ME 6124: Finite-Element Method: Theory and Practice

Offered Every Spring


Credit Hours: 3-0-3
Prerequisites: Graduate standing in engineering or related discipline
Catalog Description: Line, plane, solid, plate, and shell-elements theory; practical aspects of modeling; applications in mechanical engineering; final project.
Textbooks: J. N. Reddy, An Introduction to the Finite-Element Method, 2nd, McGraw-Hill, 1993.
Instructors: Suresh Sitaraman
References: K. J. Bathe, Finite-Element Procedures, Prentice Hall, Inc., 1996
O. C. Zienkiewicz and R. L. Taylor, The Finite-Element Method, McGraw Hill, 1989
F. L. Stasa, Applied Finite-Element Analysis for Engineers, Saunders/HBJ Publishers, 1985
E. Zahavi, The Finite-Element Method in Machine Design, Prentice-Hall, Inc., 1992
Goals: To provide an in-depth understanding of the theory and formulation behind various finite elements with exposure to applications in Mechanical Engineering. To gain hands-on experience with practical aspects of Finite-Element Modeling.
Topics:
  • Introduction
    • Basic concepts
    • Variational Formulations
    • Weighted-Residual Methods
  • Theoretical Formulation of Line Elements
    • Governing Differential Equation
    • Weak Formulation
    • Derivation of Element Equations/ Interpolation Functions
    • Assembly of Element Equations
    • Imposition of Boundary Conditions and Assembly Reduction
    • Solution of Equations
  • Theoretical Formulation of Plane Elements
    • Governing Differential Equation
    • Weak Formulation
    • Derivation of Element Equations/Interpolation Functions
    • Assembly of Element Equations
    • Imposition of Boundary Conditions and Assembly Reduction
    • Plane Stress, Plane Strain Analysis
  • Midterm Test I
  • Theoretical Formulation of Solid Elements
    • Governing Differential Equation
    • Weak Formulation
    • Derivation of Element Equations and Interpolation Functions
    • Imposition of Boundary Conditions
  • Theoretical Formulation of Plate and Shell Elements
    • Governing Differential Equation
    • Element Selection
    • Material Modeling
    • Model Simplification - Symmetry/Antisymmetry, Plane Strain, Plane Stress
    • Imposition of Boundary Conditions
    • Element Aspect ratios/biasing of elements
    • Convergence/Mesh Refinement
    • Submodeling
    • Substructuring
    • Validation of Results
  • Practical Aspects of Modeling
    • Governing Differential Equation
    • Interpolation Functions and Degrees of Freedom
    • Imposition of Boundary Conditions
  • Applications in Mechanical Engineering
    • Heat Transfer
    • Solid Mechanics
  • Midterm Test II
  • Special Topics
    • Gap Elements
    • Contact Elements
    • Fracture Elements
  • Final Project and Presentation
Delivery mode (%):

Lecture

85

Supervised Lab

15

Grading Scheme (%):

Homework

20

Midterm I

25

Midterm II

25

Final Project and Presentation

30