CONTINUITY CONTROL METHOD FOR RANCF CIRCULAR ARC ELEMENTS

Conventional finite element methods, together with the absolute nodal coordinate formulation (ANCF), are subject to inherent limitations in the accurate geometric representation of circular-arc structures. For key components with circular-arc geometric features that are commonly encountered in engineering fields such as aerospace and robotics, including ring brackets, curved guide rails, and springs, it is typically necessary to employ a multi-segment discretization, whereby the underlying circular arc is approximated piecewise by multiple elements. However, such a multi-segment approximation not only degrades the geometric consistency of flexible system models and introduces non-negligible deviations in the predicted dynamic responses, but also substantially increases the element count and the overall computational cost. To address the above issues, this study proposes a direct global-coordinate definition method for a standard circular arc element, according to its geometric characteristics, based on the rational absolute nodal coordinate formulation (RANCF). Inter-element continuity constraints and the corresponding control strategy between adjacent elements are further formulated. By explicitly introducing the unit normal vector \boldsymbol\nu associated with the plane in which each circular-arc element is embedded, together with the scalar magnitude λ of the element gradient vector, the proposed formulation provides a clear and unambiguous geometric characterization of the element, thereby guaranteeing the uniqueness of the circular-arc element definition. In addition, these two geometric descriptors allow the continuity constraints at inter-element junctions to be expressed in a more direct manner, which substantially simplifies the practical procedure for enforcing and controlling continuity at connection points. As a result, further enhances the overall geometric consistency, and controllability of the modeling process. Furthermore, a curved-beam pendulum model and a flexible circular-arch model are employed as representative examples to comparatively investigate the dynamic responses and solution efficiency under different continuity conditions (C¹ and C²). The simulation results demonstrate that the C² curvature-continuous model exhibits a pronounced advantage in the efficiency and numerical stability of dynamic simulations, thereby providing a practical modeling and analysis approach for engineering simulations of flexible components with circular-arc geometric features.