MTech in Mechanical Engineering

(Specialization: Computational Mechanics)

SEMESTER-I

Course No.	Course Name	L-P-T-C
ME 501	Advanced Engineering Mathematics	3-0-2-8
ME 541	Continuum Mechanics	3-0-0-6
ME 542	Numerical Analysis	2-0-2-6
ME 543	Computational Fluid Dynamics	3-0-0-6
ME XXX	Elective -I	3-0-0-6
	Total	14-0-4-32

SEMESTER-II

Course No.	Course Name	L-P-T-C
ME 532	Finite Element Methods in Engineering	3-0-0-6
ME XXX	Elective –II	3-0-0-6
ME XXX	Elective –III	3-0-0-6
ME XXX	Elective –IV	3-0-0-6
ME XXX	Elective –V	3-0-0-6
ME 544	Computational Mechanics Lab	0-0-2-2
	Total	15-0-0-32

SEMESTERS-III

Course No.	Course Name	L-P-T-C
ME 610	Project Phase-I	0-0-24-24

SEMESTERS-IV

Course No.	Course Name	L-P-T-C
ME 690	Project Phase-II	0-0-24-24

ME 541 Continuum Mechanics (3-0-0-6)

Introduction to continuum mechanics: Cartesian tensors, state of stress, kinematics of deformation and general principles of mechanics; Analysis of stresses and strains; Cauchy’s formula; Principal stresses and principal strains; Mohr’s Circle; Octahedral Stresses; Hydrostatic and deviatoric stress; Differential equations of equilibrium; Plane stress and plane strain; Compatibility conditions; Generalized Hooke’s law and theories of failure; Energy Methods; Bending and torsion of thin walled sections; Euler’s buckling load; Beam Column equations. Introduction to fluid kinematics; Integral and differential forms of governing equations; Conservation equations; Navier-Stokes equations and applications; Potential flow; Laminar boundary-layer; Introduction to Free-shear flows and instabilities; Basics of compressible flow.

Texts/ References:

1. R.L. Panton, Incompressible Flow, 2^nd Edn., Wiley, 1996.

2. F.M. White, Fluid Mechanics, 7^th Edn., McGraw-Hill international Editions, 2010.

3. H. Schlichting and K. Gersten, Boundary Layer Theory, 8th Edn., Springer, 2000.

4. J.N. Reddy, Principles of Continuum Mechanics, Cambridge University Press, 2010.

5. S.P. Timoshenko and J.N. Goodier, Theory of Elasticity, 3^rd Edn., McGraw Hill Publishing Co. 1970.

6. L.S. Srinath, Advanced Mechanics of Solids, 2^nd Edn., TMH Publishing Co. Ltd., New Delhi, 2003.

7. D. S. Chandrasekharaiah and L. Debnath, Continuum Mechanics, Academic Press, 1994.

ME 542 Numerical Analysis (2-0-2-6)

Round-off errors and computer arithmetic; Interpolation: Lagrange, Divided differences, Hermite and spline interpolation; Numerical differentiation, Numerical quadrature: Newton-Cotes, Simpson's rule, Gauss quadrature; Solutions of linear equations: Gauss elimination, Matrix factorizations; Iterative methods: Gauss-Seidel, Jacobi, Relaxation methods; Computation of eigenvalues and eigenvectors; Numerical solution of nonlinear equations; Numerical solutions to initial and boundary value problems.

Laboratory component: The lab is intended to be a platform for students to get used to scientific computing. Strong emphasis is laid on computer programming and the student is expected to write his own programs/codes for prototypical mathematical problems which will have real--life applications in the area of computational mechanics.

Texts/References:

1. S. D. Conte and C. de Boor, Elementary Numerical Analysis, 3^rd Edn., Tata McGraw-Hill Education, 2005.

2. F.B. Hildebrand, Introduction to Numerical Analysis, 2^nd (Revised) Edn., Courier Dover Publications, 1987.

3. E. Kreyszig, Advanced Engineering Mathematics, 10^th Edn., John Wiley and Sons, 2010.

4. R. Burden and J. Faires, Numerical Analysis, 8^th Edn., Brooks/Cole, 2001.

5. L.N. Trefethen and D. Bau III, Numerical Linear Algebra, SIAM, 1997.

6. A.Quarteroni, R. Sacco and F. Saleri, Numerical Mathematics, Springer-Verlag, New York, 2000.

ME 543 Computational Fluid Dynamics (3-0-0-6)

Basic equations of Fluid Dynamics: General form of a conservation law; Equation of mass conservation; Conservation law of momentum; Conservation equation of energy. The dynamic levels of approximation. Mathematical nature of PDEs and flow equations.

Basic Discretization techniques: Finite Difference Method (FDM); The Finite Volume Method (FVM) and conservative discretization. Analysis and Application of Numerical Schemes: Consistency; Stability; Convergence; Fourier or von Neumann stability analysis; Modified equation; Application of FDM to wave, Heat, Laplace and Burgers equations. Integration methods for systems of ODEs: Linear multi-step methods; Predictor-corrector schemes; ADI methods; The Runge-Kutta schemes. Numerical solution of the compressible Euler equations: Mathematical formulation of the system of Euler equations; Space-centred schemes; Upwind schemes for the Euler equations – flux vector and flux difference splitting; Shock-tube problem. Numerical solution of the incompressible Navier-Stokes equations: Stream function-vorticity formulation; Primitive variable formulation; Pressure correction techniques like SIMPLE, SIMPLER and SIMPLEC; Lid-driven cavity flow; Brief discussion of numerical methods for conduction and convection.

