Open Access

ARTICLE

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

by M. R. Hematiyan, M. Arezou, N. Koochak Dezfouli, M. Khoshroo

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.

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