周边桁架式大型可展开天线是载人航天、探月工程、环境监测和卫星通讯等空间任务的关键设备之一，由于其质量轻、收纳率高、成型精度稳定等特点成为目前天线发展中备受关注的一种大型星载天线。在执行空间任务的过程中，对天线的精度及精度的稳定性有着颇高的要求，天线精度的高低与稳定直接影响到天线传输信号的质量与速率。周边桁架式大型可展开天线结构中的索网结构决定反射面的形状，索网结构是由高聚物纤维绳索组成，由于纤维绳索材料的粘弹性力学特性，索网面在预紧力的作用下，以及复杂的空间环境的影响下，可能出现力学松弛现象，从而引起天线精度的不稳定，影响天线的性能。为解决这一问题，提出利用形状记忆合金与高聚物材料集成构成形状记忆索网结构。在原本全部由高聚物绳索构成的索网结构中，替换竖向拉索为形状记忆合金丝，利用形状记忆合金的形状记忆效应和超弹性等材料特性，使竖向拉索可以受驱动，从而达到调节索网面精度的作用，实现天线的在轨保型。主要工作过程如下：
1.对于索网结构中高聚物纤维绳索的力学松弛现象，基于Scapery非线性粘弹性本构模型，采用Prony级数近似线弹性蠕变柔量的瞬时增量，建立高聚物索单元蠕变行为的有限元模型。通过数值计算对比本构模型与有限元模型的分析结果，确保有限元模型对蠕变现象分析的准确性。集成索网结构的有限元模型，分析绳索的蠕变行为是怎样对索网结构的的型面精度稳定性造成影响的。
2.研究形状记忆合金的材料特性，选择用Brinson的相变本构模型描述形状记忆合金的相变过程。建立形状记忆索单元的有限元模型，通过数值计算确保模型可以体现形状记忆合金材料的材料特性，即形状记忆效应和超弹性。将形状记忆索单元有限元模型与高聚物纤维绳索有限元模型集成建立形状记忆索网结构的有限元分析模型，并利用该模型分析当形状记忆索网结构在高低交变温度环境下时，与当纤维绳索出现力学松弛现象时，索网结构的变形情况，为后续优化分析做铺垫。
3.基于以上研究，分析形状记忆合金索单元对索网面精度的优化过程，建立形状记忆索网结构的优化模型，并通过数值算例证明优化的可行性。设计形状记忆索网结构主动调节实验，通过实验验证加入形状记忆合金材料对索网结构中索网面型面精度的优化作用。

The hoop truss deployable antenna is one of the key equipment for space missions such as manned spaceflight, lunar exploration project, environmental monitoring and satellite communication. Due to its light weight, high storage rate, and stable accuracy, it has become a large-scale spaceborne antenna that has attracted much attention in the development of antennas. In the process of performing space missions, there are high requirements for the accuracy and stability of the antenna. The accuracy and stability of the antenna directly affects the quality and rate of the antenna's signal transmission. The cable net structure that determines the shape of the reflective surface of the hoop truss deployable antenna is composed of high polymer fiber rope materials. Due to the viscoelastic mechanical properties of the fiber rope material, under the action of pre-tightening force and the influence of space environment, it may lead to mechanical relaxation of the cable net structure, which will cause the instability of the antenna precision and affect the performance of the antenna. In order to solve this problem, it is proposed to use shape memory alloy and high polymer material to form a shape memory cable network structure. Replace the vertical cables in the original cable net structure with shape memory alloy wires, then the shape memory effect and superelasticity of shape memory alloys can be used to drive the vertical cables to achieve the role of adjusting the accuracy of the cable-net surface to realize the on-orbit shape protection of the antenna. The main work of this paper can be summarized as follows:
1. Regarding the mechanical relaxation phenomenon of polymer fiber ropes in the cable net structure, based on the Scapery nonlinear viscoelastic constitutive model, the Prony series is used to approximate the instantaneous increment of linear elastic creep compliance, and the finite element model of the creep behavior of polymer cable elements can be established. The analysis results of the constitutive model and the finite element model are compared by numerical calculation to ensure the accuracy of the finite element model for the analysis of creep phenomena. The finite element model of the cable-net structure is integrated to analyze how the creep behavior of the rope affects the stability of the surface accuracy of the cable-net structure.
