机器学习方法在带孔薄板应力分析中的应用  

APPLICATION OF MACHINE LEARNING METHODS TO STRESS ANALYSIS OF THIN PLATES WITH HOLE

作　　者：荆宇航[1] 王朝阳 蔺永康 杨志强[1] 方国东 赵锐 李景彤 JING Yuhang;Wang Zhaoyang;LIN Yongkang;YANG Zhiqiang;FANG Guodong;ZHAO Rui;LI Jingtong(School of Astronautics,Harbin Institute of Technology,Harbin 150001,China)

机构地区：[1]哈尔滨工业大学航天学院,哈尔滨150001

出　　处：《力学与实践》2025年第2期285-294,共10页Mechanics in Engineering

基　　金：黑龙江省高等教育教学改革研究项目(SJGY20220009);哈尔滨工业大学第十一批研究生课程思政教育教学改革项目(XYSZ2023001)资助。

摘　　要：采用机器学习结合计算力学分析了带孔薄板的应力问题,其中数据驱动神经网络依赖于输入数据,通过学习数据中的模式来进行预测。物理信息神经网络通过嵌入平衡方程,提高了准确性和泛化能力。深度能量法根据最小势能原理构造损失函数,计算效率和准确性明显更优,给出了其在双向均匀拉伸和非均匀拉伸下的Von Mises应力和误差云图,误差不超过5%。与机器学习的交叉有力地促进了计算力学研究范式的创新,并不断拓展其深度和应用范围。This paper analyzes the stress problem of a thin plate with holes using machine learning combined with computational mechanics,in which data-driven neural networks rely on input data and make predictions by learning patterns in the data.Physically informed neural network improves the accuracy and generalization ability by embedding the equilibrium equations.The deep energy method constructs the loss function based on the principle of minimum potential energy,which has significantly better computational efficiency and accuracy,and gives its Von Mises stress and error cloud maps under bi-directional uniform and non-uniform stretching with an error of no more than 5%.The intersection with machine learning strongly contributes to the innovation of computational mechanics research paradigm and continues to expand its depth and application scope.

关 键 词：机器学习 神经网络 物理信息 深度能量法 应力分析 

分 类 号：O34[理学—固体力学]