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薄板几何非线性弯曲分析的深度能量法
Deep Energy Method for Geometrical Nonlinear Bending Analysis of Thin Plates
投稿时间:2022-09-15  修订日期:2022-11-02
DOI:
中文关键词:  几何非线性  深度能量法  增量式神经网络  Von-Karman非线性理论
英文关键词:Geometric nonlinearity  Deep energy method  Incremental neural network  Von-Karman nonlinear theory
基金项目:国家自然科学基金资助项目(12162004);国家重点研发计划项目(2019YFC1511103);广西科技重大专项(桂科AA18118029);广西重点研发计划(桂科AB22036007)
作者单位邮编
彭林欣 广西大学土木建筑工程学院
广西防灾减灾与工程安全重点实验室 
530004
罗伟嫚 广西大学土木建筑工程学院 
黄钟民 广西大学土木建筑工程学院 530004
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中文摘要:
      发展了一种增量形式的深度能量法求解薄板几何非线性弯曲问题。根据最小势能原理和Von-Karman非线性理论,构建以薄板势能为驱动的增量式深度神经网络模型。薄板求解域用网格离散,通过Python读取网格数据计算Hammer积分点,并以此作为训练集代入网络模型预测板的弯曲位移,将荷载分成一系列的荷载增量,每个增量步中计算薄板势能作为神经网络的损失函数,以最小化势能为目标,结合Adam优化算法更新网络模型参数。本文求解了不同形状、不同边界条件下薄板的几何非线性弯曲问题,并将计算结果与文献解或有限元Abaqus解进行对比,研究表明本文方法在求解薄板的几何非线性弯曲问题上具备有效性和准确性,且增量式的神经网络模型能够减小计算内存,有效提高计算效率和模型的稳定性。
英文摘要:
      An incremental deep energy method with an incremental depth neural network framework is developed to solve geometric nonlinear bending problem. According to the minimum potential energy principle and Von-Karman nonlinear theory, an incremental depth neural network model driven by thin plate potential energy is constructed. In the solving process, the solution domain of the plate is discretized by a series of grids, whose location data is read by Python to calculate Hammer integral points, which are used as training sets to predict the bending displacement of the plate. the load is divided into multiple load increments, then in each increment step, the potential energy of the plate is calculated as the loss function of the neural network, which is gradually minimized until its convergence by updating the parameters of network framework with Adam optimization algorithm. In this paper, the geometric nonlinear bending problem of thin plates with different shapes and different boundary conditions are solved, and the results are compared with those from other researches or Abaqus. Finally, the research results demonstrate that the method is effective and accurate in solving the geometric nonlinear bending problem of thin plates, and the incremental neural network model can reduce the computational memory, effectively improve the computational efficiency and the stability of the model.
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