The finite element method is a numerical technique for obtaining approximate solutions to a wide spectrum of engineering problems. Although originally developed to study the stresses in complex airframe structures, it has since been extended and applied to a broad field in continuum mechanics. Because of its diversity and flexibility as an analysis tool, this particular technique is receiving much attention in both academia and industry fields.

Although this brief comment on the finite element method answers the question posed by the section heading, it does not give us the operational definition we need to apply the method to a particular problem. Such an operational definition, along with a description of the method fundamentals, requires considerably more than just one paragraph to develop. Hence, the first segment of this book is devoted to basic concepts and fundamental theory. Before discussing more aspects of the finite element method, we should first consider some of the circumstances leading to its inception, and we should briefly contrast it with other numerical techniques.

In more and more engineering situations today, we find that it is necessary to obtain approximate numerical solutions to problems rather than exact closed form solutions. For example, we may want to find the load capacity of a plate that has several stiffeners and odd-shaped holes, the concentration of pollutants during nonuniform atmospheric conditions, or the rate of fluid flow through a passage of arbitrary shape.