**09MD01/ 09MC01 COMPUTATIONAL METHODS** **3 1 0 4**
I**ntroduction 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. **Total 42**
**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** **3 1 0 4**
**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. |