基于物理信息的神经网络方法在梁非线性屈曲分析中的应用

Application of physics-informed neural networks for nonlinear buckling analysis of beams

本文提出了一种基于物理信息的神经网络(PINN)框架来分析在Winkler-Pasternak基础上的三维功能梯度FG多孔细长梁的非线性屈曲行为.使用简单的网络,PINNs只需要很少的训练数据来获得较高的精度.在这项工作中使用的强大工具可以处理任何类型的偏微分方程.我们使用深度学习平台TensorFlow和DeepXDE库来设计我们的网络.在本研究中,PINNs框架从梁系统的控制微分方程和边界条件中获取信息,并输出临界非线性屈曲载荷.利用哈密顿原理,考虑几何的非线性,建立了数学模型.通过将建模框架应用于各种边界条件情况以及三维功能梯度FG指标等物理参数对非线性力学行为的影响,仔细检验了建模框架的准确性.最后,利用广义微分求积法(GDQM)对PINNs结果进行了验证.研究结果表明,所提出的PINN框架能够较好地表征三维功能梯度FG多孔细长梁的非线性屈曲行为.此外,PINN预测梁的非线性屈曲行为的速度比数值方法快71倍.

This paper proposes a physics-informed neural network(PINN)framework to analyze the nonlinear buckling behavior of a three-dimensional(3D)FG porous,slender beam resting on a Winkler-Pasternak foundation.PINNs need much less training data to obtain high accuracy using a straightforward network.The powerful tool used in this work can handle any class of PDEs.We use the deep learning platform TensorFlow and DeepXDE library to design our network.In this study,the PINNs framework takes information from the governing differential equations of the beam system and the data from boundary conditions and outputs the critical nonlinear buckling load.The mathematical model is developed using Hamilton’s principle,considering geometry’s nonlinearity.The accuracy of the modeling framework is carefully examined by applying it to various boundary condition cases as well as the physical parameters such as 3D FG indexes on the nonlinear mechanical behaviors.Finally,the PINNs results are validated with those extracted from the generalized differential quadrature method(GDQM).It is found that the proposed PINN framework can characterize the nonlinear buckling behavior of 3D FG porous,slender beams with satisfactory accuracy.Furthermore,PINN is presented to accurately predict the nonlinear buckling behavior of the beam up to 71 times faster than the numerical method.