2026年“核理安邦”联合博士生学术论坛

基于残差驱动的自适应深度有限元方法在压力容器应力集中分析中的应用

Not scheduled

12m

地址：清华大学校内

口头报告 人工智能 人工智能

Speaker

张 雨辰 (中国原子能科学研究院)

Abstract

Stress concentration commonly arises in structures with geometric discontinuities, such as plates with holes, cylindrical shells, and pressure vessels with nozzle connections, posing challenges for accurate and efficient analysis. Conventional finite element methods address this issue through mesh refinement, which increases computational cost and relies on manual intervention. Existing deep learning-based approaches provide flexible representations but often lack adaptive resolution and consistency with physical formulations.

 This study proposes a residual-driven adaptive deep finite element method (ADFEM) for multi-scale analysis of stress-concentrated structures. A residual-based indicator is employed to identify high-error regions, where local correction networks are introduced through a hierarchical refinement strategy. The global approximation is progressively enhanced by coupling with localized corrections within a total potential energy framework, ensuring physical consistency while avoiding explicit mesh reconstruction.

Numerical examples, including a plate with a circular hole, a cylindrical shell under tensile loading, and a pressure vessel with nozzle connection, demonstrate the applicability of the proposed method. The results show that the method effectively captures stress concentration and reduces approximation error in critical regions. The proposed framework provides an alternative approach for adaptive analysis of stress-sensitive structures.

摘要

在带孔结构、圆柱壳体及压力容器接管等典型工程问题中，几何不连续性易引发显著的局部应力集中，对计算精度与效率提出了较高要求。传统有限元方法通常通过网格加密刻画该类区域，但依赖人工调整且计算成本较高；现有基于深度学习的方法虽具有一定灵活性，但在自适应能力及物理一致性方面仍存在不足。

   本文提出一种基于残差驱动的自适应深度有限元方法（ADFEM），用于应力集中结构的多尺度分析。通过构造残差指标识别高误差区域，并在局部引入修正子网络，实现全局近似与局部增强的层级耦合。该方法基于总势能框架构建，在避免显式网格重构的同时保持物理一致性。

   通过带孔平板、受拉圆柱壳体以及带接管压力容器三个算例，验证了该方法在不同结构中的适用性。结果表明，该方法能够有效定位应力集中区域，并在关键区域降低近似误差。所提出的框架为应力敏感结构的自适应分析提供了一种新的实现路径。

Presentation materials

37-张雨辰-残差驱动深度有限元.pptx

37-张雨辰-残差驱动深度有限元.pptx