A Non-linear Theory of Thin-Walled Rods of Open Profile Deduced with Incremental Shell Equations

We study the structural behaviour of rods with thin-walled open cross-sections. Such members are best known for their low torsional rigidity and extensive warping deformation when subjected to twisting. Proceeding to large deformations one needs to account for the geometrically non-linear effects in the cross-section, that affect the structural response and prevent a simple generalisation of the linear theory. We here further elaborate a novel approach that utilizes the equations of incremental shell theory to quantify these non-linear effects and incorporate them into an augmented beam theory, which is then put to test on an example of a circularly curved rod. The linear deformation analysis reveals, that arbitrarily curved and straight rods do not share the same asymptotic behaviour. The torsional-flexural buckling loads obtained with the incremental beam theory correspond well to reference computations with shell finite elements, given that subcritical pre-deformations are negligible. The narration concludes with the post-buckling analysis using shell finite elements.