Form finding and optimization design method for cable networks with flexible frames


The state of static equilibrium is a key parameter in the design of cable network structures because the geometrical shape and internal force distribution within the structures are treated concurrently. Cable network structures generally comprise of cable networks and supporting frames. Significant efforts have been made on the form-finding and design optimization of cable network structures through numerous methods such as the force density and dynamic relaxation. However, these methods do not take into consideration the flexibility of the supporting frames and thus unbale to capture the effect of the interaction between the cable networks and supporting frames, highly desirable for design optimization. This has further resulted in consistent tradeoffs between the real equilibrium states and design results.

In a recent research, Dr. Rui Nie and Professor Baiyan He from Tianjin University in collaboration with Professor Dewey Hodges at Georgia Institute of Technology and also Dr. Xiaofei Ma from Xi’an Institute of Space Radio Technology developed a form finding and design optimization approach for cable network structures with flexible frames. Their main goal was to couple the cable network and supporting frame to accurately model the real equilibrium state of the flexible supported cable networks and to derive the linear form for the determination of the free node coordinates in the form finding. Their research work is currently published in the journal, Computers & Structures.

Briefly, the network cables and beams were coupled through deformation compatibility conditions. The fully-coupled approach treated both the cables and beams as a whole during the form finding and complete optimization of the structures. Next, a linear form for the determination of the free node coordinates was derived from the systematic equilibrium equations. This, according to the authors, was instrumental in significant reduction of the computing cost of the optimization design by making it easy to realize the multi-variable optimization. In addition, boundary conditions were applied to eliminate the rotational vectors of beam nodes from the equilibrium equations. As a result, the solution of the non-compatibility problem between the cable and beam elements could be obtained more effectively.

Based on their findings, the approach proved effective for form finding and optimization of flexible supported cable network structures with multiple design variables, high shapes and enhanced surface accuracy. This was attributed to considering the flexibility of the frame and its interaction with the cable network thus avoiding the deviation between the design results and the real equilibrium states due to the presumed assumptions on the rigid support.

To actualize their study, this approach was successfully applied to mesh reflector antennas with high surface accuracy requirements thus verifying its feasibility in real practical applications. Furthermore, it was necessary to validate these results in computer software i.e. ABAQUS. Interestingly, the simulation results also confirmed the potential use of the approach in not only improving the surface accuracy but also the force distributions of the mesh antennas. According to Dr. Rui Nie, the first author explained that their study provides a reliable and promising approach for form finding and design optimization of cable network structures with flexible frames for future advanced applications.

Form finding and optimization design method  for cable networks with flexible frames - Advances in Engineering

About the author

Dr. Rui Nie is currently a postdoctoral research fellow at Tsinghua University. She received her Ph.D. (2018), Masters (2014) and Bachelors (2012) degrees, all in Mechanical engineering, from Tianjin University. She worked as a visiting scholar at Georgia Institute of Technology from Sep. 2016 to Oct. 2017. During her masters, she was dealing with the multi-body dynamics modeling and dynamics design, with the main focus on the deployment dynamics of mesh reflector antennas. Her research during Ph.D. is about the force and force design of the cable networks, especially the application on the structural analysis and design of mesh reflector antennas.

Her current research focuses on the optimization and adaptive design of space structures, the application of intelligent materials in space structures. She is the peer review expert of the National Natural Science Foundation of China.

Email: [email protected]

About the author

Baiyan He is currently a full Professor at the School of Mechanical Engineering, Tianjin University, China, and also a senior member of the Chinese Mechanical Engineering Society.

He received his Ph.D. degree from Tianjin University in 2003. His research interests include mechanism and robotics, multibody system dynamics, mechanical design theory, and he is the author over 70 journal and conferences articles of these fields.

About the author

Dr. Hodges became a Professor of Aerospace Engineering at Georgia Tech in 1986. From 1970–1986 he was a research scientist at the U.S. Army Aeroflightdynamics Directorate, located at Ames Research Center. During those years he also served as a Lecturer at Stanford University and in 1984 was a guest research scientist at the DLR in Braunschweig, Germany. Dr. Hodges has published five books and over 415 technical papers in journals and conference proceedings in the fields of rotorcraft dynamics, structural dynamics, aeroelasticity, structural mechanics and stability, computational mechanics, and optimal control.

He is an elected Fellow of The American Institute of Aeronautics and Astronautics, The American Helicopter Society, The American Society of Mechanical Engineers, and The American Academy of Mechanics. He serves on the editorial boards for the Journal of Fluids and Structures, the Journal of Mechanics of Materials and Structures, and Nonlinear Dynamics.


Nie, R., He, B., Hodges, D., & Ma, X. (2019). Form finding and design optimization of cable network structures with flexible frames. Computers & Structures, 220, 81-91.

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