Finite Element Formulation for Modelling a Frictional Sliding Cable Element

A novel sliding cable element that takes friction into account is presented to solve the analysis problem, such as the slider reefing parachute systems, the suspended cable systems and the space net systems. According to the force analysis of the slider point, a formulation is obtained, which aims to calculate the tension on both sides of the slider point using the node coordinates. Based on this formula, the principle of virtual work, the finite element method, the generalized node internal force, the body force, and the time-dependent mass matrices are derived. Two classic validation problems with analytical solutions are used for the comparison of the solutions between the analytical method and the finite element method, as well as for the comparison of the solutions with or without friction. The comparison results show that the sliding cable element is theoretically correct and that the results without considering friction are unreliable. A new approach using the sliding cable element for the accurate friction test of the space net was presented for the analysis of the two-stage projection scheme; the result indicated that the accuracy of the experimental data processing is improved. Introduction Mechanical problems from a sliding cable with friction arise in many engineering fields, such as electrical transmission lines[1, 2], protection structures[3], suspended roofing systems[4, 5] and tensioned fabric membranes[6, 7], suspended cable systems[8-10], and parachute systems[11], as well as the analysis of the space net. The sliding cable element is the core analysis method used to solve these problems. According to the main features of a cable in practical projects, numerous sliding cable elements have been proposed. The existing sliding cable elements can be divided into three-node elements and mufti-node elements. Regarding the three-node element, the central sliding node comprised of the two end node and the three-node element include the model of Aufaure[2], Zhou et al.[11]. The element proposed by Aufaure only allows sliding between two end nodes, and the element developed by Zhou allows continuous sliding with the remeshing algorithm and the searching algorithm. For the application of large-scale cable structures, the muti-node model[4, 12] was proposed to avoid assembling several single-slider elements for the analysis of systems containing multiple sliding nodes. For either the three-node element or the muti-node element, the friction is not taken into account. However, in many cases, friction has a large influence on the dynamic behavior of the system, and the frictionless model may yield unrealistic results; two validation problems have been used to show the influence of the friction in this paper. The sliding cable model proposed by Jibril[12] takes friction into account based on the unstretched length conservation constraint. However, this model ignores the inertia of the cable; when the inertia of the sliding cable cannot be ignored, errors occur in the simulation results. A three-node sliding cable element able to take friction into account is proposed in this paper. Since the remeshing algorithm and the searching algorithm have been proved to be stable and robust in the work of Zhou, the focus of this paper is to establish the dynamic equation of the sliding cable element considering friction. In section 2, by analyzing the tension on the two sides of the sliding point when it is sliding with friction, this paper proposes a formula that can calculate the tension on International Conference on Modeling, Analysis, Simulation Technologies and Applications (MASTA 2019) Copyright © 2019, the Authors. Published by Atlantis Press. This is an open access article under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/). Advances in Intelligent Systems Research, volume 168