Buckling of Structures [antikvár]

Ciinent Trends in the Theory of Bnckling AV. T. Koiter Technische Hogescliool, Delft, Netherlands Abstract Some cmi-ent trends in buckling theory are reviewed. Particular attention is given to multi-mode bifurcation buckling, the associated imperfection-sensitivity and the correlation of experimental evidence with theory. 1. Introduction The task of a speaker in an opening lecture at a meeting of selected experts in a particular field of science is hardly to be envied. In most aspects of liis topic the audience comprises members with far more specialized expertise than the lecturer has at his command, and the easy way out, a retreat into generalities, is not likely to be welcomed. Having accepted the challenge, however, I shall try and review some current trends in the tlieory of buckling as I see them. I had the good fortune to read tlie abstracts of your papers which our chairman kindly made available to me, and this may reduce to some extent the inevitable personal bias in my talk. The simplest possible model of a column, depicted in Fig. la, consists of a rigid bar supported on an elastic hinge. This simple model is employed in several elementary text-books, including the author's [28] which, incidentally, enjoys sales comparable to a volume of poetry. The perfect column, with zero eccentricity of the applied load (e = y.L = 0), loses its stability and buckles by bifurcation at the critical load i'j = D\L. The ]5ost-buokling behaviour depends on nonlinearities in the spring characteristic. Various possible load-deflection curves are shown in Fig. 1 b, and the relationship between tlie load and the overall shortening is exhibited in Fig. Ic. In cases of an unstable descending post-buckling path (a =|= 0 or « = 0, /3 < —1/6) the column is sensitive to geometric imperfections or load eccentricity. The associated drop in critical load is shown in Fig. 1 d, and the buckling load F-^ at the bifurcation point is replaced by the snap load at a limit point. In the absence of a descending post-buckling path of the perfect column, however, no loss of stability occurs in the column with imperfections or