Graph neural network-based surrogate modeling of finite element stress fields in stiffened cylindrical shells and out-of-distribution generalization

The finite element method provides high accuracy in structural strength analysis but can be computationally expensive for repeated evaluations. This study develops a graph neural network (GNN)-based surrogate model for predicting nodal von Mises stress fields in stiffened cylindrical shells and compares it with multilayer perceptron (MLP) and convolutional neural network (CNN) baselines. Parametric finite element datasets are constructed for in-distribution (ID) testing and out-of-distribution (OOD) evaluation under mesh-density variation and pressure extrapolation. The CNN achieves the highest ID accuracy. Under mesh-resolution shifts, the GNN and MLP show greater overall stability than the CNN, while the MLP performs best under pressure extrapolation. The GNN remains competitive with fewer parameters and without regular-grid resampling. These results show that model performance depends on the type of distribution shift and that GNNs provide a compact topology-based approach for stress-field surrogate modelling on original finite element meshes.