Introduction

The finite element method introduced in this chapter is the routine choice for the analysis of structures in government and industry, large companies and small. The finite element method is especially useful in the aerospace sciences and all related fields. For engineering applications, the finite element method was introduced to the engineering community by aerospace structural dynamicists in Ref. [49]. It is not the only useful, or necessary-to-know, method (one other method requires discussion), but it dominates because it is the only method suitable for large, complicated structures such as airplanes, helicopters, ships, and land vehicles, as well as the small redundant structures discussed here. It is particularly broad in scope. As a mathematical concept the finite element method is applicable to a wide variety of problems including such diverse problems as those of fluid dynamics, heat transfer, electromagnetic fields, and electrical circuits. As a mathematical concept, it is an adaptation of the Rayleigh–Ritz method. In this adaptation, instead of the requirement for choosing approximation functions for each new analysis, a finite element analysis can be computer programed because the same functions are repeatedly used for the same type of structural element. Instead of using the complicated functions that are sometimes necessary to meet boundary condition requirements of complicated structures, this adaptation uses simple functions, almost exclusively polynomial terms for quick computer processing.