A geometrically exact approach to lateral-torsional buckling of thin-walled beams with deformable cross-section

In this paper, a new geometrically exact beam formulation is presented, aiming at calculating buckling (bifurcation) loads of Euler–Bernoulli/Vlasov thin-walled beams with deformable cross-section. The resulting finite element is particularly efficient for problems involving coupling between lateral-torsional buckling and cross-section distortion/local-plate buckling. The kinematic description of the beam is geometrically exact and employs rotation tensors associated with both cross-section rotation and the relative rotations of the cross-section walls in the cross-section plane. Moreover, arbitrary deformation modes, complying with Kirchhoff’s assumption, are also included, which makes it possible to capture local/distortional/global buckling phenomena. Load height effects associated with cross-section rotation/deformation are also included. The examples presented throughout the paper show that the proposed beam finite element leads to accurate solutions with a relatively small number of degrees-of-freedom (deformation modes and finite elements).

► A geometrically exact beam formulation is developed. ► It calculates bifurcation loads of thin-walled beams with slender cross-section. ► Lateral-torsional-distortional-local coupling is accounted for. ► Load height effects resulting from cross-section rotation/deformation are included. ► The resulting beam element is very accurate and computationally efficient.