Finite Element Analysis: Preliminaries and Overview

Abstract

All of the work we have described so far has been about getting closed-form solutions, both exact and approximate, for a variety of problems in applied and structural mechanics. Much of that work is clearly “classical” as most of it was done long before the advent of computers. At the time the original edition of this book was being written, the late 1960s, engineers and mathematicians were beginning to develop discrete models of continuous structures that could be used to obtain algorithmic, computational solutions to such mechanics problems. These discretized approaches started with matrix methods for structures, which were extended into finite element analysis (FEA) of structures and of other continua. This discretization methodology now has a long, rich, and continuously growing body of literature that cannot be covered even remotely in a single book, never mind one or two chapters. Having said that, we will now provide an overview of how our general formulations can be cast in matrix representations. Then, we will describe how FEA emerges as a natural discretized extension, enabled by the advent of computers, of the classical variational approaches that have occupied us so far.