Graph-Based Intelligent Prediction of Non-Linear Buckling Capacity for Single-Layer Spherical Gridshells under Topology-Constrained Imperfection Fields

Abstract

Natural hazards such as snowstorms and earthquakes can readily trigger instability and collapse of single-layer gridshells (SLGs), making it essential to incorporate multiple factors in probability reliability analysis for structural stability design. To enhance computational efficiency in the probability analysis, this research presents an innovative framework driven by graph neural networks, aiming to predict the nonlinear buckling capacity (NBC) of imperfect SLGs. The graph embedding technique is adopted to effectively extract the global features of SLGs. On this basis, the mapping from the initial imperfection field to the NBC is established through convolution operations. The constrained stochastic imperfection modal method, considering the topology constraint, is adopted to generate reliable imperfect SLGs for training. To ensure the proposed framework accurately predicts both structural NBC and the overall probability distribution, an adaptive composite loss function considering the Kullback–Leibler divergence is introduced. Subsequently, the feasibility and superiority of the framework are illustrated by numerical examples. A holistic evaluation of prediction accuracy and universality reveals that the proposed model significantly outperforms the model employing an ordinary loss function. Particularly, the relative error in quantile prediction of the probability distribution for different shell forms is as low as 0.52%.