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.
Highlights
The method of fundamental solutions (MFS) is an integration-free meshfree method, which has found a wide application because of its accuracy and simplicity
In the MFS, the solution is expressed in terms of known fundamental solutions, which exactly satisfy the governing equations of the problem
The first category includes meshfree methods based on strong forms of differential equations [5–7], while the meshfree methods based on weak forms of governing equations [8,9] fall into the second category
Summary
The MFS is an integration-free meshfree method, which has found a wide application because of its accuracy and simplicity. CMES, 2022, vol.130, no.3 need suitable techniques for the computation of domain integrals [10–12]; the MFS is a strong-form and truly meshfree method without any need for evaluating any domain or boundary integral. The literature review shows a few studies on the MFS for the analysis of elastostatic problems in anisotropic media. Raamachandran et al [24] made use of the charge simulation method, which is the same as the MFS They solved some anisotropic elastostatic problems and obtained satisfactory results. Tsai [26] used the MFS for solving three-dimensional elastostatic problems in transversely isotropic media He proposed a rescaling method for improving the accuracy of the results of problems with natural boundary conditions. No research has been carried out on the configuration of source points for anisotopic elasticity
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