Matrix Analysis of Shell Structures with Flexible Frames

Abstract

SummaryA simple matrix method is presented for the deflection and stress analysis of cylindrical shell structures of arbitrary cross section stiffened by flexible frames. The method is an extension to fuselage structures of the Matrix Force Method developed by Argyris, in which the internal load system in the structure consists of two parts:—(a) synthetic load distribution, represented by the matrix b0, satisfying the external and internal equations of equilibrium, and(b)self-equilibrating load systems, represented by the matrix b1, which are introduced to satisfy compatibility conditions. The magnitudes of these self-equilibrating load systems are determined from the generalised compatibility equations formulated using the flexibility matrix f for the un-assembled elements of the structure. The self-equilibrating systems are non-orthogonal, but are arranged in such a way that the mixing between one system and another is kept to a minimum and, consequently, the resulting compatibility equations are well-conditioned. The three basic matrices, b0, b1;and f, are compiled using only very simple formulae. The matrices b0and b1depend on the geometry of the structure, while the flexibility matrix f is a function of geometry and elastic properties. The present analysis is applied to cut-out problems in fuselage structures. It can also be used for problems involving thermal loading and diffusion of loads in curved panels stiffened by flexible frames.