2. It is chose Brinson's phase transformation constitutive model to describe the phase transformation process of shape memory alloys, so that the material properties of shape memory alloys can be learned. Establish the finite element model of the shape memory cable element, and use the numerical calculation to ensure that the model can reflect the material properties of the shape memory alloy material, which are the shape memory effect and superelasticity. Integrate the finite element model of the shape memory cable unit and the finite element model of the polymer fiber rope to establish the finite element analysis model of the shape memory cable network structure. Use the model to analyze the shape memory cable network structure, when the temperature of the environment is alternating between high and low or the mechanical relaxation of the fiber rope occurs. The study of deformation of the cable net structure paves the way for the subsequent optimization analysis.
3. Based on the studies above, analyze the optimization process of shape memory alloy cable elements on the surface accuracy of the cable net, establish an optimization model of the shape memory cable net structure, and prove the feasibility of optimization through numerical examples. Design the mechanical relaxation adjustment experiment to verify the optimization effect of adding shape memory alloy material on the surface accuracy of the cable net surface in the cable net structure.

[1] 段宝岩, 张逸群, 杜敬利. 大型星载可展开天线设计理论、方法与应用[M]. 北京: 科学出版社,2019.
[2] MA X, LI T, MA J, et al. Recent advances in space-deployable structures in china[J]. Engineering,2022, 17: 207-219.
[3] 马小飞, 李洋, 肖勇, 等. 大型空间可展开天线反射器研究现状与展望[J]. 空间电子技术, 2018,15(2): 16-26.
[4] 段宝岩. 大型空间可展开天线的研究现状与发展趋势[J]. 电子机械工程, 2017, 33(1): 14.
[5] 万小平, 杨粉莉, 杨军刚. 空间大型可展开高精度天线的应用现状及发展趋势[J]. 空间电子技术, 2020, 17(6): 7.
[6] IM E, THOMSON M, FANG H, et al. Prospects of large deployable reflector antennas for a new generation of geostationary doppler weather radar satellites[C]//AIAA SPACE 2007 Conference and Exposition. 2007.
[7] 刘荣强, 田大可, 邓宗全. 空间可展开天线结构的研究现状与展望[J]. 机械设计, 2010(9): 10.
[8] 李团结, 马小飞. 大型空间可展开天线技术研究[J]. 空间电子技术, 2012(3): 6.
[9] MEGURO A, HARADA S, WATANABE M. Key technologies for high-accuracy large mesh antenna reflectors[J]. Acta Astronautica, 2003, 53(11): 899-908.
[10] 杨东武, 丁延康, 张逸群, 等. 一种可展开刚性反射面天线: 中国, CN201910359649.5[P]. 2021-01-19.
[11] 宋昌永, 沈世钊. 索网结构形状确定分析[J]. 空间结构, 1995, 1(4): 8.
[12] SHIVELY J, MIGLIONICO C, ROYBAL R, et al. Combined effects of the low-earth-orbit environment on polymeric materials[C]//Symposium on high temperature and environmental effects on polymeric composites. 1997.
[13] 谭巧. 形状记忆环氧聚合物及其复合材料的典型力学行为研究[D]. 哈尔滨: 哈尔滨工业大学,2015.
[14] TANG Y, LI T, WANG Z, et al. Surface accuracy analysis of large deployable antennas[J]. Acta Astronautica, 2014, 104(1): 125-133.
[15] TANG Y, LI T, MA X. Form finding of cable net reflector antennas considering creep and recovery behaviors[J]. Journal of Spacecraft and Rockets, 2016, 53(4): 610-618.
[16] LOVE A W. Some highlights in reflector antenna development[J]. Radio Science, 2016, 11(8-9):671-684.
[17] MIURA K, MIYAZAKI Y. Concept of the tension truss antenna[J]. Aiaaj, 2012, 28(6): 1098-1104.
[18] SEMLER D, TULINTSEFF A, SORRELL R, et al. Design, integration, and deployment of the terrestar 18-meter reflector[C]//28th AIAA International Communications Satellite Systems Conference (ICSSC-2010). 2010.
