EGM 6352

EGM6352 Advanced Finite Element Method

Course Description

3 credits – Advanced concepts related to the finite element method with emphasis on nonlinear analysis. Applications will include static and dynamic analysis of structures involving large deformation (geometric nonlinearity) and material nonlinearity.

Course Pre-Requisites / Co-Requisites

Credits 3, Pre-requisites: EML5526

Recommended Textbooks:
  • Introduction to Finite Element Analysis and Design
    Authors: Kim NH, Sankar BV and Kumar AV.
    Edition: 2nd Edition, Publisher: Wiley, ISBN: 9781119078739
  • Introduction to Nonlinear Finite Element Analysis
    Author: Nam-Ho Kim
    Publisher:  Springer, ISBN: 978-1441917454
Other Reference Textbooks
  1. Nonlinear Finite Elements for Continua and Structures, 2nd edition, by Belytschko, Liu, Moran and Elkhodary, Wiley Publications.
  2. The finite method for solid and structural mechanics, 6th edition, Zienkiewicz O. C. and Taylor R. L., Elsevier.
  3. A first course in the Finite Element Method, Daryl L. Logan, Thomson Publishers.
  4. A first course in finite elements, by Fish and Belytschko, Wiley Publications.
  5. Finite Element Procedures in Engineering Analysis, by K. J. Bathe, Prentice-Hall.
Course Objectives

The objective of the course is to teach advanced concepts related to the finite element method with emphasis on nonlinear analysis. Applications will include static and dynamic analysis of structures involving large deformation (geometric nonlinearity) and material nonlinearity.  

The outline of the course is as follows:

  1. Background
    • Introduction and notations
    • Review of linear finite elements
    • Review of relevant numerical methods
    • Plate and Shell elements
  2. Dynamic analysis of structures
    • Modal analysis and Modal Superposition method
    • Newmark method for linear dynamics
    • Explicit nonlinear dynamic analysis
    • Implicit nonlinear dynamic analysis
  3. Continuum mechanics concepts
    • Large deformation kinematics
    • Principle of Virtual Work in reference configuration
    • Nonlinear measures of stress and strain
  4. Nonlinear equation solving
    • Newton Raphson
    • Modified Newton-Raphson
    • Quasi-Newton methods
  5. Total Lagrange Formulation
  6. Updated Lagrange Formulation
  7. Large deformation of truss like structures
  8. Continuum nonlinear elements
    • Plane stress & Plane strain elements
    • Axisymmetric elements
    • 3D elements
  9. Constitutive equations for nonlinear materials