First-order GBT for thin-walled members with arbitrary cross-section and circular axis

Abstract

This work assesses the first-order behavior of thin-walled bars with deformable cross-section and circular axis, without pre-twist, with the help of the Generalised Beam Theory (GBT) formulation previously developed by the authors (which dealt only with simple cross-sections without distortional deformation). Moreover, this paper presents a novel and systematic procedure to obtain the deformation modes for arbitrary flat-walled cross-sections (open, closed or “mixed”). The standard GBT kinematic assumptions, although much more complex than for the prismatic case, are employed to subdivide the modes in a meaningful way, maintaining the same nomenclature used for prismatic bars, and to reduce the number of DOFs necessary to achieve accurate results. It is also shown that the curvature of the bar has a significant influence on the deformation mode shapes. Finally, a standard displacement-based GBT finite element (FE) is employed to solve a set of representative examples, proving the efficiency of the proposed formulation and showing the peculiar behavior of curved bars. A comparison with shell FE models is also provided for validation purposes.