Ebook: Basic Principles of the Finite Element Method

The objective of this book is to provide an introductory text which lays out the basic theory of the finite element method in a form that will be comprehensible to materials scientists. Although this book was written with materials scientists in mind, it will prove useful to all those interested in learning the fundamentals of the finite element method. It presents the basic ideas in a sequential and measured fashion, avoiding the use of specialist vocabulary that is not clearly defined. The basic principles are illustrated by a diversity of examples which serve to reinforce the particular aspects of the theory, and there are three finite element analyses which are presented with the detailed mathematics exposed. By this means, some of the mystery that can envelop commercial finite element packages is penetrated.
Content:
Front Matter
• Preface
• Table of Contents
• 1. Introduction
2. About Matrices
3. The Stiffness Matrix
4. One-Dimensional Finite Element Analysis
5. Energy Principles in Finite Element Analysis
6. Finite Elements That Form Part of a Continuum
7. Finite Element Analysis Using Higher Order Elements
8. Worked Examples Applying the Theory of Section (7.2) to Calculate the Stresses in a Loaded Tapered Sheet
• 9. A Cautionary Epilogue