An assessment of the linear, buckling and vibration behavior of tapered polygonal tubes using GBT

Abstract This paper concerns the application of Generalized Beam Theory (GBT) to assess the structural behaviour of tapered tubes with thin‐walled regular convex polygonal section. A recent GBT formulation is employed, which can assess, with great accuracy and computational efficiency, the linear and buckling (bifurcation) behaviour of such tubes. In this paper the formulation is extended to enable obtaining natural frequencies and vibration mode shapes. It can handle genuinely tapered members and is accurate even for very high taper angles (up to 45°). Furthermore, the deformation modes of the prismatic case can be straightforwardly employed, while preserving their inextensional‐type features and the usual GBT stress/strain assumptions, essential for the overall performance of the formulation. Several numerical examples are presented to show the capabilities of the finite element implementation of the GBT formulation, through comparison with refined shell finite element model results. Furthermore, the linear, buckling and vibration behaviours of these tubes are assessed regarding global‐local‐distortional phenomena and sensitivity to key geometric parameters.