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<p>The curved beam elements are widely used in many engineering fields. A 3D corotational constant curvature curved beam element formulated on the special Euclidean group <i>SE</i>(3) is proposed for geometrically nonlinear static and dynamic analysis. The existing corotational framework developed for the straight beam is not suitable for the curved beam. Therefore, a modified framework is presented for the curved beam by introducing the local kinematic transformations. The same kinematic description and spatial discretization scheme are employed in deriving the internal and inertial forces to preserve consistency. In contrast to the straight beam element using simplified acceleration, the curved beam element considers all the acceleration terms in the inertial force. Based on the principle of virtual work, the equations of motion are established in the context of <i>SE</i>(3). The fundamental properties, such as the absence of locking and path-independence of the presented curved beam element, are verified by numerical examples. In addition, it indicates that this element can be used for modeling both constant and varying curvature structures. The accuracy superiority over the conventional straight beam element is also illustrated. Moreover, it reveals the necessity of considering the complete acceleration in the inertial force for the curved beam element.</p>

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A 3D corotational curved beam element formulated on SE(3) group for geometrically nonlinear static and dynamic analysis

  • 期刊论文

  • 发表日期：

    2025年8月28日

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  • Boyang Wang,
  • Zhuyong Liu,
  • Ziqi Ma,
  • Shihao Xu

摘要

The curved beam elements are widely used in many engineering fields. A 3D corotational constant curvature curved beam element formulated on the special Euclidean group SE(3) is proposed for geometrically nonlinear static and dynamic analysis. The existing corotational framework developed for the straight beam is not suitable for the curved beam. Therefore, a modified framework is presented for the curved beam by introducing the local kinematic transformations. The same kinematic description and spatial discretization scheme are employed in deriving the internal and inertial forces to preserve consistency. In contrast to the straight beam element using simplified acceleration, the curved beam element considers all the acceleration terms in the inertial force. Based on the principle of virtual work, the equations of motion are established in the context of SE(3). The fundamental properties, such as the absence of locking and path-independence of the presented curved beam element, are verified by numerical examples. In addition, it indicates that this element can be used for modeling both constant and varying curvature structures. The accuracy superiority over the conventional straight beam element is also illustrated. Moreover, it reveals the necessity of considering the complete acceleration in the inertial force for the curved beam element.