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 (Spring 2004)

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:

Topics:

I. Introduction
A. Basic concepts
B. Variational Formulations
C.

 

Weighted-Residual Methods

 

II.
Theoretical Formulation of Line Elements
A.
Governing Differential Equation
B.
Weak Formulation
C.
Derivation of Element Equations/ Interpolation Functions
D.
Assembly of Element Equations
E.
Imposition of Boundary Conditions and Assembly Reduction
F.

 

Solution of Equations

 

III. Theoretical Formulation of Plane Elements
A.
Governing Differential Equation
B. Weak Formulation
C. Derivation of Element Equations/ Interpolation Functions
D. Assembly of Element Equations
E. Imposition of Boundary Conditions and Assembly Reduction
F.  Plane Stress, Plane Strain Analysis  
 
MIDTERM TEST I

 

IV. Theoretical Formulation of Solid Elements
A. Governing Differential Equation
B.  Weak Formulation
C. Derivation of Element Equations and Interpolation Functions
D.

 

Imposition of Boundary Conditions

 

V. Theoretical Formulation of Plate and Shell Elements
A. Governing Differential Equation
B. Interpolation Functions and Degrees of Freedom
C.

 

Imposition of Boundary Conditions

 

VI.
Practical Aspects of Modeling
A.
Element Selection
B. Material Modeling
C. Model Simplification - Symmetry/Antisymmetry, Plane Strain, Plane Stress
D. Imposition of Boundary Conditions  
E. Element Aspect ratios/biasing of elements  
F. Convergence/Mesh Refinement  
G. Submodeling  
H. Substructuring  
I.

 

Validation of Results

  

 
VII. Applications in Mechanical Engineering  
A. Heat Transfer  
B. Solid Mechanics  
 
MIDTERM TEST II

 

 
VIII.
Special Topics
 
A. Gap Elements  
B. Contact Elements  
C. Fracture Elements  
  FINAL PROJECT AND PRESENTATION
 

Delivery Mode

Lecture

85%

Supervised Lab

15%

Grading Scheme

Homework

20%

Midterm

25%

Midterm II

25%

Final Project and Presentation

30%

________________________
Revised June 2004