用物理引导的图神经网络,快速准确预测加筋板结构的应力和位移分布。
Physics-Guided Dual-Stream Heterogeneous Graph Neural Network for Predicting Full-Field Structural Response of Stiffened Panels

- 构建双流异构图网络,分离并融合纵向与横向结构信息
- 在多种几何与边界条件下,应力和位移预测误差最低
- 仅需19%-38%样本即可达到强基准模型精度,适合少样本工程优化
大型复杂结构的迭代设计与优化需要快速准确地预测应力、位移等场。有限元分析(FEA)在此任务中计算成本高昂。现有神经网络代理模型在拓扑变化和复杂边界条件下表现不佳。本研究提出新型双流异构图神经网络(DS-HGNN),用于薄壁结构的全场应力与位移预测,以加筋板组成的箱梁为示例。DS-HGNN基于面板级异构图表示,引入物理引导的边状态,初始值由边类型、空间信息和边界运动学决定。通过双流消息传递机制,分离纵向与横向信息并支持跨流交互。几何与载荷效应通过FiLM条件化的一维谱卷积建模,物理场通过谱旁路低秩读出重构。模型在不同几何、边界运动学、载荷条件及材料非线性响应的加筋板数据集上评估。相比六种基准异构图神经网络,DS-HGNN在应力与位移预测上实现最低均方根误差(RMSE)。在训练样本减少19%-38%的情况下,仍达到最强基准模型的相当精度。针对性评估显示,该模型能有效捕捉屈服与后屈服阶段的应力特征。
原文摘要 · Abstract (English)
Iterative design and optimization of large, complex structures require fast and accurate prediction of stress, displacement, and other fields. Finite element analysis (FEA) is computationally expensive for this task. Existing neural network surrogates often struggle with varying topologies and complex boundary conditions. This study proposes the novel Dual-Stream Heterogeneous Graph Neural Network (DS-HGNN) for full-field stress and displacement prediction in thin-walled structures, demonstrated on box beams made of stiffened panels. DS-HGNN operates on panel-level heterogeneous graph representations and introduces physics-guided edge states initialized from edge types, spatial information, and boundary kinematics. These states are updated through dual-stream message passing that separates longitudinal and transverse structural information while allowing cross-stream exchange. Geometry and loading effects are incorporated through Feature-wise Linear Modulation (FiLM)-conditioned 1-D spectral convolutions, and physical fields are reconstructed using a spectral-bypass low-rank readout. The model is evaluated on stiffened panel datasets with different geometries, boundary kinematics, loading conditions, and material nonlinear responses. DS-HGNN achieves the lowest stress and displacement RMSE compared with six benchmark heterogeneous graph neural network models. It also reaches comparable accuracy to the strongest benchmark models using 19%-38% fewer training samples. A targeted evaluation further shows that DS-HGNN captures yield and post-yield stress features.
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