dr. Dilbag Singh, Assistant Professor, Department of Mathematics, Panjab University, Chandigarh.
2. Dr. Jai Bhagwan, Assistant Professor, Department of Mathematics, Government College, Panipat, Haryana.
3. Dr. Manjeet Kumar, Assistant Professor, Department of Mathematics, Dr B R Ambedkar Government College, Dabwali, Haryana.
4. Dr. Suraj Kumar, Assistant Professor, Department of Mathematics, Punjab Engineering College (Deemed to be University), Chandigarh.

Time Table

 Day Date (June 2024) L-1 (9:00-10:30) 10:30-11:00 L-2 (11:00-12:30) 12:30-2:00 L-3 (2:00-3:30) 3:30-4:00 Discussion/ Tutorial (4:00-5:00) Mon 3rd SKT Tea/ Snacks PC Lunch PC Tea/ Snacks SKT,DS, SK Tue 4th SKT PC PC PC, DS, SK Wed 5th SKT PC PC PC, DS, SK Thu 6th SKT SCM SCM SKT,DS, SK Fri 7th SKT SCM SCM SCM,DS, SK Sat 8th SKT SCM SCM SCM,DS,SK Mon 10th JS GCS GCS JS, JB, MK Tue 11th JS GCS GCS GCS,JB, MK Wed 12th JS GCS GCS GCS,JB, MK Thu 13th JS SM SM JS, JB, MK Fri 14th JS SM SM SM, JB, MK Sat 15th JS SM SM JS, JB, MK

*Holiday on Sunday (June 09, 2024)

• SKT-Prof. S. K. Tomar
• PC-Prof. Peeyush Chandra
• GCS-Prof. Gopal Chandra Shit
• SCM-Dr S. C. Martha
• JS-Dr Jitender Singh
• SM-Dr Santanu Manna
• DS- Dr Dilbag Singh
• SK- Dr Suraj Kumar
• JB- Dr Jai Bhagwan
• MK- Dr Manjeet Kumar

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