外部圆形裂纹轴对称结构弹性分析的多神经网络联合训练方法  

MULTI-NEURAL NETWORK COMBINED TRAINING METHOD FOR ELASTIC ANALYSIS OF AXISYMMETRIC STRUCTURES WITH EXTERNAL CIRCULAR CRACK

作　　者：贺云 杜娟 李海滨[2] HE Yun;DU Juan;LI Haibin(College of Water Conservancy and Civil Engineering,Inner Mongolia Agricultural University,Hohhot 010018,China;College of Science,Inner Mongolia University of Technology,Hohhot 010051,China;College of Statistics and Mathematics,Inner Mongolia University of Finance and Economics,Hohhot 010070,China)

机构地区：[1]内蒙古农业大学水利与土木建筑工程学院,呼和浩特010018 [2]内蒙古工业大学理学院,呼和浩特010051 [3]内蒙古财经大学统计与数学学院,呼和浩特010070

出　　处：《力学与实践》2022年第5期1159-1171,共13页Mechanics in Engineering

基　　金：内蒙古自然科学基金(2019BS01006);国家自然科学基金(11962021);内蒙古农业大学高层次人才引进科研启动项目(NDYB2018-42)资助。

摘　　要：轴对称结构裂纹弹性力学分析是工程实践中重要而基础的问题,相比传统有限单元法,提出一种新的数值求解方法,从而提高计算精度和效率,得到了学者们的广泛关注。本文对于具有应力边界的规则外部圆形裂纹轴对称结构,根据弹性理论,归结为求解具有边界条件的相容方程。将应力函数假设为统一的神经网络形式,根据相容方程及边界条件与应力函数的微分关系分别构造应力函数表示的相容方程及应力边界条件的神经网络结构。通过多神经网络联合训练,提取网络参数,从而实现应力分量的求解。在本文中,针对轴对称结构裂纹给出了极坐标系下的神经网络求解方法。数值算例表明,相比传统有限单元法,本文方法在计算精度和效率上都有其优越性。The elastic mechanics analysis of axisymmetric structure cracks is an important and fundamental problem in engineering practice.Compared with the traditional finite element method,a new numerical method is proposed to improve the accuracy and efficiency of calculation,which has been widely concerned by scholars.This paper considers axisymmetric structures of regular external circular cracks with stress boundaries.The compatibility equation with boundary conditions is solved according to the elastic theory.The stress function is assumed to be a unified form of neural network.According to the differential relation between compatibility equation,boundary condition and the stress function.The neural network structures are respectively constructed by the compatible equation and stress boundary condition.Through multi-neural network combined training,network parameters are extracted.It solves the stress components.In this paper,a neural network method in polar coordinate system is proposed to solve the crack of axisymmetric structure.Numerical examples show that the proposed method has advantages over the traditional finite element method in both accuracy and efficiency.

关 键 词：轴对称结构 裂纹 相容方程 边界条件 多神经网络联合训练 

分 类 号：O343[理学—固体力学]