基于GP-GatED 的应力场快速演算方法
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重庆大学机械与运载工程学院重庆400030

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TH114TP183

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国家重点研发计划(2023YFB3406101)项目资助


A fast method for calculating stress fields based on GP-GatED
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College of Mechanical and Vehicle Engineering, Chongqing University, Chongqing 400030, China

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    摘要:

    复杂结构应力场的高精度仿真在工程分析中至关重要,但传统有限元法(FEM)高昂的计算成本限制了其在实时响应场景中的应用。针对这一瓶颈,提出一种基于几何-物理图注意力编解码网络的应力场快速演算方法(GP-GatED)。该方法通过将有限元网格单元映射为图节点,融合几何属性、物理特征与全局边界条件构建增强型图结构,基于单元的共享拓扑关系引入特定边权重函数,以表征单元间的力学耦合关系。针对大规模网格结构下模型训练的效率需求,结合研究对象的几何旋转对称性,引入基于圆周角划分的子图构建策略与并行训练方案,有效提升了大规模结构数据的处理速度。本研究以风电主轴轴承为验证对象,在300组工况下的实验结果显示,预测的Von-Mises应力场与有限元基准值高度一致,其决定系数R2达到0.999 8,平均相对误差小于1%。同时,该方法单次演算耗时0.017 7 s,相较于传统有限元分析实现了约7 500倍的加速,计算效率提升超过3个数量级。为了进一步验证模型对真实物理量的还原能力,利用5组典型工况下的试验数据进行对比,模型演算值与实测值的平均相对误差为13.25%,证实了该方法在处理真实物理数据时的性能优势。本研究为复杂结构应力场的在线映射与快速演算提供了一种兼顾保真度与计算效率的代理建模途径。

    Abstract:

    High-fidelity simulation of physical fields in complex structures is critical for structural analysis and engineering design. However, the high computational cost of the Finite Element Method (FEM) restricts its real-time application. To address this bottleneck, a novel method for rapid stress field calculation (GP-GatED) is proposed based on a geometry-physics graph attention encoder-decoder network. This method maps finite mesh elements to graph nodes, fusing geometric attributes, physical features, and global boundary conditions to construct an enhanced graph structure. Based on the shared topological relationships among mesh elements, an edge weight function is introduced to characterize the mechanical coupling. To meet the efficiency demands of training large-scale mesh models, this paper introduces a subgraph construction strategy based on circumferential angle partitioning, leveraging geometric rotational symmetry. Additionally, a parallel training scheme is integrated to accelerate large-scale data processing. Validated on wind turbine main shaft bearings, experiments under 300 operating conditions show that the predicted Von-Mises stress fields highly agree with finite element benchmarks. The coefficient of determination R2 reaches 0.999 8, and the average relative error is below 1%. The inference time for a single case is 0.017 7 s, achieving a speedup of approximately 7 500 times, which is more than three orders of magnitude faster than traditional solvers. To further verify the model′s ability to restore real physical quantities, test data under five typical operating conditions are compared. The average relative error between the simulated and measured values is 13.25%, confirming the method′s advantages in handling real physical data. This study provides a surrogate modeling approach for online mapping and rapid calculation of stress fields in complex structures, achieving a balance between fidelity and computational efficiency.

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尹爱军,袁佳涛,时正鑫,乔朝辉,祁振宇.基于GP-GatED 的应力场快速演算方法[J].仪器仪表学报,2026,47(8):293-302

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  • 在线发布日期: 2026-10-29
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