[19] CAMPBELL G, BAILEY M C, BELVIN W K. The development of the 15-meter hoop column deployable antenna system with structural and electromagnetic performance results[J]. Acta Astronautica, 1986, 17(1): 69-77.
[20] BELVIN W K, HERSTROM C L, EDIGHOFFER H H. Quasistatic shape adjustment of a 15-meterdiameter space antenna[J]. Aiaa Journal of Spacecraft and Rockets, 1989, 26(3): 129-136.
[21] HOMMA M, HAMA S, KOHATA H. Experiment plan of ets-8 in orbit: Mobile communications and navigation[J]. Acta Astronautica, 2003, 53(4-10): 477-484.
[22] RICHARD, C., GIBBONS. Potential future applications for the tracking and data relay satellite ii(tdrs ii) system[J]. Acta Astronautica, 1995, 35(8): 537-545.
[23] WOODS J, A. A., GARCIA N F. Offset wrap rib antenna concept development[J]. Large Space Systems Technology, 1982, 1: 439-470.
[24] TIBERT G. Optimal design of tension truss antennas[C]//Aiaa/asme/asce/ahs/asc Structures, Structural Dynamics, and Materials Conference. 2003.
[25] TANG Y, LI T, MA X. Pillow distortion analysis for a space mesh reflector antenna[J]. AIAA Journal, 2017, 55(9): 3206-3213.
[26] THOMSON M. Astromesh deployable reflectors for ku and ka band commercial satellites[M].2002.
[27] 丁许, 孙颖, 罗敏, 等. 航天器用高性能纤维编织绳索研究进展[J]. 纺织学报, 2021, 42(12): 180.
[28] 李伟. Vectran 纤维与绳索的蠕变与应力松弛行为研究[D]. 哈尔滨: 哈尔滨工业大学, 2010.
[29] 闫五柱, 高行山, 岳珠峰. 应力松弛法确定材料蠕变参数[J]. 稀有金属材料与工程, 2013, 42(6): 4.
[30] FETTE R, SOVINSKI M. Vectran fiber time-dependent behavior and additional static loading properties[R]. Greenbelt, MD: Goddard Space Flight Center, 2005.
[31] HUANG W, LIU H, LIAN Y, et al. Modeling nonlinear creep and recovery behaviors of synthetic fiber ropes for deepwater moorings[J]. Applied Ocean Research, 2013, 39: 113-120.
[32] TANG Y, LI T, MA X. Creep and recovery behavior analysis of space mesh structures[J]. Acta Astronautica, 2016, 128(November–December): 455-463.
[33] LIAN Y, ZHENG J, LIU H, et al. A study of the creep-rupture behavior of hmpe ropes using viscoelastic-viscoplastic-viscodamage modeling[J]. Ocean Engineering, 2018, 162: 43-54.
[34] NIE R, HE B, YAN S, et al. Design optimization of mesh antennas for on-orbit thermal effects[J].International Journal of Mechanical Sciences, 2020, 175: 105547.
[35] 韩若宇, 何柏岩, 聂锐, 等. 考虑在轨热效应的网状天线索网优化设计[J]. 中国空间科学技术,2022, 42(4): 9.
[36] ZHANG J, HE B, ZHANG L, et al. High surface accuracy and pretension design for mesh antennas based on dynamic relaxation method[J]. International Journal of Mechanical Sciences, 2021, 209:106687.
[37] 王朋朋, 刘佳, 王峰, 等. 大口径高精度星载天线的热变形优化设计与仿真计算[J]. 机械工程学报, 2022, 58(9): 8.
[38] 唐雅琼, 李团结, 陈聪聪. 环形张拉式索网可展开天线创新设计与分析[J]. 西安电子科技大学学报, 2022(004): 049.
[39] 陈花玲, 罗斌, 朱子才, 等. 4D 打印: 智能材料与结构增材制造技术的研究进展[J]. 西安交通大学学报, 2018, 52(2): 12.
[40] WANG X, ZHENG W, HU Y R. Active flatness control of space membrane structures using discrete boundary sma actuators[C]//IEEE/ASME International Conference on Advanced Intelligent
Mechatronics. 2008.
