Increase in buckling loads of plates by introduction of cutouts

Abstract

It might seem amazing: Cutting a hole in a plate can increase the buckling strength! It is the objective of this paper to present and clarify this astounding phenomenon. In lightweight design, typically thin-walled structures are used. Therefore, buckling must be considered as a possible failure mode. One might assume that removing material, and thus, reducing stiffness must result in a reduction of the buckling strength. However, perhaps surprisingly, it can be shown that introduction of cutouts, placed appropriately, can under certain conjunctures increase buckling loads. At the same time, the structural mass is reduced. Thus, the paper presents a measure, which can be used for fulfillment of a requirement in lightweight design in a twofold manner: increase in buckling strength by reduction of mass! In addition to describing a nice theoretical peculiarity, it might be of more importance from the engineering point of view that the presented methodology may help designers of lightweight structures, e.g., for aerospace applications, to place openings, which are required for some reasons in a plate being part of the construction, at such positions, at which the plate’s buckling resistance is just slightly or not at all reduced or even increased, and to avoid placing holes in unfavorable areas. Based on the Rayleigh–Ritz method in terms of the Rayleigh quotient, criteria and procedures are derived which can be used to find beneficial positions for cutouts and such ones, at which cutouts should not be placed.