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[ME501] : Mathematics for Engineers
Course Instructor: Dr. Satwinder Jit Singh
Course content: Properties of Vector Algebra, Vector space, subspace, basis, null and range space, invertibility and matrix representation; Cartesian Tensor notation and vector analysis; Matrices and Matrix algebra, Echelon form, orthogonalization; Eigen values and eigenvectors of a linear operator; Calculus of scalar, vector and tensor fields; Linear ODEs: Second and higher order Linear Differential equations; System of differential equations, Methods of Taylor and Frobenius, Laplace and Fourier transforms, Fourier series; Legendre and Bessel functions; Sturm Louville Problem; classification of PDEs; Analytical solution of linear PDEs.
Text Books:
Reference Books:
[ME502] : Applied Numerical Methods
Course Instructor: Dr. Himanshu Tyagi
(L-T-P-S-C structure; 3-0-0-6-3)
Course Content: Introduction and motivation, Types of solutions, algorithms and programming languages, error analysis, types of errors, Roots of equations, bracketing methods, graphical method, bisection method, false-position method, open methods, Newton-Raphson method, Secant method, convergence & divergence, Interpolation and polynomial approximation, Finite difference approximations, Newton’s forward and backward differences, Lagrange’s interpolation, divided differences, Cubic spline method, Numerical integration and differentiation, Differentiation using finite difference operators, Richardson’s method, differentiation using interpolation, trapezoidal rule, Simpson’s rule, Solutions of systems of linear algebraic equations, Matrix inversion and Eigen value problems, Gaussian elimination method, Gauss-Jordan elimination method, Solutions of ordinary and partial differential equations, Taylor series method, Euler method, Runge-Kutta method, finite difference methods, explicit, implicit, Crank-Nicholson method, alternate direction implicit method, finite volume method.
Text Books:
Steven C. Chapra, and Raymond P. Canale, Numerical Methods for Engineers, 8th ed., McGraw Hill Education India Pvt Ltd, India, 2021.
M.K. Jain, S.R.K. Iyenger, R.K. Jain, Numerical Methods for Scientific and Engineering Computation, 7th Ed., New Age International, New Delhi, 2019.
[ME503] : Measurements and Instrumentation
[ME506] : Non Linear FEM
Course Instructor: Dr. Sachin Kumar
(L-T-P-S-C structure; 3-0-0-6-3)
Course Content: Introduction to nonlinearities i.e. material, geometrical and contact nonlinearity, Yield criterion, Flow rule, Hardening models, Prager’s consistency condition, Tangent modulus, Elastic-plastic constitutive relations, Stress update algorithms, Virtual work principle, Finite element formulation for 1-D plasticity; Return mapping algorithm, Newton-Raphson procedure, Fundamentals of finite deformation mechanics-kinemtaics, Stress and strain measures; Balance laws, Objectivity principle, Lagrangian formulation (updated and total Lagrangian formulation), Finite element formulation of nonlinear elasticity, Finite element modelling of contact problems, Finite element programing and debugging through some practical examples
Text Books:
J.N. Reddy, An Introduction to Nonlinear Finite Element Analysis, Oxford University Press
O.C. Zienkiewicz and R.L. Taylor, The Finite Element Method, McGraw Hill
G.A. Holzapfel, Nonlinear Solid Mechanics, John Wiley & Sons Inc., 2000.
Reference Books:
P. Wriggers, Nonlinear Finite Element Methods, Springer, 2008
K.J. Bathe, Finite Element Procedures, Prentice Hall of India, New Delhi
[ME507] : Fundamentals and Modeling of Turbulent Flows
[ME508] : Wave Propagation
[ME517] : Advanced Solid Mechanics
[ME518] : Multibody Dynamics
Course Instructor: Dr. Manish Agrawal
Course Content:
Introduction: Rigid-body mechanics, Multibody systems, Reference frames and frame transformations, Derivatives of vector functions, Eigen-value analysis, Classification of multibody mechanical systems – Serial and Closed-loops.
Reference Kinematics: Rotation matrix, Successive rotations, Moving coordinate frames, Properties of Rotation Matrix, Velocity and Accelerations and important identities, Rodrigues parameters, Euler angles, Direction Cosines, Homogeneous Transformations, Orientation Coordinates.
Lagrangian Dynamics: Mass/Inertia distribution, Generalized coordinates and kinematic constraints, Degrees-of-freedom, Virtual work and Generalized forces and energy functions, Lagrangian dynamics, Application to rigid body dynamics.
