张拉整体式伸展臂结构设计与刚度分析

doi:10.7527/S1000-6893.2023.28584

Abstract

Abstract:

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

CLC Number:

V414.1

Jing ZHANG, Kai GUO, Hongwei GUO, Rongqiang LIU, Ziming KOU. Structural design and stiffness analysis of deployable tensegrity mast[J]. Acta Aeronautica et Astronautica Sinica, 2023, 44(24): 228584-228584.

Figures/Tables 27

Fig.1

Fig.2

Fig.4

Fig.5

Fig.6

Fig.7

Fig.3

Table 1

Table 2

Configuration stability and stiffness parameter information of each element

单元序号	自应力模态数n_s	机构位移模态数n_m	$K$ 的最小特征值
1	2	0	1.272
2	2	0	1.166
3	1	1	0.969
4	1	3	0.297
5	3	0	4.191
6	3	1	0.556

Table 2

Fig.8

Fig.9

Fig.10

Fig.11

Fig.12

Fig.13

Table 3

Fig.14

Fig.15

Fig.16

Fig.17

Table 4

Fig.18

Fig.19

Fig.20

Fig.21

Table 5

Table 6

References 29

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）.

单元构型序号	杆的数量	索的数量	自应力模态数n_s	自平衡性
1	4	14	0	是
2	4	14	0	是
3	4	16	2	是
4	4	14	0	是
5	4	16	2	是
6	4	16	2	是

属性类别	杆	索
构件单元类型	Link180	Link180
横截面积/mm²	703.72	58.09
初始预应变	0	0.000 5
弹性模量/GPa	206	185
泊松比	0.3	0.3
设计强度/MPa	310	1 260

类型	SN伸展臂弯曲刚度/（10⁶ N·m²）	SS伸展臂弯曲刚度/（10⁶ N·m²）
0.05%	1.600 50	1.661 93
0.10%	1.997 42	2.596 46
0.15%	2.004 37	2.604 21
0.20%	2.011 38	2.612 13
0.25%	2.018 46	2.620 17
0.50%	2.054 56	2.661 63

类型	SN伸展臂弯曲刚度/（10⁶ N·m²）	SS伸展臂弯曲刚度/（10⁶ N·m²）
0.05%	1.609 70	1.654 75
0.10%	2.036 80	2.663 36
0.15%	2.039 53	2.664 29
0.20%	2.042 29	2.665 21
0.25%	2.045 05	2.666 24
0.50%	2.059 01	2.671 74

[1]	Runchang HU, Zian WANG, Yongliang CHEN, Dapeng ZHOU, Dapeng YANG, Zheng GONG. Stability augmentation control of thrust-vectored V/STOL aircraft based on L1 adaptive control [J]. Acta Aeronautica et Astronautica Sinica, 2023, 44(S1): 727642-727642.
[2]	Siyuan CHANG, Yao XIAO, Guangli LI, Zhongwei TIAN, Kaikai ZHANG, Kai CUI. Effect of wing dihedral and anhedral angles on hypersonic aerodynamic characteristics of high-pressure capturing wing configuration [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2023, 44(8): 127349-127349.
[3]	Fangjian WANG, Ke XIE, Jin LIU, Yuhui SONG, Han QIN, Lan CHEN. Unsteady flow and wing rock characteristics of low aspect ratio flying-wing [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2023, 44(4): 126449-126449.
[4]	Bian LI, Lili QU, Yuping GAO. Methods for J0613-0200 steering a cesium clock [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2023, 44(3): 526500-526500.
[5]	Yutian WANG, Jianxin LIU, Xiaokun WANG, Xiaoming LI. Effects of porous wall on secondary instability of optimal growth streaks in high speed boundary layers [J]. Acta Aeronautica et Astronautica Sinica, 2023, 44(22): 128519-128519.
[6]	Sihua LIU, Zhanying WANG, Lijian LI, Mindi ZHANG. Influence of nose shapes on high-speed water entry stability of projectile [J]. Acta Aeronautica et Astronautica Sinica, 2023, 44(21): 528437-528437.
[7]	Xia HUANG, Fan LIU, Zhitao LIU, Jinhua WU. Correlation between numerical simulation and wind tunnel test results of soft refueling [J]. Acta Aeronautica et Astronautica Sinica, 2023, 44(20): 628447-628447.
[8]	Xinyu ZHANG, Siyu XIE, Yang TAO, Gun LI. A robust control method for close formation of aerial-refueling UAVs [J]. Acta Aeronautica et Astronautica Sinica, 2023, 44(20): 628425-628425.
[9]	Chen ZHANG, Hao ZHANG. Lunar-gravity-assisted low-energy transfer from Earth into Distant Retrograde Orbit (DRO) [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2023, 44(2): 326507-326507.
[10]	Fanmin MENG, Nuo MA, Wenchao MA, Junhui MENG, Wenguang LI. Wet modal analysis and tests for inflatable wing with swept air-beams [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2023, 44(2): 227098-227098.
[11]	Bin WANG, Jianjun ZHENG, Wei LIU, Mengmeng WANG. Optimum design method for static test of aircraft wing segment [J]. Acta Aeronautica et Astronautica Sinica, 2023, 44(18): 228065-228065.
[12]	Jingkui ZHANG, Jiapeng CHANG, Miao CUI, Qifen LI, Hongbo REN, Yongwen YANG. First Hopf bifurcation of conducting fluid in three-dimensional square cavity [J]. Acta Aeronautica et Astronautica Sinica, 2023, 44(18): 128328-128328.
[13]	Tianchun ZOU, Yuezhang JU, Yuxi GUAN, Zegang LI, Hongcheng CHEN. Effect of stacking sequence on fatigue behavior of CFRP⁃Al joint [J]. Acta Aeronautica et Astronautica Sinica, 2023, 44(18): 428264-428264.
[14]	Xiao MENG, Dan MA, Hongjun LIN, Chao CHEN. Prescribed performance control of thermoacoustic instability in aero-engine combustion chambers [J]. Acta Aeronautica et Astronautica Sinica, 2023, 44(17): 128182-128182.
[15]	Feiyan GUO, Jianhua LIU, Qingdong XIAO, Shihong XIAO, Zhongqi WANG. Monitoring and evaluation of working condition and adaptive control technology for digital assembly tooling [J]. Acta Aeronautica et Astronautica Sinica, 2023, 44(16): 427914-427914.

Structural design and stiffness analysis of deployable tensegrity mast

RichHTML

PDF (PC)

Knowledge

Abstract

Cite this article

share this article

Figures/Tables 27

References 29

Related Articles 15

Recommended Articles

Metrics

Comments