张拉整体式伸展臂结构设计与刚度分析
收稿日期: 2023-02-20
修回日期: 2023-03-20
录用日期: 2023-04-12
网络出版日期: 2023-04-21
基金资助
国家自然科学基金(51835002);国家重点研发计划(2018YFB1307900);山西省研究生教育创新项目(2022Y212)
Structural design and stiffness analysis of deployable tensegrity mast
Received date: 2023-02-20
Revised date: 2023-03-20
Accepted date: 2023-04-12
Online published: 2023-04-21
Supported by
National Natural Science Foundation of China(51835002);National Key R&D Program of China(2018YFB1307900);Graduate Education Innovation Project of Shanxi Province(2022Y212)
为了满足航天工程对空间伸展臂的需求，利用张拉整体结构轻质、刚度可调、稳定性好以及易于折展的特性设计了2种空间伸展臂。首先基于基结构法与混合整数线性规划法对张拉整体式伸展臂结构单元拓扑找形，得到多种单元构型。随后依据改进型麦克斯韦尔准则，利用结构平衡矩阵奇异值分解法完成各单元构型的稳定性判定和刚度比较，优选得到2种单元构型，并结合模块化设计思想，分别轴向拓扑得到2种张拉整体式伸展臂。最后分别建立张拉整体式伸展臂的有限元模型，分析探讨了索构件预应力水平、约束方式以及构件横截面积等因素对伸展臂弯曲刚度的影响以及不同情形下2种伸展臂的刚度大小关系。该研究结果提供了张拉整体式空间伸展臂的选取方案，并对提高伸展臂承载能力提供了一定的理论支持。
张静 , 郭凯 , 郭宏伟 , 刘荣强 , 寇子明 . 张拉整体式伸展臂结构设计与刚度分析[J]. 航空学报, 2023 , 44(24) : 228584 -228584 . DOI: 10.7527/S1000-6893.2023.28584
To meet the needs of aerospace engineering for space deployable mast， two types of space deployable masts were designed by taking advantage of the characteristics of tensegrity structure： light weight， adjustable stiffness， good stability and easy folding. Firstly， based on the ground structure method and mixed integer linear programming method， the topology form-finding of the deployable tensegrity mast structure element was performed to obtain various element configurations. Then， using the modified Maxwell's criterion and singular value decomposition method of structural equilibrium matrix， the stability assessment and stiffness comparison of each element configuration were completed， from which two element configurations were preferred. Combining these two element configurations with the modular design idea， two types of deployable tensegrity masts were obtained separately through axial topology. Finally， the finite element model of the deployable tensegrity mast was established， and the influence of prestress level， constraint mode and cross-sectional area of the cable members on the bending stiffness of the deployable mast was analyzed and discussed， as well as the relationship between the stiffness of the two types of deployable masts under different circumstances. The research results provide a selection scheme for the deployable tensegrity mast and offer some theoretical support for enhancing the bearing capacity of the deployable mast.
Key words： tensegrity; deployable mast; ground structure; topology form-finding; stability; stiffness
| 1 | 罗阿妮， 刘贺平， SKELTON R E， 等. 张拉整体基本形体稳定构型理论［J］. 机械工程学报， 2017， 53（23）： 62-73. |
| LUO A N， LIU H P， SKELTON R E， et al. The theory of basic tensegrity unit stable forming［J］. Journal of Mechanical Engineering， 2017， 53（23）： 62-73 （in Chinese）. | |
| 2 | MALIK P K， GUHA A， SESHU P. Topology identification for super-stable tensegrity structure from a given number of nodes in two dimensional space［J］. Mechanics Research Communications， 2022， 119： 103810. |
| 3 | LIU K， ZEGARD T， PRATAPA P P， et al. Unraveling tensegrity tessellations for metamaterials with tunable stiffness and bandgaps［J］. Journal of the Mechanics and Physics of Solids， 2019， 131： 147-166. |
| 4 | YILDIZ K， LESIEUTRE G A. Sizing and prestress optimization of Class-2 tensegrity structures for space boom applications［J］. Engineering with Computers， 2020， 38（2）： 1-14. |
| 5 | KAN Z Y， PENG H J， CHEN B， et al. Nonlinear dynamic and deployment analysis of clustered tensegrity structures using a positional formulation FEM［J］. Composite Structures， 2018， 187： 241-258. |
| 6 | ZHANG L Y， ZHENG Y， YIN X， et al. A tensegrity-based morphing module for assembling various deployable structures［J］. Mechanism and Machine Theory， 2022， 173： 104870. |
| 7 | 曾小飞， 叶继红， 叶冶. 动力松弛法与力密度法在索网结构找形中的比较分析［J］. 空间结构， 2003， 9（4）： 55-59. |
| ZENG X F， YE J H， YE Y. Comparisons between dynamic-relaxation method and force-density method for form finding of pretensioned cable roofs［J］. Spatial Structures， 2003， 9（4）： 55-59 （in Chinese）. | |
