Modal buckling behaviour of long polygonal tubes in uniform torsion using the generalised cFSM

Abstract

The buckling behaviour of thin-walled tubes with regular convex polygonal sections (hereafter the “convex” will be implied) has been analysed a number of times over the last half a century, yet literature on such members in torsion has traditionally been lacking. Despite recent advances, there is still significant scope to further expand understanding of the behaviour of these members in torsion. Using the generalised constrained finite strip method (cFSM) and a semi-analytical finite strip method (FSM) that utilises an augmented longitudinal displacement field of sines and cosines, the elastic buckling behaviour of long regular polygonal tubes in uniform torsion is assessed. The analysed polygons all have the same centreline perimeter and uniform thickness of constituent plate elements. It is found that the signature curves of critical stress vs. buckling half-wavelength converge as the number of sides in the tube is increased and that notable differences between the signature curves of tubes with consecutive numbers of sides occur at shorter and shorter half-wavelengths as the number of sides is increased, due to the decreasing width of the individual flats and also the occurrence of an increasing number of distortional modes. At very long half-wavelengths flexural buckling occurs in a helical-like manner, similar to the twisting of a hosepipe. The mechanics of this buckling mode are briefly investigated and it is noted that it is necessary to include all of the non-linear components of the in-plane shear strain, as opposed to only the flexural components, in order to obtain accurate solutions for this mode. Results for pure local and pure distortional buckling are also compared to those obtained via Generalised Beam Theory (GBT).