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

2022 ◽  
Vol 130 (3) ◽  
pp. 1349-1369
Author(s):  
M. R. Hematiyan ◽  
B. Jamshidi ◽  
M. Mohammadi
Keyword(s):  
Stress Concentration ◽  
Fundamental Solutions ◽  
Anisotropic Materials ◽  
Method Of Fundamental Solutions ◽  
Two Dimensional

scholarly journals Some Remarks on the Method of Fundamental Solutions for Two-Dimensional Elasticity

2019 ◽  
Vol 121 (2) ◽  
pp. 661-686
Author(s):  
M. R. Hematiyan ◽  
M. Arezou ◽  
N. Koochak Dezfouli ◽  
M. Khoshroo
Keyword(s):  
Fundamental Solutions ◽  
Method Of Fundamental Solutions ◽  
Two Dimensional

scholarly journals Directional Method of Fundamental Solutions for Three-dimensional Laplace Equation

2017 ◽  
Vol 9 (6) ◽  
pp. 112 ◽  
Author(s):  
Chein-Shan Liu ◽  
Zhuojia Fu ◽  
Chung-Lun Kuo
Keyword(s):  
Fundamental Solution ◽  
Laplace Equation ◽  
Logarithmic Singularity ◽  
Three Dimensional ◽  
Fundamental Solutions ◽  
Method Of Fundamental Solutions ◽  
Simple Extension ◽  
Two Dimensional ◽  
Problem Domain ◽  
Interior Domain

We propose a simple extension of the two-dimensional method of fundamental solutions (MFS) to a two-dimensional like MFS for the numerical solution of the three-dimensional Laplace equation in an arbitrary interior domain. In the directional MFS (DMFS) the directors are planar orientations, which can take the geometric anisotropy of the problem domain into account, and more importantly the order of the logarithmic singularity with $\ln R$ of the new fundamental solution is reduced than that of the conventional three-dimensional fundamental solution with singularity $1/r$. Some numerical examples are used to validate the performance of the DMFS.

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