薄板几何非线性弯曲分析的深度能量法

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。首先用网格离散薄板求解域,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,再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,待势能取驻值后再继续下一个荷载步的计算。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。

Deep energy method for geometrical nonlinear bending analysis of thin plates

An incremental deep energy method is developed to solve geometric nonlinear bending problems of thin plates.According to the minimum potential energy principle and Von-Karman nonlinear theory,an incremental deep neural network model driven by thin plate potential energy is constructed.Firstly,the solution domain of the thin plate is discretized into a grid,and the Hammer integral points are calculated by reading the grid data in Python,which is used as training set to be substituted into the network model to predict the bending displacement of the plate.Then,the load is divided into a series of load increments.In each increment step,the potential energy of the thin plate is calculated as the loss function of the neural network.With the goal of minimizing the potential energy,the parameters of the network model are updated by Adam optimization algorithm,and the calculation of the next load step is continued after the potential energy takes a stationary value.In this paper,the geometric nonlinear bending problem of thin plates with different shapes and different boundary conditions is solved,and the calculated results are compared with the finite element Abaqus solution using Abaqus from the literattere.The research shows that this method is effective and accurate in solving the geometric nonlinear bending problem of thin plates,and the incremental neural network model needs a low computer,and can effectively improve the computational efficiency and the stability of the model.