Abstract Based on a formulation on the special Euclidean group S E ( 3 ) , a geometrically exact thin-walled beam with an arbitrary open cross-section is proposed to deal with the finite deformation and rotation issues. The beam strains are based on a kinematic assumption where warping deformation and Wagner effects are included such that the nonlinear behavior of a thin-walled beam is predicted accurately, particular under large torsion. To reduce the nonlinearity of rigid motion, static and dynamic equations are derived in the S E ( 3 ) framework based on the local frame approach. As the value of the iteration matrix, including the Jacobian matrix of inertial and internal forces, is invariable under arbitrary rigid motion, the number of updates required during the computation process decreases sharply, which drastically improves the computational efficiency. Furthermore, the isogeometric analysis (IGA) based on the non-uniform rational B-splines (NURBS) basis functions, which promotes the integration of computer-aided design (CAD) and computer-aided engineering (CAE), is adopted to interpolate the displacement, rotation, and warping fields separately. The interpolated strain measures satisfy the objectivity by removing the rigid motion of the reference point. To obtain the symmetric Jacobian matrix of internal forces, the linearization operation is conducted based on the previously converged configuration. A Lie group S E ( 3 ) extension of the generalized- α time integration method is utilized to solve the equations of motion for thin-walled beams. Finally, the proposed formulation is successfully tested and validated in several static and dynamic numerical examples.

中文翻译：

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几何精确的薄壁梁，包括在特殊欧几里德群 SE(3) 上制定的翘曲

摘要 基于特殊欧几里得群SE ( 3 ) 的公式，提出了一种几何精确的具有任意开截面的薄壁梁来解决有限变形和旋转问题。梁应变基于运动学假设，其中包括翘曲变形和瓦格纳效应，以便准确预测薄壁梁的非线性行为，特别是在大扭矩下。为了减少刚性运动的非线性，基于局部框架方法在SE(3)框架中推导出静态和动态方程。由于迭代矩阵的值，包括惯性力和内力的雅可比矩阵，在任意刚性运动下是不变的，计算过程中所需的更新次数急剧减少，这极大地提高了计算效率。此外，基于非均匀有理 B 样条 (NURBS) 基函数的等几何分析 (IGA)，促进了计算机辅助设计 (CAD) 和计算机辅助工程 (CAE) 的集成，用于插值位移、旋转和翘曲场分开。内插应变测量通过去除参考点的刚性运动来满足客观性。为了获得对称的内力雅可比矩阵，基于先前收敛的配置进行线性化操作。利用广义α时间积分法的李群SE(3)扩展来求解薄壁梁的运动方程。最后，