三维弹性力学改进的插值型维数分裂无单元Galerkin方法权函数研究  

Study on weight function of the improved interpolating dimension splitting element-free Galerkin method for 3D elasticity problems

作　　者：孟智娟[1] 房亚楠 迟晓菲 MENG Zhi-juan;FANG Ya-nan;Chi Xiao-fei(School of Applied Science,Taiyuan University of Science and Technology,Taiyuan 030024,China)

机构地区：[1]太原科技大学应用科学学院,山西太原030024

出　　处：《西南民族大学学报（自然科学版）》2022年第5期569-577,共9页Journal of Southwest Minzu University(Natural Science Edition)

基　　金：国家自然科学基金项目(No.52004169);山西省回国留学人员科研资助项目(No.2021-132);山西省留学回国人员科技活动择优资助项目(No.20220030);太原科技大学研究生教育创新项目(SY2022082)。

摘　　要：三维弹性力学改进的插值型维数分裂无单元Galerkin方法的关键是将三维问题转化为二维问题.二维问题采用改进的插值型无单元Galerkin法进行求解,分裂方向上采用有限差分法.在构造形函数时,权函数对其具有较大影响.研究三次样条函数、四次样条函数、指数函数和正定紧支径向基函数为权函数时,三维弹性力学改进的插值型维数分裂无单元Galerkin方法数值计算结果的计算精度和计算效率.并与改进的无单元Galerkin方法计算结果进行比较,说明该方法的优越性及权函数的重要性.The key of the improved interpolation dimension splitting element-free Galerkin(IIDSEFG)method for three-dimensional(3 D)elasticity problems is to transform the 3 D problem into a series of related 2 D problems.The improved interpolation element-free Galerkin method is used to solve these 2 D problems,and the finite difference method(FDM)is used in the splitting direction.In the course of constructing the shape function,weight function has great influence on it.In this paper,the calculation accuracy and efficiency of numerical results of 3 D elasticity examples are studied when cubic spline function,quartic spline function,exponential function and compactly supported basis radial function are selected as weight function.Compared with the improved element-free Galerkin(IEFG)method,the superiority of the IIDSEFG method and the importance of weight function research are illustrated.

关 键 词：改进的插值型维数分裂无单元Galerkin方法 维数分裂法 改进的插值型无单元Galerkin方法 权函数 弹性力学 

分 类 号：O241.82[理学—计算数学] O343.2[理学—数学]