[41] WANG Z, LI T, CAO Y. Active shape adjustment of cable net structures with pzt actuators[J].Aerospace Science and Technology, 2013, 26(1): 160-168.
[42] PENG F, JIANG X X, HU Y R, et al. Actuation precision control of sma actuators used for shape control of inflatable sar antenna[C]//56th International Astronautical Congress of the International Astronautical Federation, the International Academy of Astronautics, and the International Institute of Space Law. 2005.
[43] SONG X, TAN S, WANG E, et al. Active shape control of an antenna reflector using piezoelectric actuators[J]. Journal of intelligent material systems and structures, 2019, 30(18/19): 2733-2747.
[44] 寻广彬. 星载径向肋索网天线结构设计分析与形状主动控制[D]. 大连: 大连理工大学, 2019.
[45] 董超. 基于形状记忆合金的星载桁架天线减振研究[D]. 西安: 西安电子科技大学, 2019.
[46] SHAIKH S F, PANDA S K, SHARMA N, et al. Creep behavior of nickel–titanium shape-memory alloys under static and dynamic loadings: an fem approach[J]. European Physical Journal Plus,2021, 136(1): 124.
[47] FRENZEL J, GEORGE E P, DLOUHY A, et al. Influence of ni on martensitic phase transformations in niti shape memory alloys[J]. Acta Materialia, 2007, 58(9): 3444-3458.
[48] OTSUKA K, REN X. Physical metallurgy of ti– ni-based shape memory alloys[J]. Progress in Materials Science, 2005, 50(5): 511-678.
[49] TANAKA K, KOBAYASHI S, SATO Y. Thermomechanics of transformation pseudoelasticity and shape memory effect in alloys[J]. International Journal of Plasticity, 1986, 2(1): 59-72.
[50] LIANG C, ROGERS C A. One-dimensional thermomechanical constitutive relations for shape memory materials[J]. Journal of Intelligent Material Systems and Structures, 2013, 1(2): 207-234.
[51] BRINSON L. One-dimensional constitutive behavior of shape memory alloys: Thermomechanical derivation with non-constant material functions and redefined martensite internal variable[J].Journal of Intelligent Material Systems and Structures, 1993, 4(2): 229-242.
[52] BOYD J G, LAGOUDAS D C. Thermodynamical constitutive model for the shape memory effect due to transformation and reorientation[C]//VARADAN V K. Smart Structures and Materials 1994:Smart Materials: volume 2189. SPIE, 1994: 276 - 288.
[53] BOYD J G, LAGOUDAS D C. A thermodynamical constitutive model for shape memory materials.part i. the monolithic shape memory alloy[J]. International Journal of Plasticity, 1996, 12(6): 805-842.
[54] ARGHAVANI J, AURICCHIO F, NAGHDABADI R, et al. A 3-d phenomenological constitutive model for shape memory alloys under multiaxial loadings[J]. International Journal of Plasticity,2010,26(7): 976-991.
[55] ARGHAVANI J, AURICCHIO F, NAGHDABADI R, et al. An improved, fully symmetric, finitestrain phenomenological constitutive model for shape memory alloys[J]. Finite Elements in Analysis and Design, 2011, 47(2): 166-174.
[56] DAVIES P, CHAILLEUX E, BUNSELL A, et al. Prediction of the long term behavior of synthetic mooring lines[C]. 2003.
[57] TANG Y, LI T, MA X. Creep and recovery behavior analysis of space mesh structures[J]. Acta Astronautica, 2016, 128: 455-463.
[58] 杨东武, 宁雪琪, 曹佳君, 等. 一种索网天线裁线机: 中国, CN201410563241.7[P]. 2016-09-07.
[59] HUANG W, LIU H, LIAN Y, et al. Modeling nonlinear creep and recovery behaviors of synthetic fiber ropes for deepwater moorings[J]. Applied Ocean Research, 2013, 39: 113-120.
[60] 朱程鹏. Ti-Nb-Mo-Sn 形状记忆合金室温蠕变行为及对其相关性能的影响研究[D]. 湘潭: 湘潭大学, 2019.