基于线性互补理论的可展开索-桁架结构静力学分析

doi:10.3901/JME.2022.05.018

机械工程学报 ›› 2022, Vol. 58 ›› Issue (5): 18-25.doi: 10.3901/JME.2022.05.018

扫码分享

基于线性互补理论的可展开索-桁架结构静力学分析

肖航, 吕胜男, 李龙, 罗斯达, 段海滨, 丁希仑

北京航空航天大学机械工程及自动化学院北京 100191

收稿日期:2021-03-22 修回日期:2021-05-10 出版日期:2022-03-05 发布日期:2022-04-28
通讯作者: 吕胜男(通信作者),女,1987年出生,博士,副教授,博士研究生导师。主要研究方向为折展机构、折纸及其衍生机构、模块化可重构机构等。E-mail:shengnan_lyu@buaa.edu.cn E-mail:shengnan_lyu@buaa.edu.cn
作者简介:肖航,男,1992年出生,博士后。主要研究方向为绳驱动与可展收机构设计。E-mail:xiaohang@buaa.edu.cn
基金资助:
国家自然科学基金(51635002,52075016)资助项目。

Static Analysis of Deployable Cable-truss Structures Based on Linear Complementarity Theory

XIAO Hang, Lü Sheng-nan, LI Long, LUO Si-da, DUAN Hai-bin, DING Xi-lun

School of Mechanical Engineering and Automation, Beihang University, Beijing 100191

Received:2021-03-22 Revised:2021-05-10 Online:2022-03-05 Published:2022-04-28

摘要/Abstract

摘要： 空间可展开索-桁架结构具有折展比大、重量轻、刚度高的优点,广泛应用于天线、太空望远镜、太阳翼等大型航天器关键部件中。在统一框架内进行了梁单元和索单元的刚度矩阵集成,建立了包含柔性绳索和杆件的可展开索-桁架结构刚度模型。基于线性互补理论,提出了一种反应绳索真实张紧、松弛状态的结构受力变形计算方法,得到了准确的结构受力与节点位移的映射关系。最后以剪叉机构单元和圆柱面可展开结构为例,验证了所提出方法的有效性,并分析了绳索分布对结构变形的影响。该分析方法可扩展应用于各类索-桁架结构的受力变形计算。

关键词: 可展开索-桁架结构, 柔性绳索, 线性互补理论, 静力学分析

Abstract: Deployable cable-truss structures have the advantages of large deploy/fold ratio, light weight and high stiffness, which have been widely applied in the key parts of large spacecrafts such as antennas, space telescopes and solar arrays. The stiffness matrices of beam and cable elements are assembled in a unified framework. The stiffness model of deployable cable-truss structures containing flexible cables and beams is established. Based on linear complementarity theory, a structure deformation calculation method which can reflect the actual tensity of cables, namely tensioned or slack, is proposed. The accurate relationship between the loads and deformations of nodes is obtained. The reliability of this method is validated through the simulation of a scissor-like element and a cylindrical deployable structure. The influence of cable distribution on stiffness is revealed. The proposed method can be utilized for the deformation analysis of various cable-truss structures.

Key words: deployable cable-truss structure, flexible cable, linear complementarity theory, static analysis

中图分类号:

TH123

肖航, 吕胜男, 李龙, 罗斯达, 段海滨, 丁希仑. 基于线性互补理论的可展开索-桁架结构静力学分析[J]. 机械工程学报, 2022, 58(5): 18-25.

XIAO Hang, Lü Sheng-nan, LI Long, LUO Si-da, DUAN Hai-bin, DING Xi-lun. Static Analysis of Deployable Cable-truss Structures Based on Linear Complementarity Theory[J]. Journal of Mechanical Engineering, 2022, 58(5): 18-25.

