Overview

Actual aircraft structures consist of numerous components generally arranged in an irregular manner. These components are usually continuous and therefore, theoretically, possess an infinite number of degrees of freedom and redundancies. Analysis is then only possible if the actual structure is replaced by an idealized approximation or model. This procedure is discussed to some extent in Chapter 20 where we note that the greater the simplification introduced by the idealization the less complex but more inaccurate becomes the analysis. In aircraft design, where structural weight is of paramount importance, an accurate knowledge of component loads and stresses is essential so that at some stage in the design these must be calculated as accurately as possible. This accuracy may only be achieved by considering an idealized structure which closely represents the actual structure. Standard methods of structural analysis are inadequate for coping with the necessary degree of complexity in such idealized structures. It was this situation which led, in the late 1940s and early 1950s, to the development of matrix methods of analysis and at the same time to the emergence of high-speed, electronic, digital computers. Conveniently, matrix methods are ideally suited for expressing structural theory and for expressing the theory in a form suitable for numerical solution by computer.

A structural problem may be formulated in either of two different ways. One approach proceeds with the displacements of the structure as the unknowns, the internal forces then follow from the determination of these displacements, while in the alternative...