基于共旋坐标的平面大变形梁递推方法

摘要

基于共旋坐标法提出了一种大变形梁递推建模方法,用于解决含有大变形梁的柔性多体系统的动力学问题.传统递推方法与浮动做标法相结合,已应用于柔性多体系统的小变形问题.本文将递推方法与共旋坐标相结合,把传统递推方法中物体之间的递推拓展到单元之间的递推,利用共旋坐标法能高效地解决大变形问题的优点,使得所提的递推方法可应用于梁的大变形问题.递推方法优点为获得的是一个 O(N)阶的动力学方程,N 为系统的自由度,这意味着动力学方程求解时间随着 N 线性增长,使得该方法能在解决大体量的问题时具有较高的计算效率.通过静力学以及动力学的算例验证所提方法的正确性与效率.研究结果表明,所提方法在解决平面大变形梁问题上具有较高的精度和效率.%A forward recursive formulation based on corotational frame is proposed for flexible planar beams with large displacement. The traditional recursive formulation has been successfully used for flexible mutibody dynamics to improve the computational efficiency based on floating frame, in which the assumption of small strain and deflection is adopted. The proposed recursive formulation could be used for large displacement problems based on the corotational frame. It means that the recursive scheme is used not only for adjacent bodies but also for adjacent beam elements. The nodal relative rotation coordinates of the planar beam are used to obtain equations with minimal generalized coordinates in present formulation. The proposed formulation is different from absolute nodal coordinate formulation and the geometrically exact beam formulation in which the absolute coordinates are used. The recursive scheme and minimal set of dynamic equations lead to a high computational efficiency in numerical integration. Numerical examples are carried out to demonstrate the accuracy and validity of this formulation. For all of the examples, the results of the present formulation are in good agreement with results obtained using commercial software and the published results. Moreover, it is shown that the present formulation is more efficient than the formulation in ANSYS based on GEBF.