Based on more than three decades of rod finite element theory, this publication unifies all the successful contributions found in literature and eradicates the arising drawbacks like loss of objectivity, locking, path-dependence and redundant coordinates. Specifically, the idea of interpolating the nodal orientations using relative rotation vectors, proposed by Crisfield and Jeleni\'c in 1999, is extended to the interpolation of nodal Euclidean transformation matrices with the aid of relative twists; a strategy that arises from the SE(3)-structure of the Cosserat rod kinematics. Applying a Petrov-Galerkin projection method, we propose a novel rod finite element formulation where the virtual displacements and rotations as well as the translational and angular velocities are interpolated instead of using the consistent variations and time-derivatives of the introduced interpolation formula. Properties such as the intrinsic absence of locking, preservation of objectivity after discretization and parametrization in terms of a minimal number of nodal unknowns are demonstrated by conclusive numerical examples in both statics and dynamics.

翻译：基于三十余年的杆有限元理论，本文统一了文献中所有成功的研究成果，并消除了由此产生的客观性丧失、锁死、路径依赖及冗余坐标等缺陷。具体而言，将Crisfield与Jelenić于1999年提出的利用相对旋转矢量插值节点方位的思想，推广至借助相对扭转插值节点欧几里得变换矩阵——这一策略源于Cosserat杆运动学的SE(3)结构。通过应用Petrov-Galerkin投影方法，我们提出一种新型杆有限元公式：不对引入的插值公式进行一致变分与时间导数计算，而是对虚位移、虚转动以及平动速度、角速度进行插值。静力学与动力学中的决定性数值算例证明了该方法的内蕴无锁死性、离散后客观性保持能力以及以最少节点未知量进行参数化的特性。