This paper presents a geometrically exact beam finite element for curved and twisted thin-walled bars undergoing large displacements and finite rotations, combined with cross-section in-plane and out-of-plane (warping) deformation. The underlying formulation is based on a previous work by the authors Gonçalves et al. (2010), which is now improved and extended for the pre-curved/twisted case. Cross-section deformation is allowed for by adding kinematic DOFs, the so-called “cross-section deformation modes”, which are obtained using Generalised Beam Theory. All expressions required to implement the proposed finite element are derived. For validation purposes, several numerical examples are presented and discussed. In each case, the results obtained with the proposed element and refined shell finite element models are compared, and an excellent agreement is found. In particular, it is demonstrated that the proposed element predicts very accurately the spatial behaviour of curved beams undergoing complex coupling between large displacements, finite rotations and cross-section deformation.

本文提出了一种几何精确的梁有限元，用于弯曲和扭曲的薄壁钢筋，它们经受大的位移和有限的旋转，并结合横截面的平面内和平面外（翘曲）变形。基本表述基于作者Gonçalves等人的先前工作。（2010），现在针对预弯曲/扭曲情况进行了改进和扩展。通过添加运动自由度可以实现横截面变形，所谓的“横截面变形模式”是使用广义梁理论获得的。导出了实现所提出的有限元所需的所有表达式。为了验证，给出并讨论了几个数值示例。在每种情况下，都将所提出的元素和精炼的壳有限元模型获得的结果进行比较，并找到了很好的一致性。特别地，证明了所提出的元件非常准确地预测了在大位移，有限旋转和横截面变形之间经历复杂耦合的弯曲梁的空间行为。