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ME-504 (C) · Finite Element Method/Official Syllabus

Finite Element Method (ME-504 (C)) - Official Syllabus

1
Unit 1

Introduction

  • Structural analysis, objectives, static, Dynamic and kinematics analyses
  • Skeletal and continuum structures
  • Modeling of infinite d.o.f. system into finite d.o.f. system
  • Basic steps in finite element problem formulation
  • General applicability of the method
2
Unit 2

Element Types and Characteristics

  • Discretization of the domain, Basic element shapes, Aspect ratio
  • Shape functions, Generalized co-ordinates and nodal shape functions
  • 1D spar and beam elements
  • 2D rectangular and triangular elements
  • Axisymmetirc elements
3
Unit 3

Assembly of Elements and Matrices

  • Concept of element assembly, Global and local co-ordinate systems
  • Band width and its effects, Banded and skyline assembly
  • Boundary conditions
  • Solution of simultaneous equations, Gaussian elimination and Choleksy decomposition methods
  • Numerical integration, One and 2D applications
4
Unit 4

Higher Order and Isoparametric Elements

  • One dimensional quadratic and cubic elements
  • Use of natural co-ordinate system, Area co-ordinate system continuity and convergence requirements
  • 2D rectangular and triangular requirement
5
Unit 5

Static & Dynamic Analysis

  • Analysis of trusses and frames
  • Analysis of machine subassemblies
  • Use commercial software packages, Advantages and limitations
  • Hamilton's principle, Derivation of equilibrium, Consistent and lumped mass matrices
  • Derivation of mass matrices for 1D elements
  • Determination of natural frequencies and mode shapes, Use of commercial software packages

Reference Books

  • The Finite Element Method in Engineering — Rao, S.S. — Peragamon Press, Oxford — 2nd ed.
  • Concepts and Application of Finite Element Analysis — Robert, D. Cook, David, S. Malkins, Michael E. Plesha — John Wiley — 3rd ed.
  • Introduction to Finite Elements in Engineering — Chandrupatla, T.R., Belegundu, A.D. — Prentice Hall of India Pvt. Ltd.
  • The Finite Element Method — Zienkiewicz O C — Tata McGraw Hill — 3rd ed
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