Keywords: generalised beam theory, thin-walled structures, buckling behaviour, post-buckling behaviour, vibration behaviour, shell finite element analysis.

This paper presents a state-of-the-art review on the most recent developments concerning formulations, numerical implementations and applications of generalised beam theory (GBT) to analyse the structural response of thin-walled members and frames. GBT extends Vlasov's classical thin-walled beam theory to incorporate cross-section deformations (wall flexure and distortion), making it possible to obtain very elegant and illuminating solutions for a wealth of structural problems.

Besides presenting a brief, but insightful, overview of the fundamental concepts and main procedures involved in the performance of a GBT analysis, the paper (i) provides accounts of the novel GBT formulations that were developed and numerically implemented (beam finite elements) in recent years, (ii) includes illustrative examples demonstrating the capabilities and potential of these approaches, and (iii) addresses the research work dealing with GBT developments that is currently under way. In particular, the new findings reported are related to GBT formulations intended to analyse (i) the buckling and post-buckling behaviour of open-section (i1) isotropic members and frames with arbitrary loading and support conditions (including non-uniform bending and localised constraints), and (i2) orthotropic members with standard supports and acted by uniform loadings, and (ii) the vibration behaviour of isotropic/orthotropic load-free and loaded open-section members. For validation and efficiency assessment purposes, most of the GBT-based numerical results presented are compared with values yielded by shell (mostly) and beam finite element analyses carried out using the codes ABAQUS and ANSYS. Despite the huge difference between the numbers of degrees of freedom involved in the two analyses, an excellent agreement was invariably found. Therefore, it seems fair to say that the novel GBT-based approaches (i) exhibit a high numerical efficiency and, due to their unique modal nature, (ii) provide the means to obtain fresh in-depth insight into the mechanics of the member and frame structural behaviour.

Finally, some developments currently under way and/or planned for the near future are briefly mentioned. They include formulations intended to enable the performance of (i) local, distortional and global post-buckling analyses of complex space steel frames, (ii) buckling and post-buckling analyses of frames built from RHS (rectangular hollow section) members, (iii) localised buckling and post-buckling analyses of members and frames under patch loading and/or loaded away from the shear centre axis, (iv) vibration analyses of load-free and loaded thin-walled steel frames, (v) doubly-modal dynamic analyses of open and closed-section beams and bridges, and (vi) first-order, buckling and post-buckling analyses of elastic-plastic thin-walled steel members and frames (adopting first a "spatial plastic hinge approach").

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