Hidden symmetry concepts in the elastic buckling of axially-loaded cylinders

Abstract The recognized harmonic buckling modes for the elastic axially-loaded cylinder are by nature symmetric, equal and opposite amplitudes giving equal energy levels. On the other hand, in combination they account for considerable asymmetry, inwards deflection being fundamentally different from outwards; this asymmetry is also apparent in the underlying differential equations, and in the final large-deflection Yoshimura pattern. Taking the view that underlying symmetries are closely linked to the form of bifurcation experienced on buckling, and hence to the gross instability of the phenomenon, the paper thus explores a classic problem in a new light. The wellknown Donnell equations are first employed, the analysis being neatly written in terms of the two variables radial displacement w and stress function Φ. An extension is then presented, derived from the full strain-displacement equations appropriate to genuinely large deflections. This makes use of a suite of computer programs, written for a small micro, which handle the required manipulations of multiplication and integration of harmonic functions in algebraic rather than numerical fashion.

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