摘要
在对偶神经网络原理的基础上,针对线弹性问题有限元中的单元刚度矩阵,提出了神经网络数值求解方法。根据最小位能原理得到单元刚度矩阵的积分表达式。利用有限单元法中最普遍采用的等参变换,即单元的几何形状和单元内的场函数采用相同数目的结点参数及相同的插值函数进行变换,使得等参元的单元刚度矩阵计算都在自然坐标系下形状规则的母单元内进行,方便对不同单元的单元刚度矩阵进行积分计算。构造对偶神经网络,单元刚度矩阵作为原函数神经网络的数值计算结果,实现单元刚度矩阵的高精度求解。通过算例仿真表明,与传统高斯积分进行对比,利用对偶神经网络积分法计算单元刚度矩阵在精度上有提高。
Based on the principle of the dual neural network,a neural network numerical method was proposed for the element stiffness matrix in the finite element of linear elasticity problem in this paper. The integral expression of the element stiffness matrix was obtained according to the minimum bit energy principle. The geometrical shape of the element and the field function in the element were transformed by the same number of node parameters and the same interpolation function,so that the element stiffness matrix calculation of the isoparametric element was carried out in the natural shape system under the natural coordinate system,and it was convenient to calculate the unit stiffness matrix of different elements. The dual neural network was constructed,the element stiffness matrix was used as the numerical result of the original function neural network,to realize the high-precision solution of the element stiffness matrix. The example simulation showed that the accuracy of the element stiffness matrix was improved by using the dual neural network integral method,compared with the traditional Gaussian integral.
作者
贺云
杜娟
李海滨
HE Yun;DU Juan;LI Haibin(College of Water Conservancy and Civil Engineering Jnner Mongolia Agricultural University,Hoh hot 010018,China;College of Statistics and Mathematics Jnner Mongolia University of Finance and Economics,Hohhot 010070,China;College of Science,Inner Mongolia University of Technology,Hohhot 010051,China)
出处
《内蒙古农业大学学报（自然科学版）》
CAS
2022年第1期97-104,共8页
Journal of Inner Mongolia Agricultural University(Natural Science Edition)
基金
内蒙古自治区自然科学基金项目(2019BS01006)
内蒙古农业大学高层次人才引进科研启动项目(NDYB2018-42)。
关键词
有限单元法
对偶神经网络
多重积分
单元刚度矩阵
Finite element method
Dual neural network
Multiple integral
Element stiffness matrix
