Summary of the theoretical work done on the stability of thin plates 1939 to 1946

Abstract

Most of the work done during the war on the stability of thin plates has been written up and published in reports (Refs. 1 to 8). These reports do not however form a connected series, and the object of this summary is to draw attention to the more important stability problems which were requiring solution at the beginning of the war, and to indicate the progress made towards their solution during the subsequent seven years. In 1939 there were three main problems, or types of problem, for which existing solutions were inadequate: (A) the critical buckling load of a flat rectanguiar plate when the edges are not all simply supported, with special reference to a plate under shear, (B) the post-buckling behaviour of a long flat plate under shear, (C) the initial and post-buckling behaviour of a curved plate under various combinations of shear, compression, and normal pressure. Of these three classes of problem (A) and (B) are primarily important in the design of plate web spars, while (C) is clearly of much wider application. For in any aeroplane of predominantly stressed-skin construction, the surface of the wings and fuselage consists very largely of thin and slightly curved plates. Moreover, in addition to the general and ever-present problem of making aircraft structures lighter, aerodynamic developments during the war presented the aircraft designer with the further task of constructing wings that would remain sufficiently smooth to provide laminar flow over a considerable portion of the wing surface (R. & M. 2193). As the degree of smoothness required is incompatible with buckling, this gave added importance to knowledge of the loads at which flat and slightly curved plates begin buckling.