Abstract
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 this work,
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.
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 this work,
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.
| Original language | English |
|---|---|
| Journal | CMES - Computer Modeling in Engineering and Sciences |
| DOIs | |
| Publication status | Published - 2022 |
| Externally published | Yes |