Methodology for cable network design and error analysis with high engineering consistency

• A high-precision cable network design method with enhanced prototype consistency is proposed. • The material and geometric nonlinearity of cables, as well as structural details and topological diversity, are fully integrated into the cable network modelling process. • An error analysis method that integrates material and fabrication uncertainties is presented to characterize the distribution law of prototype surface accuracy under manufacturing limitations. • Two prototypes were fabricated, and their measured surface accuracies both falls within the calculated error distribution range, thereby validating the high prototype consistency of the proposed design method. The cable network is widely used to form reflective surfaces for large-scale mesh antennas due to its advantages of lightweight structure, high precision, and cost-effectiveness in construction. The surface accuracy of the network directly affects the wavelength and frequency of the reflected electromagnetic waves. Although existing design methods can achieve relatively high surface accuracy in theory, the linearization assumptions and structural simplifications in the modeling often result in significant nodal RMS deviations between the design and the actual prototype. To address this issue, we propose a cable network design method that fully considers consistency between theoretical modeling and physical prototypes, thereby significantly improving the surface accuracy of the fabricated structure. A nonlinear material constitutive model is integrated, and the structural details of cable connectors and tension tie adjusting devices are incorporated, with geometric nonlinearity and topological diversity comprehensively considered in the systematic model. An optimization model is established to determine the optimal unstretched cable lengths, with the objective of achieving high surface accuracy. Uncertainties related to material parameters and cable lengths are quantitatively characterized, enabling a comprehensive uncertainty analysis of surface accuracy. Based on the design outcomes, two protypes were fabricated, and their nodal RMS errors were measured using a photogrammetry system. The measurement results show that the proposed design method improves the surface accuracy of the prototype by more than 60%, with the average cable tension error reduced to below 20% compared to the prototype fabricated using the previous method. Moreover, the measured data fall within the calculated RMS error distribution range, demonstrating a high level of consistency between the theoretical model and physical prototypes.