BoundAry value problems and characteristic value problems




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НазваниеBoundAry value problems and characteristic value problems
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09MD01/ 09MC01 COMPUTATIONAL METHODS

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Introduction to COMPUTATIONAL methods: Examples, solving sets of equations, Gauss elimination method, Choleski method, Iterative methods, Relaxation method, system of non-linear equations- Newton Raphson method, computer programs. (6)


NUMERICAL INTEGRATION: Newton-Cotes integration formulas, Trapezoidal rule, Simpson's rules, Gaussian quadrature, adaptive integration, cubic spline functions - Bezier curves and B-splines, computer programs. (6)


BoundAry value problems and characteristic value problems: Shooting method, solution through a set of equations, derivative boundary conditions, Rayleigh-Ritz method, characteristic value problems, solution using characteristic polynomial method, Jacobi method, power method and Inverse power method. (6)


Numerical solution of partial differential equations: Laplace's equations, representations as a difference equation, Iterative methods for Laplace's equations, Poisson equation, derivative boundary conditions, irregular and non-rectangular grids, Matrix patterns, Sparseness, ADI method, applications to heat flow problems, computer programs. (7)


Parabolic partial differential equations: Explicit method, Crank-Nicholson method, derivative boundary condition, stability and convergence criteria, Parabolic equations in two or more dimensions, applications to heat flow problems, computer programs. (6)


Hyperbolic Partial differential equations: Solving wave equation by finite differences, stability of numerical method, method of characteristics, Wave equation in two space dimensions, computer programs. (6)


Curve fitting and approximation of functions: Least square approximation, fitting of non-linear curves by least squares, regression analysis, computer programs. (5)


Note: Exposure to MATLAB / C / C++ for the solution of design problems will be given to the students and they have to submit Assignments/Term papers using Computer programs.

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REFERENCES:

1. Curtis F Gerald and Patrick O Wheatley, "Applied Numerical Analysis", Pearson Education, 2002.

2. Rajasekaran S, “Numerical Methods in Science and Engineering – A Practical Approach”, Wheeler Publishing, 1999, Second

Edition.

3. Douglas J Faires and Riched Burden, "Numerical Methods", Brooks/Cole Publishing Company, 1998, Second Edition.

4. Steven C Chapra and Raymond P Canale, “Numerical Methods for Engineers with Software and Programming Applications”,

Tata McGraw Hill Edition, 2004.

5. John H Mathews and Kurtis D Fink, “Numerical Methods using MATLAB”, Prentice Hall, 1998.

6. Ward Cheney and David Kincaid, "Numerical Mathematics and Computing", Brooks/Cole Publishing Company, 1999, Fourth

Edition.


09MD02 MECHANICAL SYSTEM DESIGN

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INTRODUCTION: The design process, morphology of design, statistical consideration in design- frequency distribution-histogram and frequency polygon – normal distribution – units of measurement of central tendency and dispersion, statistical analysis of tolerances. (8)


OPTIMUM DESIGN: Objectives of optimum design, optimum design with normal specifications of simple machine elements like tension bar, transmission shaft, helical spring, design space exploration-design of experiments, introduction to robust design, probabilistic methods in mechanical design. (8)


ADVANCED MACHINE DESIGN: Design of machine elements under shock, impact, inertial forces, initial and residual stresses, corrosion environments, wear, elevated temperatures and low temperatures. Design of bolted and bonded joints. (8)


DESIGN AND ANALYSIS OF STRUCTURES: Design of box type structures, design of weldments, design of curved beams-stress distribution in curved beams, design of stiffeners . (8)


DESIGN OF COMPOSITE STRUCTURES: Classification of composites, micro mechanical behavior of lamina-evaluation of elastic modulus and strength of unidirectional lamina, macro mechanical behavior of lamina, stress-strain relation for a lamina at arbitrary orientation, macro mechanical behavior of laminate. (10)


Total 42

REFERENCES:

1. Franklin E Fisher, “Probability Application in Mechanical Design”, CRC Press, 2000.

2. Omer W Blodgett, James F Lincoln, “Design of Weldments”, James F. Lincoln Arc Welding Foundation, 1963.

3. Patil S P, “Mechanical System Design” Jaico Publishing House, 2005.

4. Rao S S, “Engineering Design Optimization-Theory and Practices”, New Age International, 2000.

5. Autar K  Kaw, "Mechanics of Composite Materials", CRC Press, NY, 2005.

6. Thomas A Grause, “Reliability Based Mechanical Design”, Margham Publications, 1997.

7. Rao S S, “Reliability-Based Design”, McGraw Hill, 1992.

8. Sadhu Singh, “Experimental Stress Analysis”, Khanna Publishers, 2006.

9. Allen S Hall, Alfred R Holowenko and Herman G Laughl, “Schaum's Outline of Theory and Problems of Machine Design”

McGraw Hill Professional, 1968.
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