The Method of Fundamental Solutions for Two-Dimensional Elastostatic Problems with Stress Concentration and Highly Anisotropic Materials  

作　　者：M.R.Hematiyan B.Jamshidi M.Mohammadi 

机构地区：[1]Department of Mechanical Engineering,Shiraz University,Shiraz,71936,Iran [2]Department of Mechanical Engineering,College of Engineering,Shiraz Branch,Islamic Azad University,Shiraz,71993,Iran

出　　处：《Computer Modeling in Engineering & Sciences》2022年第3期1349-1369,共21页工程与科学中的计算机建模（英文）

基　　金：The first author would like to acknowledge the support received from the Vice Chancellor of Research at Shiraz University under Grant No.99GRC1M1820.

摘　　要：The method of fundamental solutions(MFS)is a boundary-type and truly meshfree method,which is recognized as an efficient numerical tool for solving boundary value problems.The geometrical shape,boundary conditions,and applied loads can be easily modeled in the MFS.This capability makes the MFS particularly suitable for shape optimization,moving load,and inverse problems.However,it is observed that the standard MFS lead to inaccurate solutions for some elastostatic problems with stress concentration and/or highly anisotropic materials.In thiswork,by a numerical study,the important parameters,which have significant influence on the accuracy of the MFS for the analysis of two-dimensional anisotropic elastostatic problems,are investigated.The studied parameters are the degree of anisotropy of the problem,the ratio of the number of collocation points to the number of source points,and the distance between main and pseudo boundaries.It is observed that as the anisotropy of the material increases,there will be more errors in the results.It is also observed that for simple problems,increasing the distance between main and pseudo boundaries enhances the accuracy of the results;however,it is not the case for complicated problems.Moreover,it is concluded that more collocation points than source points can significantly improve the accuracy of the results.

关 键 词：Meshfree method degree of anisotropy location of source points anisotropic elasticity least squares MFS 

分 类 号：O17[理学—数学]