Heterogeneous Graph Representation of Stiffened Panels with Non-Uniform Boundary Conditions and Loads

Abstract

Surrogate models are essential in structural analysis and optimization. We propose a heterogeneous graph representation of stiffened panels that accounts for geometrical variability, non-uniform boundary conditions, and diverse loading scenarios, using heterogeneous graph neural networks (HGNNs). The structure is partitioned into multiple structural units, such as stiffeners and the plates between them, with each unit represented by three distinct node types: geometry, boundary, and loading nodes. Edge heterogeneity is introduced by incorporating local orientations and spatial relationships of the connecting nodes. Several heterogeneous graph representations, each with varying degrees of heterogeneity, are proposed and analyzed. These representations are implemented into a heterogeneous graph transformer (HGT) to predict von Mises stress and displacement fields across stiffened panels, based on loading and degrees of freedom at their boundaries. To assess the efficacy of our approach, we conducted numerical tests on panels subjected to patch loads and box beams composed of stiffened panels under various loading conditions. The heterogeneous graph representation was compared with a homogeneous counterpart, demonstrating superior performance. Additionally, an ablation analysis was performed to evaluate the impact of graph heterogeneity on HGT performance. The results show strong predictive accuracy for both displacement and von Mises stress, effectively capturing structural behavior patterns and maximum values.