Efficient graph representation in graph neural networks for stress predictions in stiffened panels

Machine learning (ML) and deep learning (DL) techniques have gained significant attention as reduced order models (ROMs) to computationally expensive structural analysis methods, such as finite element analysis (FEA). Graph neural network (GNN) is a particular type of neural network which processes data that can be represented as graphs. This allows for efficient representation of complex geometries that can change during the conceptual design of a structure or a product. In this study, we propose a novel graph embedding for the efficient representation of 3D stiffened panels by considering separate plate domains as vertices. This approach is considered using Graph Sampling and Aggregation (GraphSAGE) to predict stress distributions in stiffened panels with varying geometries. A comparison between a finite element-vertex graph representation is conducted to demonstrate the effectiveness of the proposed approach. A comprehensive parametric study is performed to examine the effect of structural variables on stress predictions. A wide range of geometries is considered, material nonlinearity, a few boundary conditions, together with uniform and patch loading at various positions. The study involves straight and curved panels with uni- and bi-directional stiffeners. The proposed unit-vertex representation of the panel requires only about 2% of GPU memory and about 4% of training time in comparison to a finite element-vertex embedding. The GraphSAGE model with the proposed unit-vertex representation accurately captures stress distribution across all panels, achieving an average prediction accuracy of 92.3% for the maximum von Mises stress. Our results demonstrate the immense potential of graph neural networks with the proposed graph embedding as a robust reduced-order model for 3D structures.