Mesh reflectors with large apertures have been used in many communication satellites. The performance of antenna reflectors crucially depends on the faceting error of the reflective surface, which is approximated by using meshes. The force density method (FDM) has been widely used for the form-finding analysis of mesh reflectors. However, after performing form-finding of some meshes, the effective reflective area will decrease. In addition, the form-finding of the auxiliary mesh has received little attention, and it cannot be achieved by using the FDM. Thus, in this study, an effective form-finding methodology that combines the iterative FDM and the minimum norm method (MNM) is proposed. To consider the flexibility of the reflector ring truss, a static analysis of the ring truss under the tension force actions is also performed in the form-finding processes. The reflector flexible parts are described by the absolute nodal coordinate formulation (ANCF). Finally, the form-finding analysis of the reflector with the standard configuration, the central hub configuration, and the circular configuration is performed to validate the proposed methodology. The influence of the mesh tension force on the reflector natural frequencies is also studied. After performing the form-finding analysis, the initial configuration of the reflector with tensioned meshes for the deployment dynamics study can be determined. Based on this paper, the deployment dynamics of a complex AstroMesh reflector will be studied in a successive paper “Dynamics of a Deployable Mesh Reflector of Satellite Antenna: Parallel Computation and Deployment Simulation.”

References

References
1.
Tibert
,
A. G.
,
2002
, “
Deployable Tensegrity Structure for Space Applications
,”
Ph.D. dissertation
, Royal Institute of Technology, Stockholm, Sweden.
2.
Thomson
,
M. W.
,
1999
, “
The Astromesh Deployable Reflector
,”
IEEE Trans. Antennas Propag.
,
3
, pp.
1516
1535
.
3.
Meguro
,
A.
,
Harada
,
S.
, and
Watanabe
,
M.
,
2003
, “
Key Technologies for High-Accuracy Large Mesh Antenna Reflectors
,”
Acta Astronaut.
,
53
(
11
), pp.
899
908
.
4.
You
,
Z.
, and
Pellegrino
,
S.
,
1996
, “
Cable-Stiffened Pantographic Deployable Structures Part 2: Mesh Reflector
,”
AIAA J.
,
35
(
8
), pp.
1348
1355
.
5.
Thomson
,
M. W.
,
Marks
,
G. W.
, and
Hedgepeth
,
J. M.
,
1997
, “
Light-Weight Reflector for Concentrating Radiation
,”
U.S. Patent No. 5,680,145
.
6.
Hedgepeth
,
J. M.
,
1982
, “
Influence of Fabrication Tolerances on the Surface Accuracy of Large Antenna Structures
,”
AIAA J.
,
20
(
5
), pp.
680
686
.
7.
Northrop Grumman
, “
AstroMesh Reflector Family
,” Northrop Grumman Corp., Falls Church, VA.
8.
Ma
,
X. F.
,
Song
,
Y. P.
,
Li
,
Z. J.
,
Li
,
T. J.
,
Wang
,
Z. W.
, and
Deng
,
H. Q.
,
2013
, “
Mesh Reflector Antennas: Form-Finding Analysis Review
,”
AIAA
Paper No. 2013-1576.
9.
Wang
,
Z. W.
,
Li
,
T. J.
, and
Cao
,
Y. Y.
,
2013
, “
Active Shape Adjustment of Cable Net Structures With PZT Actuators
,”
Aerosp. Sci. Technol.
,
26
(
1
), pp.
160
168
.
10.
Tibert
,
A. G.
, and
Pellegrino
,
S.
,
2003
, “
Review of Form-Finding Methods for Tensegrity Structures
,”
Int. J. Solids Struct.
,
18
(
4
), pp.
209
223
.
11.
Li
,
T. J.
,
Guo
,
J.
, and
Cao
,
Y. Y.
,
2011
, “
Dynamic Characteristics Analysis of Deployable Space Structures Considering Joint Clearance
,”
Acta Astronaut.
,
68
(
7–8
), pp.
974
983
.
12.
Tran
,
H. C.
, and
Lee
,
J.
,
2010
, “
Advanced Form-Finding of Tensegrity Structures
,”
Comput. Struct.
,
88
(
3–4
), pp.
237
246
.
13.
Tran
,
H. C.
, and
Lee
,
J.
,
2010
, “
Initial Self-Stress Design of Tensegrity Grid Structures
,”
Comput. Struct.
,
88
(
9–10
), pp.
558
566
.
14.
Linkwitz
,
K.
,
1999
, “
Form-Finding by the ‘Direct Approach’ and Pertinent Strategies for the Conceptual Design of Prestressed and Hanging Structures
,”
Int. J. Space Struct.
,
14
(
2
), pp.
73
87
.
15.
Linkwitz
,
K.
, and
Schek
,
H. J.
,
1971
, “
Remarks Concerning the Analysis of Prestressed Cable Structures
,”
Ing.-Arch.
,
40
(
3
), pp.
145
158
.
16.
Tibert
,
A. G.
,
2003
, “
Optimal Design of Tension Truss Antennas
,”
AIAA
Paper No. 2003-1629.
17.
Tanaka
,
H.
,
Shimozono
,
N.
, and
Natori
,
M. C.
,
2008
, “
A Design Method for Cable Network Structures Considering the Flexibility of Supporting Structures
,”
Trans. Jpn. Soc. Aeronaut. Space Sci.
,
50
(
170
), pp.
267
273
.
18.
Tanaka
,
H.
