Heterogeneous Graph Representation of Stiffened Panels with Non-Uniform Boundary Conditions and Loads
Yuecheng Cai, Jasmin Jelovica
TL;DR
The paper targets efficient surrogate modeling for stiffened panels under non-uniform boundary conditions and loads by introducing a heterogeneous graph representation that separates geometry, boundary, and loading information into distinct node types. It leverages a heterogeneous graph transformer (HGT) with edge-type and spatial-relationship awareness to predict von Mises stress and displacement fields, outperforming a prior homogeneous-graph approach. Through ablation studies and four case analyses (including patch loads and box-beam scenarios), the authors demonstrate that graph heterogeneity significantly improves predictive accuracy, especially for non-uniform boundary conditions, while exposing trade-offs in parameter count and training complexity. The work offers a robust framework for rapid, physics-informed surrogate modeling of thin-walled structural components with complex loading and support patterns, facilitating design optimization and real-time decision-making.
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.