Numerical form-finding of geotensoid tension truss for mesh reflector

Abstract

The parabolic surface of most large deployable reflectors is formed by a reflective mesh attached to a cable net. This paper presents a new approach to calculate a geodesic tension truss that ensures both appropriate node positioning and uniform tension. It is based on a force density strategy coupled with geometrical constraints. Uniform tension is achieved by iterations on coefficients of force density. Nodes of net are located on the paraboloid by controlling additional forces. Several applications illustrate the method on various types of net patterns and parabolic surfaces. The accuracy of obtained net is then evaluated by calculation of the systematic surface error due to faceting. Attachment of the net to a rim structure with additional cables is also discussed.

Uniform-tension form-finding design for asymmetric cable-mesh deployable reflector antennas

“…Step 1 is for the front net: to consider both cable tension and membrane stress simultaneously, an iterative design technique which combines FDM and surface stress density method (SSDM) is presented based on the works of Morterolle et al 8 and Maurin and Motro, 10 through which both the cable tension and membrane stress are designed to be uniform. In step 2, the rear net of asymmetric AstroMesh antennas is considered.…”

“…Therefore, study on AstroMesh antennas, which considers both surface accuracy requirements and tension uniformity, becomes a hot issue in recent years. [6][7][8][9] Currently, there are mainly two research approaches to address this problem: approach I, ''tension-finding for given shape'' 6,7 and approach II, ''shape-finding for given tension.'' 8 Based on approach I, the initial tensions of AstroMesh antennas were designed with the geometry unchanged using the equilibrium matrix method (EMM) in Yang and Shi 6 and Yang and Duan, 7 but the maximum tension ratio is relatively large for asymmetric offset AstroMesh antennas.…”

“…[6][7][8][9] Currently, there are mainly two research approaches to address this problem: approach I, ''tension-finding for given shape'' 6,7 and approach II, ''shape-finding for given tension.'' 8 Based on approach I, the initial tensions of AstroMesh antennas were designed with the geometry unchanged using the equilibrium matrix method (EMM) in Yang and Shi 6 and Yang and Duan, 7 but the maximum tension ratio is relatively large for asymmetric offset AstroMesh antennas. To improve the tension uniformity, employing force density method (FDM), an iterative form-finding technique was presented in Morterolle et al, 8 on the basis of approach II.…”

“…8 Based on approach I, the initial tensions of AstroMesh antennas were designed with the geometry unchanged using the equilibrium matrix method (EMM) in Yang and Shi 6 and Yang and Duan, 7 but the maximum tension ratio is relatively large for asymmetric offset AstroMesh antennas. To improve the tension uniformity, employing force density method (FDM), an iterative form-finding technique was presented in Morterolle et al, 8 on the basis of approach II. In this study, cable tensions of the front and rear nets were designed to be completely uniform, under the assumption that the two nets were symmetric.…”

Stiffness estimation for large–sized umbrella space reflector

“…Such antennas are usually classified as hoop («AstroMesh») and umbrella («Halca», «Garuda-1») type [1,2].…”