Accuracy analysis and form-finding design of uncertain mesh reflectors based on interval force density method

Abstract

Mesh reflectors are uncertain structures because of the existing errors of dimension and material in the procedure of design and manufacture. These uncertainties have significant impacts on the mechanical and electrical properties, which must be considered during the design phase. Three directly related factors of cable uncertainties in mesh reflectors are considered in this paper, including the initial length, cross-sectional area, and elastic modulus. The analytical relationship between the cable uncertainties and the surface accuracy of mesh reflectors is deduced by interval analysis, and an interval force density method is thus proposed. First, this method is used to analyze the influence of the cable uncertainties on the surface accuracy. Then it is applied into the form-finding optimization of uncertain mesh reflectors to minimize the influence of cable uncertainties on the surface accuracy. Three kinds of cable nets of mesh reflectors are illustrated to analyze the influence of the cable uncertainties on the surface accuracy, and the mesh reflectors with high surface accuracy are obtained by the proposed method. Finally, the influences of both the design values and deviation amplitudes of cable uncertainties on the surface accuracy are revealed.

Keywords

Mesh reflectors uncertainty interval analysis force density method form-finding design

Get full access to this article

View all access options for this article.

References

. Deployment analysis and control of deployable space antenna. Aerosp Sci Technol 2012; 18: 42–47.

Lewis

. Tension structures: Form and behaviour, London: Thomas Telford, 2003.

Dieringer

Bletzinger

Wuchner

. Practical advances in numerical form finding and cutting pattern generation for membrane structures. J Int Assoc Shell Spatial Struct 2012; 53: 147–156.

Veenendaal

Block

. An overview and comparison of structural form finding methods for general networks. Int J Solids Struct 2012; 49: 3741–3753.

Barnes

. Form finding and analysis of tension structures by dynamic relaxation. Int J Space Struct 1999; 14: 89–104.

Linkwitz

Schek

. Einige Bemerkungen zur Berechnung von vorgespannten Seilnetzkonstruktionen. Ingenieur Archiv 1971; 40: 145–158.

Schek

. The force density method for form finding and computation of general networks. Comput Meth Appl Mech Eng 1974; 3: 115–134.

Tibert AG. Optimal design of tension truss antennas. In: 44th AIAA/ASME/ASCE/AHS/ASC structures, structural dynamics and material conference, 2003, AIAA 2003-1629.

Morterolle

Maurin

Quirant

et al.

Numerical form-finding of geotensoid tension truss for mesh reflector. Acta Astronaut 2012; 76: 154–163.

10.

Ma XF, Song YP, Li ZJ, et al. Mesh reflector antennas: Form-finding analysis review. In: 54th AIAA/ASME/ASCE/AHS/ASC structures, structural dynamics, and materials conference, 2013, AIAA 2013-1576.

11.

Jiang

Deng

et al.

Form-finding methods for deployable mesh reflector antennas. Chin J Aeronaut 2013; 26: 1276–1282.

12.

Wang

Deng

. Form-finding analysis and active shape adjustment of cable net reflectors with PZT actuators. J Aerosp Eng 2014; 140: 575–586.

13.

Deng

Wang

et al.

Pretension design of space mesh reflector antennas based on projection principle. J Aerosp Eng 2014. DOI: 10.1061/(ASCE)AS.1943- 5525.0000483.

14.

Yang B, Shi H, Thomson M, et al. Optimal design of initial surface profile of deployable mesh reflectors via static modeling and quadratic programming. In: 50th AIAA/ASME/ASCE/AHS/ASC structures, structural dynamics, and materials conference, Palm Springs, CA, USA, 2009, AIAA 2009-2173.

15.

Shi H, Yang B and Fang H. Offset-feed surface mesh generation for design of space deployable mesh reflectors. In: 54th AIAA/ASME/ASCE/AHS/ASC structures, structural dynamics, and materials conference, Boston, MA, USA, 2013, AIAA 2013-1526.

16.

John

. Influence of fabrication tolerances on the surface accuracy of large antenna structures. AIAA J 1982; 20: 680–686.

17.

Lombardi

. Optimization of uncertain structures using non-probabilistic models. Comput Struct 1998; 67: 99–103.

18.

Elishakofff

Ohsaki

. Optimization and anti-optimization of structures under uncertainty, London: Imperial College Press, 2010.

19.

Maurin

Motro

. Investigation of minimal forms with density methods. J Int Assoc Shell Spatial Struct 1997; 38: 143–154.

20.

Sánchez

Má

Paz

. A multi-step force-density method and surface-fitting approach for the preliminary shape design of tensile structures. Eng Struct 2007; 29: 1966–1976.

21.

Kuttler

. A fourth-order finite-difference approximation for the fixed membrane eigenproblem. Math Comput 1971; 25: 237–256.

22.

John

. Accuracy potentials for large space antenna reflectors with passive structure. J Spacecraft Rockets 1982; 19: 211–217.