    Optional class

# Mathematics of the Finite Element Method

Andreas Stahel Berner Fachhochschule
University of Applied Sciences

Biel School of Engineering and Architecture      Objectives
Content of course
Documentation
Language

### Objectives

In this optional class the mathematical foundation of the Finite Element Method (short FEM) will examined. A few sample problems will be solved to illustrate the method. Students will learn how the differents steps are implemented in a programming language.

### Content of course

The finite element method can be used to find solution to a great variety of problems: conduction of heat, elasticity, electric and magnet fields, fluid flow problems and many more. This course will present the mathematical foundation of the Finite Element Method. We examine the theory with the help of a few sample problems. These presented algorithms will be implemented in a programming language and the resulting code is presented in class. More complex problems can be solved with the PDE toolbox of Matlab.

The keywords below indicate the topics to be covered

• extremas of functions of one or multiple variables
• Finite Element solution of the problem of a system of bars
• Finite Element solution of the problem of one streched bar with variable cross section
• Finite Element solution for a transversal vibrations of a bar, using eigenvalues to determine the resonance frequencies
• General FEM problems with functions of one variable, e.g. heat conduction in a bar, bending of beams.
• FEM problems with functions of two variables, e.g. heat conduction in a plate, electric fields.
• Matlab PDE-Toolbox
• How to solve large systems of linear equations
• Solving elastic problems with the FEM, plain strain and plane stress

### Documentation

Extensive lecture notes will be handed out. The notes are written in English.

### Language to be used in class

The language is to be chosen by the participants. The options are: English, French or German. The use of multiple languages is possible.

Andreas Stahel Andreas.Stahel@hta-bi.bfh.ch