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Pretension design of a flexible support cable net structure with high node position precision

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Abstract

A prestressed cable net structure is applied to shape and support the reflective surface of mesh antennas. The radiation pattern of an antenna highly depends on the positions of the cable net nodes. The pretension force and node positions of the cable net structure are strongly coupled. The deformation of the flexible support frame changes the positions of the cable net nodes, causing the radiation pattern to deteriorate. To achieve high node position precision, this study proposes the pretension design method of a cable net structure with flexible supports. To improve calculation efficiency, finite element method and force density method are combined to calculate structural deformation directly and accurately. Furthermore, a pretension optimization model is established by considering the rigid body displacements of the nodes. This model is solved iteratively. Numerical results show that the proposed pretension design method can achieve high design accuracy for a flexible support cable net structure and significantly improve the mechanical properties of a support frame.

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Abbreviations

l ij :

Length of the cable that connects nodes i and j

F ij :

Tension force of the cable that connects nodes i and j

q ij :

Force density of the cable that connects nodes i and j

Q :

Diagonal force of the density matrix

C s :

Connectivity matrix

C f :

Connectivity matrix related to the fixed nodes

C u :

Connectivity matrix related to the free nodes

S a :

Self-equilibrium stress matrix

k :

Coefficient vector of Sa

N q :

Number of self-stress states

Γ :

External force vector applied to the support nodes

K :

Stiffness matrix of the flexible support

a :

Deformation vector of the support nodes

L u0 :

Target length vector of the internal cable net

L u :

Actual length vector of the internal cable net

L :

Actual length vector of all the cable nets

ε :

Allowable cable length error value

F L :

Lower limit value of the allowable cable forces

F U :

Upper limit value of the allowable cable forces

\({\boldsymbol{K}}_R^\prime \) :

Stiffness matrix of the flexible support with specific constraints

\({\boldsymbol{a}}_R^\prime \) :

Node deformation vector of the flexible support with specific constraints

X f0, Y f0, Z f0 :

Coordinates of the support nodes before deformed

X u, Y u, Z u :

Coordinate vectors of the free nodes

X f, Y f, Z f :

Coordinate vectors of the fixed nodes

P xu, P yu, P zu :

External forces applied to the free nodes

P xf, P yf, P zf :

External forces applied to the fixed nodes

P ix, P iy, P iz :

Tension force of the cable

F R :

Force vector applied to the flexible support with specific constraints

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Acknowledgments

This work was supported by the National Natural Science Foundation of China [grant number: 51775403].

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Authors and Affiliations

  1. School of Mechano-electronic Engineering, Xidian University, Xi’an, 710071, China

    Hangjia Dong, Tuanjie Li & Congcong Chen

Authors
  1. Hangjia Dong
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  2. Tuanjie Li
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Corresponding author

Correspondence to Tuanjie Li.

Additional information

Hangjia Dong obtained his master’s degree in engineering from Xidian University, Xi’an, China in 2016. He is currently a Ph.D. student at the Department of Electro-mechanical Engineering, Xidian University. His research interests include space-deployable structures and nonlinear dynamics.

Tuanjie Li (corresponding author) obtained his Ph.D. in engineering from Xi’an University of Technology, Xi’an, China in 1999. He was promoted to Associate Professor in 2001 and became Professor in 2006 at Xidian University. He is on the list of the top 2 % scientists in 2020–2022. His research interests include space-deployable structures and antennas, intelligent robot technology, and electro-mechanical thermal technology for electronic equipment.

Congcong Chen is currently a Ph.D. student in the School of Mechano-electronic Engineering, Xidian University, China. She obtained her bachelor’s degree in mechanical design manufacturing and automation in 2016. Her current research interests include space-deployable structures.

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Dong, H., Li, T. & Chen, C. Pretension design of a flexible support cable net structure with high node position precision. J Mech Sci Technol 37, 3017–3025 (2023). https://doi.org/10.1007/s12206-023-0527-1

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  • DOI: https://doi.org/10.1007/s12206-023-0527-1

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