平面细长梁基于无网格径向基点插值的绝对节点坐标法

摘要

In order to alleviate or eliminate the'distortion phenomenon'of the deficient beam elements in the traditional absolute nodal coordinate formulation (ANCF),an ANCF based on radial point interpolation method (RPIM) for flexible beams is proposed in which a new RPIM shape functions are constructed to describe the absolute configuration of flexible beams.For a pure bending cantilever beam (an arc),there is always difference between configuration of the beams by using the gradient deficient beam elements and the actual configuration of the beam in the traditional ANCF.The difference,namely'distortion phenomenon',becomes more obvious with the increase of the bending deformation of the beam,which may cause the pseudo strain and have serious influence on accuracy of numerical solution.In the present method,the RPIM is used to discretize the deformation field through a set of field nodes and the shape functions are generally established based on field nodes within a support domain of the calculating point.The calculating points are generally located in the central region of the support domain,and the support domain of different calculating points can have more coincident parts.Thus,the connection between field nodes is strengthened,which makes the method describe the configuration in more reasonable and effectively alleviate influence of the distortion and pseudo strain.The simulation results show that the proposed method has higher calculation accuracy and efficiency and is more adaptive for the non-equidistant nodes compared with the traditional ANCF,which can be further extended in the dynamic field of flexible multi body system.%为了消除或减弱传统绝对节点坐标法(Absolute Nodal Coordinate Formulation,ANCF)中缩减梁单元的“失真现象”,构造了一种适用于描述柔性梁绝对位形的无网格径向基点插值(Radial Point Interpolation Method,RPIM)形函数,提出了柔性梁基于无网格RPIM的ANCF法.传统ANCF梁单元在描述纯弯曲悬臂梁的位形(一段圆弧)时,即便获得精确的单元节点坐标,通过梁单元插值得到的位形与悬臂梁的实际位形存在差异,即失真现象,悬臂梁越弯曲该差异越明显,失真越大.失真导致伪应变的产生,极大地影响数值求解的精度.而RPIM法采用一组场节点离散问题域,通过计算点支持域内的场节点构造形函数,计算点一般位于支持域的中心区域,不同计算点之间的支持域有较多重合的部分,加强了节点之间的联系,能更合理、准确地描述绝对位形,能有效减小失真.研究表明:基于RPIM的ANCF法较传统ANCF法精度更高、计算效率更快、对不等距分布节点的适应性更强,在大变形柔性多体系统动力学领域内具有推广性.