Generalised Beam Theory formulation for the buckling analysis of thin-walled members with circular axis

This paper presents an extension of Generalised Beam Theory (GBT) that enables performing buckling (bifurcation) analyses of thin-walled members with circular axis (and no pre-twist). The bifurcation eigenvalue problem is obtained by applying the linear stability analysis concept to the non-linear equilibrium equations, while incorporating the classic GBT kinematic assumptions, which are essential to obtain significant computational savings. A displacement-based finite element is proposed and used to assess the accuracy and efficiency of the developed GBT formulation in several illustrative numerical examples involving complex global-distortional-local buckling. It is shown that the proposed finite element leads to results that match accurately those obtained with refined shell finite element models (such refinement is essential to obtain correct solutions in curved members), but with much less DOFs. Moreover, it is also shown that the GBT modal features can provide an in-depth insight into the nature of the buckling modes in curved members.