Extension of GBT to the buckling analysis of tapered regular convex polygonal tubes

Abstract

This paper extends the first-order Generalized Beam Theory (GBT) formulation for tapered regular convex polygonal tubes, recently developed by the author (Gonçalves, 2025), to the buckling (linear stability analysis) case. The proposed extension allows calculating global-distortional-local bifurcation loads and buckling modes with great accuracy and a very low computational cost, even for high taper angles, due to the fact that it inherits the key features of its first-order counterpart: (i) it uses the GBT deformation modes of the prismatic case, which have a clear physical meaning, (ii) no additional simplifications are introduced, even though the member is genuinely tapered, and (iii) the optional membrane strain assumptions of the prismatic GBT are satisfied exactly. Naturally, the proposed extension retains the unique GBT modal decomposition features, which allow a straightforward classification of the buckling mode nature (global, distortional and local). Even though the proposed formulation is necessarily complex, due to the tapered geometry, all expressions required to implement a suitable displacement-based finite element are provided in a simple vector–matrix format. The computational efficiency of the element is shown in several numerical examples, where results obtained with refined shell finite element meshes are reported for comparison purposes.