| Appendix E |
List of GIKI courses forming the Core & Elective Curriculum of the Computational Mechanics Program
COURSE DESCRIPTION
Core Courses:
ME 506 Continuum Mechanics (3-0-3)
Introduction to Vectors and Cartesian Tensors, Analysis of Stress in a Continuum, Analysis of deformation in a Continuum, Eulerian Forms of the Basic Physical Laws Governing the Motion of a Continuum Media, Application to Solids, Application to Fluids
ME 524 Computational Fluid Mechanics (3-0-3)
Introduction to CF, Classification of Partial Differential Equations and Solution Types, Finite Difference Representation of PDEs, Application of Finite Difference Methods to Selected Equations, Application of Finite Difference Equations to Fluid Mechanics & Heat Transfer, Numerical Methods for Inviscid Flow Equations, Numerical Methods for Boundary Layer Type Equations, Numerical Methods for the “Parabolized” Navier-Stokes Equations, Numerical Methods for Navier-Stokes Equations, Grid Generation
ME 514 Advanced Stress Analyses (3-0-3)
Stress Strain Compatibility, Stress Transformations; Elasto plastic Behavior of Materials (Beams, Shafts); Behavior of Thin Walled Sections, Energy Methods including FEM: Buckling Analysis of Columns; Experimental Stress Analysis
i.e. Strain gauges (2D and 3D) analysis; Fracture behavior of Materials; Strength Theories;
ME 515 Finite Element Method (3-0-3)
Introduction to FEM; The Stiffness Method and the Plane Truss; Two-Dimensional Stress Analysis by FEM; Energy, Variational Principles and Ritz Technique; Elements based on Assumed Displacement Fields; The Isoparametric Formulation; Coordinate Transformation; Topics in Element Formulation and Use; Solids of Revolution; Bending of Flat Plates; Three-Dimensional Stress Analysis; General Field Problems; A sample Computer Code and other Practical Considerations.
ME-5xx Partial Differential Equations (3-0-3)
Introduction and Classification, Boundary Conditions, Wave equation, D'Alembert's solution, Method of characteristics, Separation of variables, Diffusion equation. Application of Fourier series, Sturm-Liouville theory, Orthogonal eigenfunctions, PDEs in cylindrical coordinates, Fourier-Bessel series, Steady-state and time-dependent problems involving cylinders, Problems in spherical geometry. Fourier-Legendre series, Spherical Bessel functions for time-dependent problems, Non-homogeneous PDEs, Poisson's equation, Green's functions for partial differential equations.
ES-541 Variational Methods in Mechanics (3-0-3)
The Euler-Lagrange equation, Ritz’s method, boundary conditions, continuity conditions, Galerkin’s method, minimizing sequence, transformation in variational problems, elasticity, Castgliano’s theorem, and eigen values, the finite element method, general use of Lagrange multiplier.
ME 512 Advanced Solid Mechanics (3-0-3)
Physical Elements of deformation and fracture. Elements of continuum mechanics and thermodynamics, Identification and rheological classification of real solids. Linear elasticity, Thermoplasticity, Viscoelaticity, Plasticity, Viscoplasticity, Damage mechanics, Crack mechanics.
Elective Courses:
ME 516 Applied Finite Element Analyses (3-0-3)
Introduction to FEA, Structures, Geometric Nonlinearities, Material Nonlinearities, Structural Analysis, Thermal Analysis, Thermal Stress Analysis, Dynamic Analysis, Couple Field Analysis, Element Performance, Shape Functions, Element Tools, Element Library, Analysis Tools, Analysis Procedures, Pre and Post Processing Tools, Design Optimization.
ME-532 Heat Transfer II
Governing equations. Formulation of laminar free and forced convection including integral techniques. Methods of solution: similarity; perturbation, computational convection. Turbulence models. Analogy between heat and momentum transfer; Reynolds, Prandtl-Taylor and Martinelli analogies. Dimensional analysis.
CS 417 Parallel Processing (3-0-3)
High Performance Architectures & Programming Languages; Graph Concepts: Control Flow Graph, Dominance Frontiers, Data Dependence in Loops and Parallel Constructs; Program Dependence Graph; Loop Transformations, Inter-procedural Transformations; Concurrency Analysis: Synchronization, Strength Reduction, Nested Loops; Vector Analysis; Message-Passing Machines; Communicating Sequential Processes.
ES-531 Computational Methods for Engineers (3-0-3)
Direct and indirect methods for linear equations, eigen value problems and eigen vectors, finite difference methods for boundary value problems and partial differential equations.
ES-534 Numerical Functional Analysis (3-0-3)
Sets, metric space, limit, completeness, convergence, contraction mapping, linear space, norm, vector, matrix norm, normed space, Branch space, inner product, Hilbert space, operations.
ES-533 Numerical Methods for Partial Differential Equations (3-0-3)
Parabolic equations, Explicit and implicit methods, Consistency, stability and convergence. Hyperbolic Equations, Method of characteristic and lines, Finite difference methods. Elliptic equations, Finite difference replacements, Finite element methods for elliptic problems.
