用异构图建模带非均匀载荷的加强板,提升结构预测精度。
Heterogeneous Graph Representation of Stiffened Panels with Non-Uniform Boundary Conditions and Loads
- 将结构拆分为几何、边界、载荷三类节点,构建异构图表示。
- 在多种载荷下预测位移和冯·米塞斯应力,误差低于同类型方法。
- 适合结构优化与快速仿真,尤其适用于复杂边界条件场景。
代理模型在结构分析与优化中至关重要。本文提出一种考虑几何变化、非均匀边界条件和多样载荷场景的加强板异构图表示方法,采用异构图神经网络(HGNNs)实现。结构被划分为多个单元,如腹板和筋条,每个单元以几何、边界、载荷三类节点表示。通过引入连接节点的局部方向与空间关系,实现边的异构性。设计了多种异构程度不同的图表示,并在异构图变压器(HGT)中验证其性能,用于基于边界载荷和自由度预测整个加强板的冯·米塞斯应力场与位移场。针对受局部载荷作用的面板及不同工况下的箱形梁(由加强板构成)进行数值测试,结果显示该方法优于同质图基线。消融实验表明图异构性显著提升模型表现。结果证明其对位移与应力的预测具有高精度,能有效捕捉结构行为模式与最大值。
原文摘要 · Abstract (English)
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.
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