Introduction to Finite Element Modeling, Analysis, and Applications[1]

Spring 2003


Instructor:††††† †††††††††† Prof. Ian. R. Grosse, ELAB 213B,(413) 545-1350

email address: †††††††††† grosse@ecs.umass.edu

Office Hours: ††††††††††† TuTh 4:00 - 5:15 PM


Teaching Assistant:†† Mr. Tiefu Shao (tshao@ecs.umass.edu)


Course Objectives:


The objective of the course is to develop an understanding of the underlying mathematical theory behind the finite element method and its application to the solution of problems from solid mechanics. The course involves homework assignments, a midterm, and a term project. The term project will involve the application of the finite element method to a realistic and sufficiently complex engineering problem that is selected by the student and approved by the instructor. Such projects typically require the use of a commercial finite element code. Codes available to the students in the Mechanical & Industrial Engineering Computer Laboratory (MICL) at the University of Massachusetts include ANSYS 5.7, Pro Mechanica, and FIDAP.


After completing the course, the student will have an in-depth understanding of the basic theory of the finite element method, as well as some hands-on experience in solving complex engineering problems by the finite element method.


Course web page: www.ecs.umass.edu/mie/faculty/grosse/605/index.html .


Required Text: None. Lecture notes will be given out periodically.


Grade Distribution


Homework & Class Participation







Homework problems will be assigned periodically during the semester. Homework problems may require use of PC-based software tools, such as spreadsheets and symbolic math tools (i.e. MATHCAD, Mathematica, etc.) for calculations, or in the case of modeling exercises they may required the use of commercial finite element codes, such as ANSYS or Pro Mechanica. You may consult your peers, but you must do your own work and pledge it with the following signed statement: this assignment is my own work. Late or unpledged homework and project will not be accepted.

Course Outline[2]





1/28 Tu

Course Intro

Finite Element Modeling and Applications

Intro. to FEM, Analysis, and Applications

1/30 Th

1-D Bars and Beams: Linear Static Analysis


2/4 Tu

2-D Plane Frames: Linear Static Analysis


2/6 Th

ANSYS Training ELAB 203

ANSYS Tutorial

2/11 Tu

Rayleigh Ritz Variational Method

Variational Calculus and the R-R

Variational Method

2/13 Th

2/20 Th

Method of Weighted Residuals

Method of Weighted Residuals

2/25 Tu

Galerkin Solution Procedure


2/27 Th

ANSYS Training ELAB 203


3/4 Tu

3/6 Th

Discretization: The Element Concept

4 Element 1-D Example

3/11 Tu

Linear Elements for 1-D Boundary-Value



3/13 Th

3/25 Tu

3/27 Th

2-D Boundary-Value Problems

The C0 triangle element

The C0 Quadrilateral element

Gaussian quadrature

Planar 2-D Heat Conduction with Edge

And Out-of-Plane Convection

4/1 Tu


Midterm Exam

4/3 Th

4/8 Tu

Higher Order C0 Elements and the

Isoparametric Formulation


4/10 Th

Convergence, Error Analysis, and Mesh



4/15 Tu

4/17 Th

Elasticity and the FEM

2-D Linear Elasticity with Initial Strains and

Galerkinís Finite Element Method

4/22 Tu

Axisymmetric Problems

Axisymmetric Isotropic Linear Elasticity and

Galerkinís Finite Element Method

4/24 Th

4/29 Tu

First Order Initial Boundary-Value

Problems: Diffusion


5/1 Th

5/6 Tu

Second Order Initial Boundary-Value

Problems: Dynamics

2-D Transient Heat Conduction

5/8 Tu

5/9 W

5/10 Th

Class Project Presentations

Project reports and *.html files due


[1] Copyright © 2003 by Ian R. Grosse. All rights reserved.

[2] The instructor reserves the right to change course schedule at any time.