GBT pre-buckling and buckling analyses of thin-walled members under axial and transverse loads

Convergence of Hencky-Type Discrete Beam Model to Euler Inextensible Elastica in Large Deformation: Rigorous Proof

“…We proved a Γ-convergence result for a Hencky-type discretization of an inextensible Euler beam in large deformation regime. Future investigations should generalize the result (in a suitable form) for extensible beam models; moreover, it will be interesting to extend the convergence argument to Generalized Beam Models ( [32,31,30,25]) and also to the dynamics of the dicrete system, which should of course take into account the possibility of various kinds of dynamic instabilities ( [43,27,26]). Finally, it has to be remarked that Hencky-type discretization for Elastica has proven to be very effective, and is in fact used by several computational software packages (as for instance by MATLAB ).…”

Generalised Beam Theory for composite beams with longitudinal and transverse partial interaction

“…In the spirit of the dynamic GBT approach [73][74][75][76][77][78][79][80][81], the deformation modes will be determined from the free dynamics of an unrestrained planar frame model, representing the cross-section with its plates located at their mid-lines. In this context, two eigenvalue problems will be considered, namely (a) the planar eigenvalue problem and (b) the warping eigenvalue problem, which are aimed at the identification of the conventional and extension modes, and of the warping eigenmodes, respectively.…”

“…Its novelty relies on the ability to account for both longitudinal and transverse partial interaction taking place within the plane of the shear connection interface in the evaluation of the GBT deformation modes, therefore extending the applicability of a longitudinal partial interaction model developed by the authors [73]. This method falls within a category of cross-sectional analyses available in the literature for which a suitable set of deformation modes, including conventional, extension and shear, is determined from dynamic analyses of discrete planar frame models representing the cross-section [74][75][76][77][78][79][80][81]. The transverse partial interaction is described by means of shear deformable spring elements and is accounted for in the planar dynamic analysis during the evaluation of the conventional and extension modes, while the longitudinal partial interaction behaviour associated with the shear modes is included in the out-of-plane dynamic analyses.…”

A thin-walled beam element based on semi-analytical solution modes

“…Since then, different academic groups have contributed to its development -e.g. Simão & da Silva [11], the group around Camotim [12,13,14,15,16,17], or by Ranzi and his colleges [18,19] just to mention some of the many contributors. The general idea of GBT is to represent and discretise the cross-section along the wall centre line to find distortional transverse displacement modes that have orthogonal warping modes.…”