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Non-Singular Method of Fundamental Solutions for Two-Dimensional Isotropic Elasticity Problems

Q. G. Liu1, B. Šarler1,2,3,4

University of Nova Gorica , Nova Gorica, Slovenia.
Institute of Metals and Technology, Ljubljana, Slovenia.
COBIK, Solkan, Slovenia.
Corresponding author: Professor Božidar Šarler (,,

Computer Modeling in Engineering & Sciences 2013, 91(4), 235-266.


The purpose of the present paper is development of a Non-singular Method of Fundamental Solutions (NMFS) for two-dimensional isotropic linear elasticity problems. The NMFS is based on the classical Method of Fundamental Solutions (MFS) with regularization of the singularities. This is achieved by replacement of the concentrated point sources by distributed sources over circular discs around the singularity, as originally suggested by [Liu (2010)] for potential problems. The Kelvin’s fundamental solution is employed in collocation of the governing plane strain force balance equations. In case of the displacement boundary conditions, the values of distributed sources are calculated directly and analytically. In case of traction boundary conditions, the respective desingularized values of the derivatives of the fundamental solution in the coordinate directions, as required in the calculations, are calculated indirectly from the considerations of two reference solutions of the linearly varying simple displacement fields. The developments represent a first use of NMFS for solid mechanics problems. With this, the main drawback of MFS for these types of problems is removed, since the artificial boundary is not present. In order to demonstrate the feasibility and accuracy of the newly developed method, is the NMFS solution compared to the MFS solution and analytical solutions for a spectra of plane strain elasticity problems, including bi-material problems. NMFS turns out to give similar results than the MFS in all spectra of performed tests. The lack of artificial boundary is particularly advantageous for using NMFS in multi-body problems.


Cite This Article

Liu, Q. G., Šarler, B. (2013). Non-Singular Method of Fundamental Solutions for Two-Dimensional Isotropic Elasticity Problems. CMES-Computer Modeling in Engineering & Sciences, 91(4), 235–266.

cc 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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