Arbitrary Quadrilateral Spar Webs for the Matrix Displacement Method

Abstract

Ever since the realisation of the matrix Displacement Method, the introduction of a kinematically satisfactory spar element has remained a difficult and, as yet, not fully resolved problem. Two cardinal points have to be considered in establishing a suitable spar model: first, it must reproduce adequately both shearing and bending deformations, and second, it must satisfy everywhere the kinematic compatibility conditions, especially at the junction with the wing cover. Of course, if we were to restrict ourselves to a uniform rectangular element, the corresponding theory could be written down in a few lines. However, from the practical point of view, it is essential to take account, ab initio, of taper, and this necessitates some subtle considerations, especially if we have to allow for asymmetrical taper, as becomes indispensable with some modern flying vehicles.