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.
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.