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Introduction
1–1
Chapter 1: INTRODUCTION 1–2
§ SUMMARY
This report presents the plete implementation of the Finite Element Method (FEM) using
the Mathematica language. The report focuses on data structures, data flow and programming
modules for linear structural mechanics.
The material collected herein directly supports most of the syllabus of the course Finite Element
Programming with Mathematica (ASEN 5519). The programming modules are also used to
puter homework in the course Introduction to Finite Element Methods (ASEN
5007); however, the logic of those modules is not studied.
The present implementation has been designed with the following extensions in mind:
putation
Dynamic analysis, both transient and modal
Nonlinear analysis
Multiphysics problems
Extensibility is achieved by presenting data structures that are likely to change in list form. Lists
are highly flexible because they can odate objects of any type in an arbitrary number of
hierarchical levels. Some list structures can (and should) be readily implemented as arrays to
increase processing efficiency putational intensive tasks, whereas others may be implemented
as derived data types in languages such as C, C++ or Fortran 90.
Source
Data
Computational
Data
Result
Data
Figure . High level data flow in a Finite Element program.
§ OF A FEM PROGRAM
§ Data Flow
The high level data flow in any FEM program is schematized in Figure . This flows naturally
suggests the grouping of data structures into three classes:
Source Data Structures. These bear a close relation to the FE model as the user defined it. For
example, a table of node coordinates.
1–2
1–3 § OF A FEM PROGRAM
Computational Data Structures. As the name suggests, these anized with processing effi-
ciency in mind. The use of arrays is important for this goal. Example are sparsely stored coefficient
matrices, and partitioned solution vectors.
Result Data Structure