Analytical Techniques: Calculus of Variations, Euler’s equation for several variables, Formulation of equations of motion. Application to two and three degrees-of-freedom mechanisms, Newton-Euler Equations, Applications to multibody linearization and integrals of equations of motion, Extraction of information from equations of motion
Mechanics of deformable bodies: Kinematics of deformable bodies, Stress components and strain components, Equation of equilibrium, Constitutive equations and Elastic forces.
Numerical lab: Numerical Algorithms for Inverse and Forward dynamics, Computational issues, Efficiency and numerical stability aspects of algorithms, multibody dynamics simulations in software platform like Simscape(MATLAB).
Reference Books:
Dynamics of multibody systems By Ahmed A Shabana.
Planar Multibody Dynamics by Parviz E. Nikravesh
Chaudhary, H., and Saha, S.K., Dynamics and Balancing of Multibody Systems
Angeles J., Kecskemethy A., Kinematics and Dynamics of Multibody Systems
Amirouche F. Fundamentals of multibody dynamics: theory and applications.
Kane TR, Levinson DA. Dynamics, theory and applications. McGraw Hill
Introduction to Mechanics by Andy Ruina and Rudra Pratap
Flexible Multibody dynamics by O.A. Bauchau
[ME521] : Fundamentals of Fatigue
[ME547] : Analysis of Material Removal Processes
Course Instructor: Dr. Chandrakant K Nirala
(L-T-P-S-C structure; 3-0-0-6-3)
Course Content: Overview of manufacturing and machining processes, Scientific classification and field of study, Processes such as EDM, ECM, ECDM, LBM, EBM, USM etc. Science of materials removal and analytical modelling for these processes, Realization of these processes in micro-scale, Typical conditions in machining; Orthogonal cutting; Oblique cutting, Chip formation in conventional and hybrid processes, Typical conditions in grinding; Basic modelling for material removal, Evaluation of individually executed projects selected based on student.
Text Books:
Groover, M. P., Fundamentals of modern manufacturing, Latest edition
Lal, G. K., Introduction to Machining Science, New Age International, Latest Edition.
Reference Books:
Gupta, K. and Pramanik, A., Series: Handbook in advanced manufacturing. Advanced machining and finishing 2021.
Jain, V. K., Advanced Machining Processes, Allied Publishers Ltd.
*Few reference materials and NPTEL notes/lectures will be suggested as reference materials
[ME548] : Analysis of Casting, Forming and Joining Processes
[ME549] : Additive Manufacturing
Course Instructor: Dr. Prabir Sarkar
(L-T-P-S-C structure; 3-0-0-6-3)
Course Content: General overview of AM, what is AM, Benefits and applications of AM, Traditional manufacturing v/s AM, Computer aided design (CAD), Reverse engineering and AM; Introduction to Industry 4.0, Introduction to product design and manufacturing, History of RP, Generic AM process; Details of various steps in AM; Different AM processes (The seven major additive manufacturing processes as classified per ASTM F42 are: Photo-Polymerization, Material jetting, Binder jetting, Material extrusion, Powder Bed Fusion, Sheet Lamination, Direct Energy Deposition)
Various direct write (DW) technologies, such as Ink-based, Laser transfer, Thermal spray, Liquid phase direct deposition and hybrid technologies Materials, Material usage, materials for AM, Design for AM (DFAM) concepts; AM capabilities; Design freedoms; Design tools; AM process, selection methods; Challenges of AM-process selection; AM production planning and control; Preparation of CAD models, STL files; Common problems with STL files; STL file manipulation, Sustainable design and sustainable manufacturing, Project presentations and submission.
Text Books:
Gibson, D. W. Rosen, B. Stucker, Additive Manufacturing Technologies: Rapid Prototyping to Direct Digital Manufacturing, Springer, 2010*
Gebhardt, Understanding Additive Manufacturing: Rapid Prototyping, Rapid Tooling, Rapid Manufacturing, Hanser Publishers, 2011.
Reference Books:
C.K. Chua, K.F. Leong, 3D Printing and Additive Manufacturing, World Scientific, 5th Edition, 2017.
J.D. Majumdar, I. Manna, Laser-assisted Fabrication of Materials, Springer Series in Material Science, eISBN: 9783642283598.
L. Lu, J. Fuh, Y. S. Wong, Laser-induced Materials and Processes for Rapid Prototyping, Kluwer Academic Press, 2001.
Z. Fan, F. Liou, Numerical Modeling of the Additive Manufacturing (AM) Processes of Titanium Alloy, InTech, 2012.
[ME571] : Advanced Fluid Mechanics
[ME579] : Advanced Thermodynamics
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