在绝对节点坐标缆索单元和Bézier/B样条几何体关系的基础上，构造了分段连续的ANCF缆索单元。单元形函数为分段连续函数，给出了其递推形式的定义式。单元在内节点处的连续性取决于单元节点坐标的选取以及形函数的定义方式。给出了单元弹性力及其对节点坐标雅可比矩阵的定义。进而采用该单元，建立了输电线缆架设过程中断线工况的动力学分析模型。可以实现用一个单元表示整条电缆线，从而在动力学仿真程序中避免了反复进行的单元到系统的集成及系统到单元的离散过程。用静力学分析计算得到输电线缆在重力、张紧力等外力共同作用下达到平衡时的节点坐标值，将其作为初值输入给动力学仿真程序，以模拟张紧力对输电线缆动力学行为的影响。建立了静、动力学仿真算例验证了单元的准确性，并给出了输电线缆的动力学仿真结果。
於祖庆
,
兰朋
,
李昆昆
,
陆念力
. 基于分段连续ANCF缆索单元的输电线缆动力学建模与仿真[J]. 机械工程学报, 2018
, 54(19)
: 70
-77
.
DOI: 10.3901/JME.2018.19.070
Based on the relationship between ANCF cable element and Bézier/B-spline curve, the concept of piecewise ANCF cable element is proposed. The recursive form of the element shape function with arbitrary number of inner nodes is presented. The continuity condition of the element on a inner node can be automatically included in the selection of nodal vectors and definition of the element shape function. The elastic force and its Jacobian matrix with respect to the nodal coordinates are derived. The new element is used to model the high voltage wire when the rupture accident happens. Only one element is required to model the entire wire. As a result, the integration and the discretization between the finite elements and the whole system can be omitted. The static analysis is performed to obtain the nodal coordinate when the element achieves equilibrium under the external force. Then the nodal coordinate is used as the initial value in the dynamic analysis so the effect of the tensile force can be accounted for. The numerical examples are proposed to demonstrate the feasibility of the element. The result of the high voltage wire is also presented.
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