A Geometrically Exact Beam Finite Element for Non-Prismatic Strip Beams: The Spatial Case

Abstract

A new beam finite element for non-prismatic (tapered and curved) beams with thin rectangular cross-section (“strip” beams) is proposed in this paper. The element is geometrically exact and constitutes the extension, to the large 3D displacement and rotation setting, of those proposed by the author for the 2D [R. Gonçalves, Int. J. Struct. Stab. Dyn. 23 (2022) 2350037] and linearized lateral-torsional buckling [R. Gonçalves, Int. J. Struct. Stab. Dyn. 23(12) (2023) 2350139] cases. The element incorporates torsion-related warping, as well as arbitrary mid-line warping, and allows nonlinear tapered geometries, arbitrary initially curved configurations (including pre-twist) and eccentric loads (loads offset from the centroid). All expressions required to implement the proposed element are given in a straightforward vector/matrix format. Several numerical tests are presented to show that the element has a very good predictive capability and a low computational cost, when compared with solutions obtained with refined shell finite element meshes, even for members with a high taper ratio and initial curvature.