A Geometric Nonlinear Calculation Method for Spatial Suspension Cable

doi:10.3901/JME.2022.09.147

Abstract

Abstract: The radius vector and tangent vector of the two nodes of the element are used as the description variables to discretize the spatial suspension cable, and the Hermite interpolation is used to establish the suspension cable element. Based on the physical fact that the curvature of the suspension cable is continuous, the second derivative of the radius vector of the common node is continuous. The tangent vector of the middle nodes is expressed by the radius vector and tangent vector of the two ending nodes, which reduces the system freedom. According to the principle of virtual power, the nonlinear equilibrium equation of spatial suspension cable is established. The time derivative of the equation and the Jacobian matrix of the system equation are obtained. The initial shape of suspension cable is established by using three-point parabola to approximate catenary, and the initial value of nonlinear equation is obtained. For the suspension cable with only gravity and known initial length without strain, the load at both ends of suspension cable is calculated by balancing the ending load and gravity. On this basis, the initial length of the suspension without strain can be calculated under the condition of the load at one end of the cable. A geometric nonlinear method of spatial flexible suspension cable is proposed. The reliability of the method is verified by numerical examples. A new method is provided for the calculation of spatial static suspension cable.

Key words: spatial suspension cable, geometric nonlinear, principle virtual power, initial length without strain

CLC Number:

TH213

XU Jinshuai, QI Zhaohui, ZHUO Yingpeng, ZHAO Tianjiao, TENG Rumin. A Geometric Nonlinear Calculation Method for Spatial Suspension Cable[J]. Journal of Mechanical Engineering, 2022, 58(9): 147-156.

