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ME 501 Advanced Engineering Mathematics (4 0 0 8) Vector and Tensor Analysis (Cartesian and Curvilinear): Orthogonal coordinate systems, Transformation of coordinate systems. Review of ODEs; Laplace & Fourier methods, series solutions, and orthogonal polynomials. SturmLiouville problem, Review of 1^{st} and 2^{nd} order PDEs. Similarity transformations for converting PDEs to ODEs. Linear systems of algebraic equations, Gauss elimination, LU decomposition etc., GramSchmidt orthogonalization. Matrix inversion, illconditioned systems. Numerical eigen solution techniques (Power, Jacobi, Given, Householder, and QR methods). Numerical solution of systems of nonlinear algebraic equations; NewtonRaphson method. Numerical integration: NewtonCotes methods, error estimates, Gaussian quadrature, Numerical integration of ODEs: Euler, Adams, RungeKutta methods, and predictorcorrector procedures; stability of solutions; solution of stiff equations. Solution of PDEs: finite difference techniques. Functions of Complex Variable: analytic functions and mapping. Probability and Statistics – Probability Distribution, Bays Theorem, Random numbers, Parameter Estimation, Testing of Hypothesis, Goodness of Fit. Texts/References:
ME 530 Advanced Mechanics of Solids (3 0 0 6)Analysis of Stresses and Strains in rectangular and polar coordinates: Cauchy’s formula, Principal stresses and principal strains, 3D Mohr’s Circle, Octahedral Stresses, Hydrostatic and deviatoric stress, Differential equations of equilibrium, Plane stress and plane strain, compatibility conditions. Introduction to curvilinear coordinates. Generalized Hooke’s law and theories of failure. Energy Methods. Bending of symmetric and unsymmetric straight beams, effect of shear stresses, Curved beams, Shear center and shear flow, shear stresses in thin walled sections, thick curved bars. Torsion of prismatic solid sections, thin walled sections, circular, rectangular and elliptical bars, membrane analogy. Thick and thin walled cylinders, Composite tubes, Rotating disks and cylinders. Euler’s buckling load, Beam Column equations. Strain measurement techniques using strain gages, characteristics, instrumentations, principles of photoelasticity. Text:
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ME 531 Mechanical Vibration (3 0 0 6) Generalised coordinates, constraints, virtual work; Hamilton's principle, Lagrange's equations; Discrete and continuous system; Vibration absorbers; Response of discrete systems  SDOF & MDOF: freevibration, periodic excitation and Fourier series, impulse and step response, convolution integral; Modal analysis: undamped and damped nongyroscopic, undamped gyroscopic, and general dynamical systems. Effect of damping; Continuous systems: vibration of strings, beams, bars, membranes and plates, free and forced vibrations; RaleighRitz and Galerkin's methods. Measurement techniques. Texts:
ME 532 Finite Element Methods in Engineering (3 0 0 6) Introduction: Historical background, basic concept of the finite element method, comparison with finite difference method; Variational methods: calculus of variation, the RayleighRitz and Galerkin methods; Finite element analysis of 1D problems: formulation by different approaches (direct, potential energy and Galerkin); Derivation of elemental equations and their assembly, solution and its postprocessing. Applications in heat transfer, fluid mechanics and solid mechanics. Bending of beams, analysis of truss and frame. Finite element analysis of 2D problems: finite element modelling of single variable problems, triangular and rectangular elements; Applications in heat transfer, fluid mechanics and solid mechanics; Numerical considerations: numerical integration, error analysis, mesh refinement. Plane stress and plane strain problems; Bending of plates; Eigen value and time dependent problems; Discussion about preprocessors, postprocessors and finite element packages. Texts: 1. J N Reddy, An introduction to the Finite Element Method, McGrawHill, New York, 1993. 2. R D Cook, D S Malkus and M E Plesha, Concepts and Applications of Finite Element Analysis, 3d ed., John Wiley, New York, 1989. 3. K J Bathe, Finite Element Procedures in Engineering Analysis, PrenticeHall, Englewood Cliffs, NJ, 1982. 4. T J T Hughes, The Finite Element Method, PrenticeHall, Englewood Cliffs, NJ, 1986. 5. O C Zienkiewicz and R L Taylor, The Finite Element Method, 3d ed. McGrawHill, 1989. SEMESTERII ME 533 Engineering Design Methodology (2 0 2 6) Fundamentals: principles of design, systematic approach, need analysis and design of specification; Conceptual design: developing function structure, developing concepts by systematic search with physical principles, classifying schemes; Concept selection: matrix methods, necessity methods, probability methods, fuzzy set based methods, case study on consumer product; Embodiment design: basic rules, system modeling, preliminary design calculations and material selection, design considerations like force alignment, vibration etc., failure modes and effects analysis, design for manufacturability and assembly, case studies on design of machines; Optimal and robust design: design problem formulation for analytical and numerical solution, design of experiments, Taguchi’s method; Reverse engineering; Physical prototyping; Lab: conceptual design, reverse engineering, design of simple sensors and actuators, hydraulic and pneumatic systems, motors and controller, product teardown and redesign, embodiment design, CAE analysis, prototyping, design project. 