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基于物理信息的深度学习求解矩形薄板力学正反问题
A Physics-informed Deep Learning Method for solving Forward and Inverse Mechanics Problems of Thin Rectangular Plates
投稿时间:2020-11-10  修订日期:2020-12-05
DOI:
中文关键词:  基于物理信息的神经网络  深度学习  矩形薄板  力学正反问题
英文关键词:Physics-informed neural network  deep learning  thin rectangular plates  forward and inverse mechanics problems
基金项目:科技部国家重点实验室基金资助项目 (SLDRCE19-B-02)
作者单位邮编
唐明健 同济大学 200092
唐和生 同济大学 200092
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中文摘要:
      本文建立了基于物理信息的神经网络框架,利用深度学习求解矩形薄板力学正反问题。力学正问题为已知矩形薄板的基本参数、边界条件和受力情况,求薄板各点挠度;反问题为已知薄板部分点的挠度、基本参数和受力情况等,识别边界条件。基于物理信息的神经网络模型中,损失函数除基于数据驱动模型中的挠度数据拟合部分以外,还引入薄板弯曲基本方程、应力应变本构关系等物理信息。结果显示,该模型的预测效果非常良好。为了验证该方法的有效性,将其与基于数据驱动的神经网络模型进行对比分析,发现在保证一定精度的情况下,基于数据驱动的模型需要大范围的训练数据集,且迭代次数较大,而基于物理信息的模型则可以减小所需数据的范围,计算效率显著提高。
英文摘要:
      In this paper, a physics-informed neural network model is developed using deep learning method to figure out both the forward and inverse mechanics problems of thin rectangular plates. In the forward mechanics problem, the basic parameters, boundary conditions and load distributions are known to solve the deflection. In the inverse problem, part of deflection and basic parameters, load distributions are known to identify the boundary conditions. In the physics-informed deep neural network, the loss function takes the basic bending equation and stress-strain constitutive relation of thin rectangular plates into consideration apart from the deflection data fitting in data-driven model. The results show the excellent predictive effect of the model. Furthermore, the comparison between physics-informed and data-driven neural networks states that the data-driven model needs a larger range of training data set, and its number of iterations is larger, while the physics-informed model can reduce the coverage of required data and improve computational efficiency under the condition of certain accuracy.
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