Chapter 6 - Matrix methods

Abstract

Publisher Summary In aircraft design, where structural weight is of paramount importance, an accurate knowledge of component loads and stresses is essential, so at some stage in the design, these must be calculated as accurately as possible. This accuracy is achieved only 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. This situation 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 expressing that theory in a form suitable for numerical solution by computer. A structural problem may be formulated in either of the two ways. One approach proceeds with the displacements of the structure as the unknowns, and then, the internal forces follow from the determination of these displacements. In the alternative approach, forces are treated as being initially unknown. In the language of matrix methods, these two approaches are known as the stiffness (or displacement) method and the flexibility (or force) method, respectively. The most widely used of these two methods is the stiffness method, and for this reason, this chapter concentrates on this particular approach. The behavior of each element may be determined by basic methods of structural analysis, and hence the behavior of the complete structure is obtained by superposition. Operations such as this are easily carried out by matrix methods in the chapter. Initially, the matrix stiffness method of solution in the chapter is developed for simple skeletal and beam structures.