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

  • 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。

     

    Abstract: 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.

     

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