This study presents a discrete–continuous flux-guided shape-refinement framework for freeform shell geometries under self-weight. The method evaluates the directional relation between a prescribed support-directed transmission field and the shell surface normal, identifies locally underperforming regions, applies top-down geometric updates, and reconstructs a continuous surface at each step. It is intended as a transparent intermediate stage between intuitive freeform design and high-fidelity structural verification. The framework is demonstrated on nine shell cases with different geometries, support conditions, height ranges, and surface irregularities. Across all the cases, the results show reduced normal-component misalignment and increased tangential alignment relative to the prescribed transmission field. A representative finite-element comparison provides case-specific supporting evidence that under a linear-elastic gravity-load model the refined geometry can reduce deformation and stress levels over large surface regions; however, it does not prove general structural optimality or fully membrane-dominated behavior. Geometric roughness remains a key limitation requiring explicit regularization in future work. The approach is positioned as a lightweight geometric pre-optimization tool for conceptual shell design, rather than as a substitute for equilibrium-based form-finding or detailed structural optimization.
Baghdadi et al. (Sun,) studied this question.