非齐次弹性力学问题双互易边界元方法研究  

Research on the Dual Reciprocity Boundary Element Method for Non-Homogeneous Elasticity Problems

作　　者：潘先云 余江鸿[1,2] 周枫林 PAN Xianyun;YU Jianghong;ZHOU Fenglin(School of Mechanical Engineering,Hunan University of Technology,Zhuzhou,Hunan 412007,P.R.China;Key Laboratory of Highway Engineering of Ministry of Education,Changsha University of Science&Technology,Changsha 410001,P.R.China)

机构地区：[1]湖南工业大学机械工程学院,湖南株洲412007 [2]长沙理工大学公路工程教育部重点实验室,长沙410001

出　　处：《应用数学和力学》2022年第9期1004-1015,共12页Applied Mathematics and Mechanics

基　　金：国家自然科学基金(11602082);湖南省教育厅科学研究项目(19B145);湖南省自然科学基金(2021JJ30211,2021JJ50043)。

摘　　要：基于弹性力学边界元方法理论,将边界元法与双互易法结合,采用指数型基函数对非齐次项进行插值得到双互易边界积分方程.将边界积分方程离散为代数方程组,利用已知边界条件和方程特解求解方程组,得出域内位移和边界面力.指数型基函数的形状参数是由插值点最近距离的最小值决定,采用这种形状参数变化方案,分析径向基函数(RBF)插值精度以及插值稳定性.再次将指数型基函数应用到双互易边界元法中,分析双互易边界元方法下计算精度及稳定性,验证了指数型插值函数作为双互易边界元方法的径向基函数解决弹性力学域内体力项问题的有效性.Based on the boundary element method theory of elasticity,the boundary element method was combined with the dual reciprocity method,and the exponential basis function was used to interpolate the non-homogeneous term to obtain the dual reciprocity boundary integral equation.Then the boundary integral equation was discretized into algebraic equations,and the equations were solved with the known boundary conditions and equation particular solutions to obtain the displacement and boundary surface forces in the domain.The shape parameter of the exponential basis function was decided by the minimum value of the nearest distance between interpolation points.With this shape parameter change scheme,the RBF interpolation accuracy and stability were analyzed.Again,the exponential basis function was applied to the dual reciprocal boundary element method to analyze the calculation accuracy and stability,and verify the effectiveness of the exponential interpolation function as the radial basis function of the dual reciprocal boundary element method to solve the body force problem in the elastic domain.

关 键 词：弹性力学 边界元法 双互易法 径向基函数 指数型基函数 

分 类 号：O343[理学—固体力学]