TABLE OF CONTENTS A field problem in engineering science is associated with a domain of specified geometry within which the field variables are required to be investigated. The physical behavior represented by these field variables is characterized by differential equations and must satisfy the given boundary conditions. Except in simple cases, closed-form solutions are not available and recourse is made to approximate solutions obtained from numerical analysis techniques. Approximate solutions of the differential equations are obtained by several techniques including Fourier analysis, finite difference techniques, Rayleigh Ritz functions over the whole region, or by functions prescribed over discretized finite regions of the original domain, to name but a few of the methods available. All of these have their particular appeal for different applications.
The method developed in the present book is, of course, the last and perhaps latest of these techniques and has come to be known as the finite element method. In this technique an approximate numerical solution is obtained by satisfying the conditions of the differential equations (equilibrium, continuity, etc.) at discrete points. The accuracy being improved by successive refinement of the size of the contributing domains and the consequent increase in the points at which the field conditions are satisfied. In setting up the nodal equations for approximation of the differential equations, a variety of techniques can be used.
For example, in the weighted residual method, an approximate solution of the differential equation is sought within each element by choosing a set of trial functions exclusive to that element.
