Pretension design of cable-network antennas considering the deformation of the supporting truss: A double-loop iterative approach

Abstract Cable-network structures are usually adopted as an ideal form of satellite antennas. The performance of cable-network antennas crucially depends on the surface accuracy and the tension distribution. In some cases, conventional algorithms, such as the equal tension algorithm and the equal force density algorithm, may lead to the decrease of the effective region. Thus the equal length algorithm based on the force density method is proposed in this paper. In this algorithm, the free nodes are restricted as close as possible to their desired positions, which ensures the area of the effective region and the high surface accuracy. The cable tensions are restricted by the maximum tension ratios, which ensures the uniform tension distribution. Furthermore, the elastic deformation of the supporting truss seriously affects the antenna’s performance. Therefore, a double-loop iterative form-finding approach for the cable-network antenna with flexible supporting truss is proposed to find a pre-tensioned configuration that meets the requirements of the surface accuracy and the tension distribution. Firstly, an inner loop based on the equal length algorithm is established for the form-finding of the cable-network. Through this inner loop, the high surface accuracy and the uniform tension distribution can be achieved. Secondly, a compatible strategy between the cable-network and the flexible supporting truss is proposed. Through this strategy, a nonlinear finite element (FE) model of the cable-network antenna is established to capture the compatible deformation. Thirdly, an outer loop combining the equal length algorithm and the compatible strategy is established, in which the node coordinates and the cable tensions are iteratively fed to the force density model and the FE model in steps 1 and 2. Through this outer loop, the compatible deformation is fully considered. The whole loop will stop and converge to a reasonable solution of the surface accuracy and the tension distribution within given criterions. Numerical examples of an offset cable-network antenna are provided, and the results are compared with previous literature.

[1]  Du Jingli,et al.  Method for Deployable Mesh Antenna Cable Network Structures' Form-finding Design Based on Force Density , 2016 .

[2]  Gunnar Tibert,et al.  Deployable Tensegrity Structures for Space Applications , 2002 .

[3]  Wang Liu,et al.  Exact mesh shape design of large cable-network antenna reflectors with flexible ring truss supports , 2014 .

[4]  Jian Feng,et al.  Form-finding of tensegrity structures using an optimization method , 2015 .

[5]  Hang Shi,et al.  New Methodology of Surface Mesh Geometry Design for Deployable Mesh Reflectors , 2017 .

[6]  Wei WANG,et al.  Two-step Structural Design of Mesh Antennas for High Beam Pointing Accuracy , 2017 .

[7]  Xiao-Dong Yang,et al.  Continuous model and nonlinear dynamic responses of circular mesh antenna clamped at one side , 2017 .

[8]  Akira Meguro,et al.  Key technologies for high-accuracy large mesh antenna reflectors , 2003 .

[9]  Tuanjie Li,et al.  Preliminary design of paraboloidal reflectors with flat facets , 2013 .

[10]  Jingli Du,et al.  Integrated Structural–Electromagnetic Shape Control of Cable Mesh Reflector Antennas , 2015 .

[11]  K. Linkwitz,et al.  Einige Bemerkungen zur Berechnung von vorgespannten Seilnetzkonstruktionen , 1971 .

[12]  Klaus Linkwitz,et al.  Formfinding by the “Direct Approach” and Pertinent Strategies for the Conceptual Design of Prestressed and Hanging Structures , 1999 .

[13]  Baiyan He,et al.  Deployment analysis for space cable net structures with varying topologies and parameters , 2017 .

[14]  Tuanjie Li,et al.  Form-Finding Analysis and Active Shape Adjustment of Cable Net Reflectors with PZT Actuators , 2014 .

[15]  Tuanjie Li,et al.  Equivalent-force density method as a shape-finding tool for cable-membrane structures , 2017 .

[16]  H. Schek.  The force density method for form finding and computation of general networks , 1974 .

[17]  Gunnar Tibert,et al.  Optimal design of tension truss antennas , 2003 .

[18]  Hiroaki Tanaka,et al.  A Design Method for Cable Network Structures Considering the Flexibility of Supporting Structures , 2008 .

[19]  Sergio Pellegrino,et al.  Shape and stress analysis of offset CRTS reflectors , 2001 .

[20]  Ke-Zheng Li,et al.  Moduli of supersingular abelian varieties , 1998 .

[21]  Baiyan He,et al.  Deployment dynamics modeling and analysis for mesh reflector antennas considering the motion feasibility , 2017 .

[22]  Li Pei,et al.  Dynamics of a Deployable Mesh Reflector of Satellite Antenna: Form-Finding and Modal Analysis , 2016 .

[23]  Paz Morer,et al.  A multi-step force-density method and surface-fitting approach for the preliminary shape design of tensile structures , 2007 .

[24]  A. Tibert,et al.  Review of Form-Finding Methods for Tensegrity Structures , 2011 .

[25]  Bernard Maurin,et al.  Numerical form-finding of geotensoid tension truss for mesh reflector , 2012 .

[26]  Jun Zhang,et al.  Stiffness Modeling and Evaluation for Exechon Parallel Kinematic Machine Module , 2016 .

[27]  Shilin Dong,et al.  Optimal Prestress Design and Construction Technique of Cable-Strut Tension Structures with Multi-Overall Selfstress Modes , 2013 .

[28]  P. Agrawal,et al.  Preliminary design of large reflectors with flat facets , 1981 .

[29]  R. Contro,et al.  Prestressing design method for cable net structures , 1985 .

[30]  Jie Jiang,et al.  Form-finding methods for deployable mesh reflector antennas , 2013 .