References

[1] ZIENKIEWICZ O, TAYLOR R, ZHU J. The finite element method: its basis and fundamentals[M]. Amsterdam: Elsevier Science, 2013.
[2] ZIENKIEWICZ O, TAYLOR R. The finite element method for solid and structural mechanics[M]. Amsterdam: Elsevier Science, 2013.
[3] TAN Dongyao, GUO Hua. Review of suspension mechanics[J]. Journal of Harbin University of Civil Engineering and Architecture, 1985(2): 102-120. 谭东耀, 郭骅. 悬索力学研究综述[J]. 哈尔滨建筑工程学院学报, 1985(2): 102-120.
[4] QIAN Weichang. Generalized variational principle[M]. Shanghai: Knowledge Publishing Press, 1985. 钱伟长. 广义变分原理[M]. 上海: 知识出版社, 1985.
[5] 王勖成. 有限单元法[M]. 北京: 清华大学出版社, 2013.
[6] SHEN Jian, HAN Feng, CHEN Fang, et al. Modeling and simulation of flexible cable-body by absolute nodal coordinate formulation[J]. Science Technology and Engineering, 2016, 16(31): 1-7. 沈剑, 韩峰, 陈放, 等. 基于绝对节点坐标法的柔性绳索体建模仿真研究[J]. 科学技术与工程, 2016, 16(31): 1-7.
[7] WANG Dan, LIU Jiaxin. Application of the catenary curve's equation in common condition[J]. Ship & Ocean Engineering, 2007(3): 26-28. 王丹, 刘家新. 一般状态下悬链线方程的应用[J]. 船海工程, 2007(3): 26-28.
[8] YUAN Jianming, YIN Feng, LI Yongzhi, et al Application of suspension cable length calculation in crane wire rope[J]. Hoisting and Transportation Machinery, 2010 (8): 7-9 袁建明, 尹锋, 李勇智, 等. 悬索长度计算在起重机钢丝绳中的应用[J]. 起重运输机械, 2010(8): 7-9.
[9] JAYARAMAN H, KNUDSON W. A curved element for the analysis of cable structures[J]. Pergamon, 1981, 14(3-4).
[10] LIU Xiao. Nonlinear analysis of large span cable structure using a two-node curved element [D]. Nanning: Guangxi University, 2004. 刘晓. 大跨度悬索结构正弦曲线单元几何非线性分析[D]. 南宁: 广西大学, 2004.
[11] HU Song, HE Yanli, WANG Zhaomin. Nonlinear analysis of flexible cable structures using the finite element method[J]. Engineering Mechanics, 2000(2): 36-43. 胡松, 何艳丽, 王肇民. 大挠度索结构的非线性有限元分析[J]. 工程力学, 2000(2): 36-43.
[12] YANG Menggang, CHEN Zhengqing. The nonlinear finite element analysis for two-node catenary of cable structure based on UL formulation[J]. China Civil Engineering Journal, 2003(8): 63-68. 杨孟刚, 陈政清. 基于UL列式的两节点悬链线索元非线性有限元分析[J]. 土木工程学报, 2003(8): 63-68.
[13] KNUDSON W. Static and dynamic analysis of cable-net structures[D]. Califormia: University of Califormia, Berkely, 1971.
[14] WANG Han, XIE De. Analysis and experimental verification of the catenary component with the finite element method[J]. Chinese Journal of Ship Research, 2015, 10(6): 34-38. 王瀚, 解德. 悬链线构件的有限元方法[J]. 中国舰船研究, 2015, 10(6): 34-38.
[15] TANG Jianmin, ZHUO Jiashou. An improved two-node cable element for large deformation analysis of cable structures[J]. Journal of Hohai University, 1999(4): 16-19. 唐建民, 卓家寿. 悬索结构大位移分析改进的两节点索单元模型[J]. 河海大学学报, 1999(4): 16-19.
[16] YUAN Xingfei, DONG Shilin. A two-node curved cable element for nonlinear analysis[J]. Engineering Mechanics, 1999(4): 59-64, 46. 袁行飞, 董石麟. 二节点曲线索单元非线性分析[J]. 工程力学, 1999(4): 59-64, 46.
[17] SU Wenzhang. The nonlinear finite element analysis of cable structures[D]. Chongqing: Chongqing University, 2005. 苏文章. 悬索结构的非线性有限元分析[D]. 重庆: 重庆大学, 2005.
[18] TANG J, SHEN Z, QIAN R. A nonlinear finite element method with five-node element for analysis of cable structures[J]. Proceedings of the LASS International Symposium, 1995, 2: 929-935.
[19] YANG W, SHEN R, CHONG W. A finite element method with six-node isoparametric element for nonlinear analysis of cable structures[J]. Applied Mechanics and Materials, 2013, 2212.
[20] CHI Haibo, CHEN Li, WANG Dianlong, et al. Research on the method about guy-rope pretightening of all terrain crane[J]. Construction Machinery, 2013(11): 90-93, 12. 迟海波, 陈礼, 王殿龙, 等. 全地面起重机超起拉索预紧计算方法研究[J]. 建筑机械, 2013(11): 90-93, 12.
[21] PAN Chenggong. Research on boom structure and superlift system of all terrain tuck crane[D]. Changchun: Jilin University, 2014. 潘成功. 全地面起重机臂架及超起结构研究[D]. 长春: 吉林大学, 2014.
[22] JAYARAMAN H, KNUDSON W. A curved element for the analysis of cable structures[J]. Pergamon, 1981, 14(3-4).
[23] NIE Jianguo, CHEN Bilei, XIAO Jianchun. An improved algorithm for catenary cable element[J]. Mechanics in Engineering, 2003(4): 28-32. 聂建国, 陈必磊, 肖建春. 悬链线索单元算法的改进[J]. 力学与实践, 2003(4): 28-32.
[24] WANG Jing. Research on dynamics modeling and simulation of cable-pulley multibody systems[D]. Dalian: Dalian University of Technology, 2017. 汪菁. 滑轮绳索多体系统的动力学建模与仿真研究[D]. 大连: 大连理工大学, 2017.
[25] WANG Gang, QI Zhaohui, WANG Xin. Load-carrying capacity of hinged boom structures for crawler cranes[J]. Journal of Mechanical Engineering, 2015, 51(3): 111-120. 王刚, 齐朝晖, 王欣. 履带式起重机折线式臂架结构承载能力[J]. 机械工程学报, 2015, 51(3): 111-120.
[26] YAN Zhitao, LIU Caolan, LI Zhengliang. Non-linear finite element analysis based on the spatial catenary cables[J]. Journal of Chongqing University, 2010, 33(10): 64-69. 晏致涛, 刘操兰, 李正良. 空间悬链线索单元的非线性有限元分析[J]. 重庆大学学报, 2010, 33(10): 64-69.
[27] NING Wei, WANG Jin. Study on calculation methods of lifting capacity for big tonnage mobile crane[J]. Journal of Mechanical Engineering, 2017, 53(13): 90-100. 宁玮, 王瑾. 大吨位汽车起重机起重性能计算方法研究[J]. 机械工程学报, 2017, 53(13): 90-100.