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.

翻译：代理模型在结构分析与优化中至关重要。本文提出了一种加筋板的异质图表示方法，该方法利用异质图神经网络（HGNNs）来考虑几何变异性、非均匀边界条件以及多样化的载荷工况。结构被划分为多个结构单元（如加强筋及其间的板），每个单元由三种不同的节点类型表示：几何节点、边界节点和载荷节点。通过引入连接节点的局部方向与空间关系来定义边的异质性。本文提出并分析了多种具有不同异质程度的异质图表示。这些表示被集成到一个异质图Transformer（HGT）中，用于基于边界载荷与自由度，预测加筋板上的冯·米塞斯应力与位移场。为评估所提方法的有效性，我们对承受面载荷的板以及由加筋板构成、处于多种载荷条件下的箱梁进行了数值测试。异质图表示与同质图表示进行了对比，结果表明其性能更优。此外，还进行了消融分析以评估图异质性对HGT性能的影响。结果显示，该方法对位移和冯·米塞斯应力均具有强大的预测精度，能有效捕捉结构行为模式与最大值。