A Geometrically Exact Beam Finite Element for Non-Prismatic Strip Beams: Linearized Lateral-Torsional Stability

Abstract

This paper presents a new geometrically exact beam finite element able to perform, accurately and efficiently, linear stability analyses of curved and tapered elastic strip beams (beams with thin rectangular cross-section) susceptible to lateral-torsional bucking. This element constitutes a non-trivial extension, to the spatial (3D) case, of that previously reported by the author for the in-plane (2D) case in Gonçalves [R. Gonçalves, A geometrically exact beam finite element for non-prismatic strip beams: The 2D case, Int. J. Struct. Stab. Dyn. (2022) 2350037]. To allow capturing accurately torsion effects, a torsion-related warping function is derived and included as an additional cross-section degree-of-freedom (DOF). Since the element is developed using a geometrically exact framework, complex effects such as load height and out-of-plane flexural-torsional effects are straightforwardly included. For implementation purposes, all fundamental expressions are provided in simple vector/matrix forms. A set of numerical examples is presented and discussed, to show that the proposed element provides very accurate solutions with a small DOF number, even for heavily curved and tapered members.