Shape accuracy optimization for cable-rib tension deployable antenna structure with tensioned cables

Abstract Shape accuracy is of substantial importance in deployable structures as the demand for large-scale deployable structures in various fields, especially in aerospace engineering, increases. The main purpose of this paper is to present a shape accuracy optimization method to find the optimal pretensions for the desired shape of cable-rib tension deployable antenna structure with tensioned cables. First, an analysis model of the deployable structure is established by using finite element method. In this model, geometrical nonlinearity is considered for the cable element and beam element. Flexible deformations of the deployable structure under the action of cable network and tensioned cables are subsequently analyzed separately. Moreover, the influence of pretension of tensioned cables on natural frequencies is studied. Based on the results, a genetic algorithm is used to find a set of reasonable pretension and thus minimize structural deformation under the first natural frequency constraint. Finally, numerical simulations are presented to analyze the deployable structure under two kinds of constraints. Results show that the shape accuracy and natural frequencies of deployable structure can be effectively improved by pretension optimization.

[1]  M. Barnes,et al.  Form Finding and Analysis of Tension Structures by Dynamic Relaxation , 1999 .

[2]  Cornel Sultan.  Stiffness formulations and necessary and sufficient conditions for exponential stability of prestressable structures , 2013 .

[3]  S. Guest.  The stiffness of tensegrity structures , 2011 .

[4]  Nasseradeen Ashwear,et al.  Natural frequencies describe the pre-stress in tensegrity structures , 2014 .

[5]  A. Tibert,et al.  Review of Form-Finding Methods for Tensegrity Structures , 2003 .

[6]  Simon D. Guest,et al.  A new approach to the analytical and numerical form-finding of tensegrity structures , 2013 .

[7]  Toshiyoshi Kimura,et al.  Concept Design of 15m class Light Weight Deployable Antenna Reflector for L-band SAR Application , 2016 .

[8]  David Coley,et al.  Introduction to Genetic Algorithms for Scientists and Engineers , 1999 .

[9]  Gunnar Tibert,et al.  On an innovative deployment concept for large space structures , 2012 .

[10]  Sergio Pellegrino,et al.  Deployable Tensegrity Reflectors for Small Satellites , 2002 .

[11]  H. Murakami,et al.  Static and Dynamic Characterization of Some Tensegrity Modules , 2001 .

[12]  Jian Feng,et al.  Prestress stability of pin-jointed assemblies using ant colony systems , 2012 .

[13]  Jian Feng,et al.  Efficient Symmetry Method for Calculating Integral Prestress Modes of Statically Indeterminate Cable-Strut Structures , 2015 .

[14]  Ramana V. Grandhi,et al.  Structural optimization with frequency constraints - A review , 1992 .

[15]  Ian F. C. Smith,et al.  Design optimization and dynamic analysis of a tensegrity-based footbridge , 2010 .

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

[17]  Akira Meguro,et al.  In-orbit deployment characteristics of large deployable antenna reflector onboard Engineering Test Satellite VIII , 2009 .

[18]  Peter I. Kattan,et al.  MATLAB Guide to Finite Elements: An Interactive Approach , 2003 .

[19]  Tuanjie Li,et al.  Active shape adjustment of cable net structures with PZT actuators , 2013 .

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

[21]  Tuanjie Li,et al.  Pretension design for space deployable mesh reflectors under multi-uncertainty , 2015 .

[22]  Ivar Talvik,et al.  Finite element modelling of cable networks with flexible supports , 2001 .

[23]  Nasseradeen Ashwear,et al.  Optimization of modular tensegrity structures for high stiffness and frequency separation requirements , 2016 .

[24]  Jean-François Dubé,et al.  Modal behavior of a new large reflector conceptual design , 2015 .

[25]  Ian F. C. Smith,et al.  Dynamic behavior and vibration control of a tensegrity structure , 2010 .

[26]  John W. Leonard,et al.  Tension Structures: Behavior and Analysis , 1987 .

[27]  Klaus-Jürgen Bathe,et al.  The subspace iteration method - Revisited , 2013 .

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

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

[30]  A. Barton,et al.  A review on large deployable structures for astrophysics missions , 2010 .

[31]  Bing Li,et al.  A large ring deployable mechanism for space satellite antenna , 2016 .

[32]  Dennis Semler,et al.  Design, Integration, and Deployment of the TerreStar 18-meter Reflector , 2010 .

[33]  Yiqun Zhang,et al.  Form-finding design of cable-mesh reflector antennas with minimal length configuration , 2017 .

[34]  Jian Feng,et al.  Generalized Eigenvalue Analysis of Symmetric Prestressed Structures Using Group Theory , 2012, J. Comput. Civ. Eng..