| 8 | LEE S， LEE J. A novel method for topology design of tensegrity structures［J］. Composite Structures， 2016， 152： 11-19. |
| 9 | LU C J， ZHU H M， LI S A. Initial form-finding design of deployable Tensegrity structures with dynamic relaxation method［J］. Journal of Intelligent & Fuzzy Systems， 2017， 33（5）： 2861-2868. |
| 10 | PELLEGRINO S. Mechanics of kinematically indeterminate structures［D］. Cambridge： University of Cambridge， 1986. |
| 11 | EHARA S， KANNO Y. Topology design of tensegrity structures via mixed integer programming［J］. International Journal of Solids and Structures， 2010， 47（5）： 571-579. |
| 12 | KANNO Y. Topology optimization of tensegrity structures under self-weight loads［J］. Journal of the Operations Research Society of Japan， 2012， 55（2）： 125-145. |
| 13 | KANNO Y. Topology optimization of tensegrity structures under compliance constraint： a mixed integer linear programming approach［J］. Optimization and Engineering， 2013， 14（1）： 61-96. |
| 14 | WANG Y F， XU X A， LUO Y Z. Topology-finding of tensegrity structures considering global stability condition［J］. Journal of Structural Engineering， 2020， 146（12）： 04020260. |
| 15 | XU X A， WANG Y F， LUO Y Z. General approach for topology-finding of tensegrity structures［J］. Journal of Structural Engineering， 2016， 142（10）： 04016061. |
| 16 | CONNELLY R， WHITELEY W. Second-order rigidity and prestress stability for tensegrity frameworks［J］. SIAM Journal on Discrete Mathematics， 1996， 9（3）： 453-491. |
| 17 | CONNELLY R. Tensegrity structures： why are they stable？［M］∥THORPE M F， DUXBURY P M. Rigidity Theory and Applications， Boston ：Springer， 2002： 47-54. |
| 18 | GUEST S. The stiffness of prestressed frameworks： a unifying approach［J］. International Journal of Solids and Structures， 2006， 43（3-4）： 842-854. |
| 19 | 张沛. 张拉整体结构形态问题的若干研究与优化分析［D］. 南京： 东南大学， 2017： 59-62. |
| ZHANG P. Study on morphology of tensegrity structures using optimization methods［D］. Nanjing： Southeast University， 2017： 59-62 （in Chinese）. | |
| 20 | 罗阿妮， 伍承旭， 刘贺平. 三杆张拉整体的结构刚度分析［J］. 哈尔滨工程大学学报， 2017， 38（9）： 1450-1455. |
| LUO A N， WU C X， LIU H P. Structural stiffness of three-bar tensegrity［J］. Journal of Harbin Engineering University， 2017， 38（9）： 1450-1455 （in Chinese）. | |
| 21 | CAI J G， ZHOU Y H， FENG J A， et al. Effects of the prestress levels on the stiffness of prismatic and star-shaped tensegrity structures［J］. Mathematics and Mechanics of Solids， 2017， 22（9）： 1866-1875. |
| 22 | XU X A， WANG Y F， LUO Y Z， et al. Topology optimization of tensegrity structures considering buckling constraints［J］. Journal of Structural Engineering， 2018， 144（10）： 04018173. |
| 23 | SKELTON R E， DE OLIVEIRA M C. Tensegrity systems［M］. New York： Springer， 2009. |
| 24 | ZAWADZKI A， SABOUNI-ZAWADZKA A AL. In search of lightweight deployable tensegrity columns［J］. Applied Sciences， 2020， 10（23）： 8676. |
| 25 | MAXWELL J C. L. On the calculation of the equilibrium and stiffness of frames［J］. The London， Edinburgh， and Dublin Philosophical Magazine and Journal of Science， 1864， 27（182）： 294-299. |
| 26 | 罗阿妮， 王龙昆， 刘贺平， 等. 张拉整体三棱柱构型和结构稳定性分析［J］. 哈尔滨工业大学学报， 2016， 48（7）： 82-87. |
| LUO A N， WANG L K， LIU H P， et al. Analysis of configuration and structural stability of 3-bar tensegrity prism［J］. Journal of Harbin Institute of Technology， 2016， 48（7）： 82-87 （in Chinese）. | |
| 27 | 张沛， 冯健. 张拉整体结构的稳定性判定及刚度分析［J］. 土木工程学报， 2013， 46（10）： 48-57. |
| ZHANG P， FENG J. Stability criterion and stiffness analysis of tensegrity structures［J］. China Civil Engineering Journal， 2013， 46（10）： 48-57 （in Chinese）. | |
| 28 | 陈志华， 史杰， 刘锡良. 张拉整体三棱柱单元体试验［J］. 天津大学学报， 2004， 37（12）： 1053-1058. |
| CHEN Z H， SHI J， LIU X L. Experimental study on triangular prism unit of tensegrity［J］. Journal of Tianjin University， 2004， 37（12）： 1053-1058 （in Chinese）. | |
| 29 | 陈志华， 史杰， 刘锡良. 张拉整体四棱柱单元体试验［J］. 天津大学学报， 2005， 38（6）： 533-537. |
| CHEN Z H， SHI J， LIU X L. Experimental study on quadrangular prism unit of tensegrity［J］. Journal of Tianjin University， 2005， 38（6）： 533-537 （in Chinese）. |
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