Energy Theorems and Structural Analysis

Abstract

THE application of the general theory with displacements as unknowns to frameworks—both of the pin‐jointed and stiff‐jointed type—is straightforward. For the stiff‐jointed system the method is particularly simple when direct and shear deformations are ignored. In fact, for all frameworks the determination of the matrices C and C0 is trivial once we consider all possible degrees of freedom of the joints. See for example, the systems of figs. (23), (24) and (48) investigated on pp. 48, and 91, which show clearly how elementary the matrices a and stiffness k are when we break up the structure into its simplest constituent components. We need not therefore concern ourselves any more here with frameworks, and we turn our attention to the membrane type of system characteristic of aircraft applications. Essentially, a major aircraft structure like a wing consists of an assembly of plates (fields) stiffened by flanges along their edges. The field may be a curved and/or tapered surface but we ignore here both these effects and consider only rectangular flat elements of constant thickness. For convenience the element formed by the plate (sheet) and its fouredge members is denoted by the term unit panel. It is assumed that the flange areas are constant along each edge.