Rajasthan Technical University - RTU Courses

M.Tech. (Machine Design)

Course Structure

Course Syllabus

1MEMD1: Advanced Solid Mechanics

Continuum concepts- Stress field (stress tensor, Cauchy’s principle, equilibrium equation), Deformation (strain tensor, compatibility), Constitutive equations. Uniqueness and superposition- Boundary value problems in plane stress and plain strain. Torsion of non circular cross section (St. Venant’s theory), Timoshenko beam theory and Kirchoff’s plate theory. Failure theories, introduction to concepts of fracture mechanics. Numerical and Experimental methods, Introduction to Photo-elasticity and strain gauge techniques. Principle of virtual work, Energy theorems.

1MEMD2: Advanced Vibrations

• Vibration of continuous systems: Hamilton’s principle, Lagrange’s equations. Longitudinal vibration of bars, lateral vibration beams, vibration of membranes and plates. Wave motion in continuous systems.
• Nonlinear vibrations: Phase space, singular points, limit cycle; Analytical methods, perturbationtechniques, equivalent linearization; Duffing’s equation, jump phenomenon, Van der Pol’s equation. Stability criterion; Floquet’s theory, Hill’s and Mathieu’s equations, Bifurcation and chaos.

1MEMD3: Numerical Methods

Approximations: Accuracy and precision, definitions of round off and truncation errors, error propagation Algebraic equations : Formulation and solution of linear algebraic equations, Gauss elimination, LU decomposition, iteration methods ( Gauss - Siedel ), convergence of iteration methods, eigen values and eigen vectors. Interpolation methods: Newton's divided difference, interpolation polynomials, Lagrange interpolation polynomials. Differentiation and Integration: High accuracy differentiation formulae, extrapolation, derivatives of unequally spaced data, Gauss quadrature and integration. Introduction to optimization methods: Local and global minima, Line searches, Steepest descent method, Conjugate gradient method, Quasi Newton method, Penalty function.

1MEMD4: Computer Aided Graphics and Design

Brief introduction to solid modeling: Fundamentals of Solid Modeling, Half -spaces, Boundary Representation (B-rep), Constructive Solid Geometry (CSG), Sweep Representation, Analytical Solid Modeling. Solid Manipulations Methodology of interactive, graphical, engineering design; Discretization, optimization, simulation in CAED. Design of curves and surfaces. Design of volumes. Intersection of surface and interference of volumes.

1MEMD5: CAD Lab

Computer aided drafting. Solid modeling: part creation, surface generation and assembly of parts.Exercise problems using software.