A First Course in Finite Elements
Chapter One
Introduction
1.1 BACKGROUND
Many physical phenomena in engineering and science can be described in terms of partial differential
equations. In general, solving these equations by classical analytical methods for arbitrary shapes is almost
impossible. The finite element method (FEM) is a numerical approach by which these partial differential
equations can be solved approximately. From an engineering standpoint, the FEM is a method for solving
engineering problems such as stress analysis, heat transfer, fluid flow and electromagnetics by computer
simulation.
Millions of engineers and scientists worldwide use the FEM to predict the behavior of structural,
mechanical, thermal, electrical and chemical systems for both design and performance analyses. Its
popularity can be gleaned by the fact that over $1 billion is spent annually in the United States on FEM
software and computer time. A 1991 bibliography (Noor, 1991) lists nearly 400 finite element books in
English and other languages. A web search (in 2006) for the phrase 'finite element' ... read full excerpt from A First Course in Finite Elements ebook