, and
Natori
,
M. C.
,
2006
, “
Shape Control of Cable Net Structures Based on Concept of Self-Equilibrated Stresses
,”
JSME Int. J. Ser. C: Mech. Syst. Mach. Elem. Manuf.
,
49
(
4
), pp.
1067
1072
.
19.
Tanaka
,
H.
, and
Natori
,
M. C.
,
2004
, “
Shape Control of Space Antennas Consisting of Cable Networks
,”
Acta Astronaut.
,
55
(
3–9
), pp.
519
527
.
20.
Morterolle
,
S.
,
Maurin
,
B.
,
Quirant
,
J.
, and
Dupuy
,
C.
,
2012
, “
Numerical Form-Finding of Geotensoid Tension Truss for Mesh Reflector
,”
Acta Astronaut.
,
76
, pp.
154
163
.
21.
Li
,
T. J.
,
Zhou
,
M. H.
, and
Duan
,
B. Y.
,
2008
, “
A Method of Form-Finding Analysis for Flexible Cable Net Structures of Deployable Antennas
,”
J. Astronaut.
,
29
, pp.
794
798
.
22.
Yang
,
D. W.
,
2010
, “
Structure Design and Profile Adjustment of Large Deployable Mesh Antenna for Satellite
,” Ph.D. dissertation, Xidian University, Xi'an, China.
23.
Shabana
,
A. A.
,
1996
, “
An Absolute Nodal Coordinates Formulation for the Large Rotation and Deformation Analysis of Flexible Bodies
,” University of Illinois at Chicago, Chicago, IL, Technical Report No. MBS96-1-UIC.
24.
Eberhard
,
P.
, and
Schiehlen
,
W.
,
2006
, “
Computational Dynamics of Multibody Systems History, Formalisms, and Applications
,”
ASME J. Comput. Nonlinear Dyn.
,
1
(
1
), pp.
3
12
.
25.
Schiehlen
,
W.
,
2007
, “
Research Trends in Multibody System Dynamics
,”
Multibody Syst. Dyn.
,
18
(
1
), pp.
3
13
.
26.
Gerstmayr
,
J.
, and
Shabana
,
A. A.
,
2006
, “
Analysis of Thin Beams and Cables Using the Absolute Nodal Coordinate Formulation
,”
Nonlinear Dyn.
,
45
, pp.
109
130
.
27.
Shabana
,
A. A.
, and
Mikkola
,
A. M.
,
2003
, “
Use of the Finite Element Absolute Nodal Coordinate Formulation in Modeling Slope Discontinuity
,”
ASME J. Mech. Des.
,
125
(
2
), pp.
342
350
.
28.
Tian
,
Q.
,
Chen
,
L.
,
Zhang
,
Y.
, and
Yang
,
J.
,
2009
, “
An Efficient Hybrid Method for Multibody Dynamics Simulation Based on Absolute Nodal Coordinate Formulation
,”
ASME J. Comput. Nonlinear Dyn.
,
4
(
2
), p.
021009
.
29.
Liu
,
C.
,
Tian
,
Q.
, and
Hu
,
H. Y.
,
2013
, “
Dynamic Analysis of Membrane Systems Undergoing Overall Motions, Large Deformations and Wrinkles Via Thin Shell Elements of ANCF
,”
Comput. Methods Appl. Mech. Eng.
,
258
, pp.
81
95
.
30.
Lai
,
C. Y.
, and
Pellegrino
,
S.
,
1999
, “
Shape and Stress Analysis of Offset CRTS Reflectors
,” Department of Engineering, University of Cambridge, Cambridge, UK,
Report No. CUED/D-STRUCT/TR177
.
31.
Pontoppidan
,
K.
,
1984
, “
Electrical Consequences of Mechanical Antenna Characteristics
,”
ESA Workshop on Mechanical Technology for Antennas
, pp.
41
47
.
32.
Penrose
,
R. A.
,
1955
, “
A Generalized Inverse for Matrices
,”
Proc. Cambridge Philos. Soc.
,
51
(3), pp.
406
413
.
33.
Al-Sumait
,
J. S.
,
AL-Othman
,
A. K.
, and
Sykulski
,
J. K.
,
2007
, “
Application of Pattern Search Method to Power System Valve-Point Economic Load Dispatch
,”
Int. J. Electr. Power Energy Syst.
,
29
(
10
), pp.
720
730
.
34.
Liu
,
C.
,
Tian
,
Q.
, and
Hu
,
H. Y.
,
2012
, “
New Spatial Curved Beam and Cylindrical Shell Elements of Gradient-Deficient Absolute Nodal Coordinate Formulation
,”
Nonlinear Dyn.
,
70
(
3
), pp.
1903
1918
.
35.
Shabana
,
A. A.
,
2008
,
Computational Continuum Mechanics
,
Cambridge University Press
,
Cambridge, UK
.
36.
Shabana
,
A. A.
, and
Yakoub
,
R. Y.
,
2001
, “
Three-Dimensional Absolute Nodal Coordinate Formulation for Beam Elements: Theory
,”
ASME J. Mech. Des.
,
123
(
4
), pp.
606
613
.
37.
Shabana
,
A. A.
, and
Maqueda
,
L. G.
,
2008
, “
Slope Discontinuities in the Finite Element Absolute Nodal Coordinate Formulation: Gradient Deficient Elements
,”
Multibody Syst. Dyn.
,
20
(
3
), pp.
239
249
.
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