We present a novel consistent singularity-free strain-based finite element formulation for the analysis of three-dimensional frame-like structures. Our model is based on a geometrically exact finite-strain beam theory, quaternion parametrization of spatial rotations, assumption that the strain measures are constant along the length of the element and a proper choice of basis for the translational strain vector representation. As it is common for strain-based elements, the present formulation does not suffer from shear locking. A comparison of our results with the results from the literature and a commercial finite element analysis software demonstrates the advantages of the proposed formulation, especially when the structure is subjected to larger shear deformations. This stems from the fact that our model ensures a mathematically consistent updating procedure for all the quantities describing the beam. This aspect is often overlooked, since most of the numerical cases from other studies on this topic engage rather small-shear strains for which the consistent update is not crucial as the number of elements is increased.

中文翻译：

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具有四元数旋转表示的一致的基于应变的梁单元

我们提出了一种新颖的基于一致无奇异性应变的有限元公式，用于分析三维框架状结构。我们的模型基于几何上精确的有限应变光束理论，空间旋转的四元数参数化，假设应变测量沿元素的长度和平移应职载体表示的正确选择。由于基于应变的单元很常见，因此本公式不会受到剪切锁定的影响。我们的结果与文献结果和商业有限元分析软件的比较表明了所提出的公式的优点，特别是当结构受到较大的剪切变形时。这源于这样一个事实，即我们的模型确保了描述光束的所有数量在数学上一致的更新程序。这方面经常被忽视，因为大多数关于这个主题的其他研究的数值案例涉及相当小的剪切应变，随着元素数量的增加，一致的更新并不重要。