参考文献

[1] 邓宗全.空间折展机构设计[M].哈尔滨:哈尔滨工业大学出版社,2013.DENG Zongquan.Design of space deployable and foldable mechanisms[M].Harbin:Harbin Institute of Technology Press,2013.
[2] 秦波,吕胜男,刘全,等.可展收抛物柱面天线机构的设计及分析[J].机械工程学报,2020,56(5):114-121.QIN Bo,LÜShengnan,LIU Quan,et al.Structural design and analysis of a deployable parabolic-cylinder antenna[J].Journal of Mechanical Engineering,2020,56(5):114-121.
[3] 刘荣强,史创,郭宏伟,等.空间可展开天线机构研究与展望[J].机械工程学报,2020,56(5):15-26.LIU Rongqiang,SHI Chuang,GUO Hongwei,et al.Review of space deployable antenna mechanisms[J].Journal of Mechanical Engineering,2020,56(5):1-12.
[4] LIEW J,VU K K,KRISHNAPILLAI A.Recent development of deployable tension-strut structures[J].Advances in Structural Engineering,2008,11(6):599-614.
[5] XIAO H,LYU S N,DING X L.Optimizing accuracy of a parabolic cylindrical deployable antenna mechanism based on stiffness analysis[J].Chinese Journal of Aeronautics,2020,33(5):192-202.
[6] KWAN A S K,YOU Z,PELLEGRINO S.Active and passive cable elements in deployable/retractable masts[J].International Journal of Space Structures,1993,8(1-2):29-40.
[7] YOU Z,PELLEGRINO S.Cable-stiffened pantographic deployable structures part 2:Mesh reflector[J].AIAAJournal,1997,35(8):813-820.
[8] LIU R W,GUO H W,LIU R Q,et al.Shape accuracy optimization for cable-rib tension deployable antenna structure with tensioned cables[J].Acta Astronautica,2017,140:66-77.
[9] XIAO H,LU S N,DING X L.Tension cable distribution of a membrane antenna frame based on stiffness analysis of the equivalent 4-SPS-S parallel mechanism[J].Mechanism and Machine Theory,2018,124:133-149.
[10] 宋小科.空间展开机构的单元构型综合与组网的研究[D].哈尔滨:哈尔滨工业大学,2018.SONG Xiaoke.Configuration synthesis and networking of units for spatial deployable mechanism[D].Harbin:Harbin Institute of Technology,2018
[11] NAGARAJ B P,PANDIYAN R,GHOSAL A.Aconstraint Jacobian based approach for static analysis of pantograph masts[J].Computers & Structures,2010,88(1):95-104.
[12] CAI J,MA R,DENG X,et al.Static behavior of deployable cable-strut structures[J].Journal of Constructional Steel Research,2016,119:63-75.
[13] LIU R W,GUO H W,ZHANG Q,et al.Dynamic characteristics analysis of cable-rib tension deployable antenna[C]//ASME 2016 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference,Charlotte,USA:ASME,2016:1-8.
[14] SHAN W.Computer analysis of foldable structures[J].Computer Structures,1992,42(6):903-912.
[15] LEMKE C E.Bimatrix equilibrium points and mathematical programming[J].Management Science,1965,11(7):681-689.

基于线性互补理论的可展开索-桁架结构静力学分析

Static Analysis of Deployable Cable-truss Structures Based on Linear Complementarity Theory

PDF

可视化

摘要/Abstract

引用本文

使用本文

参考文献

相关文章 4

编辑推荐

Metrics

本文评价

[1]	杨慧, 冯健, 刘永斌, 刘荣强. 百米级多超弹性铰链抛物柱面天线折展机构设计与运动学分析[J]. 机械工程学报, 2022, 58(3): 75-83.
[2]	申理精, 耿坤, 李盘浩, 张静. 索杆桁架式可展开机构设计与力学分析[J]. 机械工程学报, 2022, 58(17): 135-143.
[3]	薛栋良. 高压线路抱臂式巡检机器人越塔规划及辅助金具设计[J]. 电气工程学报, 2019, 14(4): 106-112.
[4]	李辉;朱文白;潘高峰. 500 m口径球面射电望远镜进舱缆线连接机构的设计及其静力学分析[J]. , 2010, 46(7): 7-15.