M Tech (Computational Mechanics)
SEMESTERI
Course No. 
Course Name 
L 
T 
P 
C 
ME 501 
Advanced Engineering Mathematics 
3 
0 
0 
6 
ME 532 
Finite Element Methods in Engineering 
3 
0 
0 
6 
ME543 
Computational Fluid Dynamics 
3 
0 
0 
6 
ME 502 
Engineering Computing Laboratory 
0 
0 
3 
3 
ME xxx 
Elective – I 
3 
0 
0 
6 
ME xxx 
Elective – II 
3 
0 
0 
6 

15 
0 
3 
33 
SEMESTERII
Course No. 
Course Name 
L 
T 
P 
C 
ME541 
Continuum Mechanics 
3 
0 
0 
6 
ME542 
Numerical Analysis 
2 
0 
2 
6 
ME544 
Computational Mechanics Laboratory 
0 
0 
2 
2 
ME xxx 
Elective – III 
3 
0 
0 
6 
ME xxx 
Elective – IV 
3 
0 
0 
6 
ME xxx 
Elective – V 
3 
0 
0 
6 

15 
0 
0 
32 
SEMESTERIII
Course No. 
Course Name 
L 
T 
P 
C 
ME 503 
Technical Writing 
1 
0 
2 
4 
ME 504 
Project Phase I 
0 
0 
20 
20 

1 
0 
22 
24 
SEMESTERIV
Course No. 
Course Name 
L 
T 
P 
C 
ME 505 
Project Phase II 
0 
0 
24 
24 

0 
0 
24 
24 
ME 541 Continuum Mechanics
Introduction to Tensors: Vectors and second order tensors; Tensor operation; Properties of tensors; Invariants, eigenvalues and eigenvectors of second order tensors; Tensor fields; Differentiation of tensors; Divergence, Stokes and Localization theorems.; Kinematics of Deformation: Continuum hypothesis; Deformation mapping; Material (Lagrangian) and Spatial (Eulerian) field descriptions; Length, area and volume elements in deformed configuration; Material and spatial time derivatives  velocity and acceleration; Linearized kinematics; Balance Laws: Conservation of mass; Balance of linear and angular momentum  Cauchy stress tensor, state of stress; Spatial and material forms of balance laws  concept of first and second PiolaKirchoff stress tensors; Conservation of energy; Continuum Thermodynamics: Basic laws of thermodynamics; Energy equation; Entropy; ClausiusDuhem inequality. Constitutive Equations: Material frameindifference; Objective stress and stressrates; Material symmetry; Constitutive relations for Hyperelastic Solids, Generalized Hooke's law; Simple fluids; NavierStokes equation.
Texts/References:
ME 542 Numerical Analysis
Introduction to numerical analysis, Significant digits, Types of errors; Stability; Accuracy; Solutions of Linear Algebraic Equations: Direct elimination methods, Pitfalls of elimination methods, Norm and condition number; Iterative methods, Accuracy and convergence of iterative methods; Solution of Eigenvalue Problems; Solutions of Nonlinear Equations: Newton’s method, System of nonlinear equations, Convergence and Error analysis; Interpolation: Lagrange polynomials, Divided difference polynomials, Hermite and cubic spline interpolation, Least square approximation; Numerical Differentiation – Unequally spaced data and Equally spaced data, Error estimation and extrapolation; Numerical quadrature – NewtonCotes, Gauss quadrature, Multiple integrals; Initial and boundary value problems – Classification of ODEs, One step methods, Convergence and numerical stability analysis, Solution of higher order equations, Multistep methods, Convergence and stability analysis.
Laboratory component : The lab is intended to be a platform for students to get used to scientific computing. Strong emphasis is laid on computer programming and the student is expected to write his own programs/codes for prototypical mathematical problems which will have reallife applications in the area of computational mechanics.
Texts/References:
ME 543 Computational Fluid Dynamics
Basic equations of Fluid Dynamics: General form of a conservation law; Equation of mass conservation; Conservation law of momentum; Conservation equation of energy. The dynamic levels of approximation. Mathematical nature of PDEs and flow equations. Basic Discretization techniques: Finite Difference Method (FDM); Analysis and Application of Numerical Schemes: Consistency; Stability; Convergence; Fourier or von Neumann stability analysis; Modified equation; Application of FDM to wave, Heat, Laplace and Burgers equations. Integration methods for systems of ODEs: Linear multistep methods; Predictorcorrector schemes; ADI methods; The RungeKutta schemes. Vorticitystream function formulation. Solution of NavierStokes equations using MAC algorithm. The Finite Volume Method (FVM) and conservative discretization. Numerical solution of the incompressible NavierStokes equations: Primitive variable formulation; Pressure correction techniques like SIMPLE, SIMPLER and SIMPLEC; Brief introduction to compressible flows and numerical schemes – quick idea of Euler equations, homogenity and flux jacobian. Introduction to upwind schemes.
Texts/References:
ME 544 Computational Mechanics Lab
Introduction to Ansys modules including general steps for solving a problem. Simple mesh generation for onedimensional or twodimensional domain; Using appropriate commercial package: A simple 2D heat conduction problem. Heat convection in a heated cavity. A problem from bluff body flows/shear flows; Using appropriate commercial package: One dimensional problem: A cantilevered beam/simply supported beam with distributed load/concentrated load. An Ibeam under distributed/concentrated load. A two dimensional problem: plate under tensile loading. Truss, closed cylinder under pressure.
ME 532 Finite Element Methods in Engineering
00