Building Finite Element Models With Mathematica

C.J. PurcellDefence Research Establishment AtlanticPO Box 1012, 9 Grove St., Dartmouth, N.S., Canada B2Y3Z7

Abstract

The goal of this work was to assess the utility of Mathematica for finite element analysis, specifically in the areas of model generation and results display. This document will describe a prototype Mathematica package that can be used to create finite element (FE) models, both 2D and 3D. The application area is sonar transducer design, and the target finite element code is MAVART3D.  However, the package will readily generalize to other FE codes, for example, the node and element descriptions are not hardwired, but are user definable. Transducer models are usually simple enough that they can be built by command files, with 3D visualization most useful for debugging, and results display. Mathematica is well suited to this method of model building. A number of commercial mesh generators use a WYSIWYG approach where changes to a model often require starting from scratch. In the parametric approach used here, the model is  described by parameters contained in a notebook and revisions to a design are easily made.

1.  Introduction

2.  The ModelMaker Package

3.  Examples

4.  Future Directions for the Code

5.  Conclusions

6.  References