An enhanced absolute nodal coordinate formulation for efficient modeling and analysis of long torsion-free cable structures

Abstract

Long cable structures can be accurately modeled in the absolute nodal coordinate formulation (ANCF), but often at the expense of using too many degrees of freedom (DOFs). This research refines the section of node coordinates and configuration description of the element and forms an enhanced ANCF that required modeling DOFs are greatly reduced. In this formulation, the cable is treated as an elastic line and discretized with two-node elements. The gradients of all nodes and the absolute positions of only head node are selected as generalized coordinates. The gradient field of the element is linearly interpolated in nodal gradients. Unlike the traditional ANCFs, the absolute position vector of an arbitrary point of the element is calculated by evaluating an integral of the element gradient over the element length plus the position vector of the starting node of the element, instead of cubic polynomial interpolation of nodal position and gradient vectors of the element. This leads to considerable DOFs saving. Governing motion equations of the cable are derived. Benchmark examples are used to show the performance of the enhanced formulation against with the classical ANCF cable element. Comparative studies show the validity and the efficiency of the enhanced formulation.