Integrated form-finding and optimization of grid-shell structures using coupled iterative algorithms and specialized graph neural networks

Abstract

A primary inefficiency in the design of complex grid-shell structures arises from the separation of form-finding and member sizing into distinct stages. This decoupled approach is problematic because the optimal structural form is directly dependent on the dimensions of its members, making the optimization process computationally demanding. This research addresses these challenges through two primary contributions. First, it introduces an enhanced iterative algorithm that couples form- finding, based on the Potential Energy Method, with member sizing optimization. This methodology is implemented in two novel MATLAB-based software tools, providing a flexible design environment that accommodates arbitrary geometries, materials, and loading conditions, which were validated against established analytical methods. Secondly, to significantly accelerate this workflow, the study explores the application of Graph Neural Networks for near-instantaneous prediction of optimal forms and member properties. A generalized Graph Neural Network model trained on a diverse dataset of mixed topologies struggled with generalization, showing limited accuracy. In contrast, a specialized Graph Neural Network model trained exclusively on dome- type grid-shells demonstrated outstanding predictive accuracy, with coefficient of determination values exceeding 0.99 for both final nodal coordinates and optimal member properties. This specialized model drastically reduces computational time compared to traditional iterative simulations. The findings demonstrate that while the developed software provides a robust tool for detailed analysis, a topology-specific Graph Neural Network approach offers a robust and viable strategy for real-time structural feedback in the conceptual design phase. This work lays the groundwork for integrating physics-informed machine learning into structural engineering to create more efficient and intuitive design tools.