7.1 Introduction

In Chapters 4 6, all structural characteristic matrices, such as stiffness and inertia matrices, have been conveniently expressed in individual element, attached local coordinate systems (LCS). Usually an entire structure is defined in terms of a single global coordinate system (GCS). Also, for many practical structures, because of ease of data input, each substructure is defined in terms of the coordinate system unique to that substructure, which may conveniently be referred to as the local global coordinate system (LGCS). The relevant element characteristic matrices expressed in any specific coordinate system, either in LCS or LGCS, are then required to be transformed in the GCS before they can be assembled for the entire structure. ^{[1] , [2]} Once assembled, the various displacement boundary conditions (DBC) need to be incorporated into such matrices before the relevant solution process may be started.

Typically, an assembled matrix tends to be highly banded because of the very nature of FEM discretization. Incorporation of DBCs have a tendency to increase the bandwidth. Because the solution effort of these matrices is usually a function of ( N M ^[2]), N being the order and M the semibandwidth, it is essential to evolve efficient bandwidth minimization techniques to keep the bandwidth to a possible minimum. These features are addressed in this chapter.

7.2 Coordinate...