Finite Element Method (FEM)

This report presents the first complete 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
support computer homework in the course Introduction to Finite Element Methods (ASEN
5007); however, the logic of those modules is not studied.

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Table of contents :
Introduction……Page 1
Nodes……Page 11
Individual Elements……Page 22
Element Grouping……Page 36
Element Constitutive Properties……Page 48
Element Fabrication Properties……Page 60
Freedom Assignment……Page 70
Nodal State……Page 89
Global Connectivity……Page 101
Pre-Skyline Processing……Page 116
Symmetric Skyline Solver……Page 127
Skyline Assembly……Page 145
The Master Element Library……Page 164
Implementation of One-Dimensional Elements……Page 176