Form finding of cable-membrane structures with flexible frames: Finite element implementation and application to surface accuracy analysis of umbrella-like rib-mesh reflectors

Deployable rib-mesh reflector antennas, known for their ultralight nature and high deployment-to-stowage ratio, have been attracting attention from both the aerospace industry and academia. Form finding is a critical step in determining the equilibrium shape of the reflector under a specific internal stress distribution, which is a prerequisite in evaluating the surface accuracy of these antennas. This paper presents a comprehensive methodology for iteratively implementing the nonlinear finite element method for form finding of cable-membrane structures supported by flexible frames. The method is integrated into the commercial finite element code ABAQUS with Python scripts, and its accuracy and efficiency are validated through a few benchmark examples. Subsequently, the proposed method is applied to analyze the surface accuracy of umbrella-like rib-mesh reflector antennas. The effect of key design parameters such as the number and rigidity of ribs, the magnitude and anisotropy of membrane stress, and the amount of pretension force in boundary cables on the antenna's surface accuracy has been highlighted. The effort not only establishes a robust and user-friendly strategy for form finding of cable-membrane structures supported by flexible frames but also provides valuable insights into the surface accuracy of umbrella-like rib-mesh reflector antennas. To facilitate the application of the FEM-based form-finding method, the source code for this paper is publicly available via a permanent link on GitHub https://github.com/SCU-An-Group/FEM-based-Form-Finding.