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

M. R. Hematiyan1,*, M. Arezou1, N. Koochak Dezfouli1, M. Khoshroo1
1 Department of Mechanical Engineering, Shiraz University, Shiraz, 71936, Iran.
* Corresponding Author: M. R. Hematiyan. Email: .

Computer Modeling in Engineering & Sciences 2019, 121(2), 661-686. https://doi.org/10.32604/cmes.2019.08275

Abstract

In this paper, some remarks for more efficient analysis of two-dimensional elastostatic problems using the method of fundamental solutions are made. First, the effects of the distance between pseudo and main boundaries on the solution are investigated and by a numerical study a lower bound for the distance of each source point to the main boundary is suggested. In some cases, the resulting system of equations becomes ill-conditioned for which, the truncated singular value decomposition with a criterion based on the accuracy of the imposition of boundary conditions is used. Moreover, a procedure for normalizing the shear modulus is presented that significantly reduces the condition number of the system of equations. By solving two example problems with stress concentration, the effectiveness of the proposed methods is demonstrated.

Keywords

Method of fundamental solutions, elastostatic, location parameter, configuration of source points, Ill-conditioned system of equations, shear modulus normalizing.

Cite This Article

Hematiyan, M. R., Arezou, M., Dezfouli, N. K., Khoshroo, M. (2019). Some Remarks on the Method of Fundamental Solutions for Two Dimensional Elasticity. CMES-Computer Modeling in Engineering & Sciences, 121(2), 661–686.



This work is licensed under a Creative Commons Attribution 4.0 International License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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