Texts/References:

1.R. Pletcher, J. Tannehill and D. Anderson, Computational Fluid Mechanics and Heat Transfer, 3^rd Edn., CRC Press, 2012.

2.H.K. Versteeg and W. Malalasekera, An introduction to computational fluid dynamics: The finite volume method, 3^rd Edn., Pearson Education, 2007.

3.C. Hirsch, Numerical Computation of Internal and External Flows, Vol.1 (1988) and Vol.2 (1990), John Wiley & Sons.

4.J. H. Fergiger and M. Peric, Computational Methods for Fluid Dynamics, 3^rd Edn., Springer, 2002.

5.T. J. Chung, Computational Fluid Dynamics, 2^nd Edn., Cambridge University Press, 2010.

6.C. A. J. Fletcher, Computational Techniques for Fluid Dynamics Vols. 1 and 2, 2^nd Edn., , Springer, 1991.

7.S.V. Patankar, Numerical Heat Transfer and Fluid Flow, Hemisphere, 1980.

8.J. D. Anderson (Jr.), Computational Fluid Dynamics, McGraw-Hill International Edition, 1995.

 
ME 544 Computational Mechanics Lab (0-0-2-2) 
 
 
Introduction to operating systems and high-level programming languages, Use of symbolic software packages like MATLAB, MAPLE and MATHEMATICA, Hands-on practice using finite element software packages like ANSYS and ABAQUS as well as computational fluid dynamics related software such as COMSOL,OpenFOAM and FLUENT, Code development for problems involving solid mechanics, fluid mechanics and heat transfer. 

 ME 610/690   Project Phase – I / II  (0-0-24-24)

The dissertation project is intended to be a work primarily in the area of computational mechanics involving problems of fluid flow, heat transfer and/or solid mechanics. The student is expected to make some genuine contribution into his field of research and learn to apply the fundamental principles of mechanics to a problem of engineering interest. Research in interdisciplinary areas is highly encouraged and theoretical and/or experimental work are also welcome, provided they complement the computational studies undertaken as part of the project. The project, which must be predominantly computational, is to be completed over two semesters, with equal credits being awarded in both semesters.

LIST OF ELECTIVES AND SYLLABI OF NEWLY PROPOSED ELECTIVES

The following are the list of electives for the Computational Mechanics program. All elective courses have 6 credits.

ME 531 Mechanical Vibrations

ME 522 Convective Heat and Mass Transfer

ME 601 Gas Dynamics

ME 607 Introduction to Composite Materials

ME 609 Optimisation Methods in Engineering

ME 613 Nonlinear Vibrations

ME 625 Fracture Mechanics

ME 648 Viscous Fluid Flow

ME 651 Numerical Methods for Thermal Radiation Heat Transfer

ME 656 Numerical Simulation and Modelling of Turbulent Flows

ME 668 Aerodynamics

ME 670 Advanced Computational Fluid Dynamics

ME 674 Soft Computing in Engineering

ME 682 Nonlinear Finite Element Methods

ME 683 Computational Gas Dynamics

ME 682 Nonlinear Finite Element Methods (3-0-0-6)

Fundamentals of finite deformation mechanics; Kinematics; Stress measures; Balance laws; Objectivity principle; Newton-Raphson procedure; Finite element formulation for plasticity and nonlinear elasticity; Stress update algorithms for plasticity; Finite element procedures for dynamic analysis; Explicit and implicit time integration. Finite element modelling of contact problems; Slide-line methods and penalty approach; Adaptive finite element analysis - Automatic mesh generation, Error estimation, Choice of new mesh, and Transfer of state variables.

Texts/References:

1. K.J. Bathe, Finite Element Procedures, 2nd Edn., Prentice Hall, 1996.
2. T. Belythschko, W.K. Liu and B. Moran, Nonlinear Finite Elements for Continua and Structures, Wiley, 2000.
3. P.K. Kythe and D.Wei, An Introduction to Linear and Nonlinear Finite Element Analysis: a Computational Approach, Birkhauser, 2004.
4. P. Wriggers, Nonlinear Finite Element Methods, Springer, 2008.

ME 683 Computational Gas Dynamics (3-0-0-6)

Review of PDEs and their classification; Conservation laws; Concepts of characteristics; Riemann problem for linear equations; Concept of finite volume methods; Conservation, consistency and stability; Upwind methods; Godunov scheme; High resolution schemes; TVD and limiting; Euler equations; Approximate Riemann solvers; Temporal discretisation; Boundary conditions; Convergence acceleration techniques; Unsteady flows; Introduction to unstructured grids.

Texts/References:

1. R. J. LeVeque, Numerical methods for conservation laws, 2nd Edn., Birkhauser, 1992.
2. R. J. LeVeque, Finite volume methods for hyperbolic problems, Cambridge University Press, 2002.
3. C.B. Laney, Computational Gas Dynamics, Cambridge University Press, 1998.
4. J. Blazek, Computational Fluid Dynamics: Principles and Applications, 2nd Edn., Elsevier, 2005.
5. D. Knight, Elements of Numerical Methods for Compressible Flows, Cambridge University Press, 2006.

6. C. Hirsch, Numerical Computation of Internal and External Flows: Fundamentals of Computational Fluid Dynamics, Vol.1, 2^nd Edn., Butterworth-Heinemann, 2007.