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 circles 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.

COBISS.SI-ID: 2649595

This study presents the development of a suitable numerical method for porous media flow with free and moving boundary (Stefan) problems arising in systems with wetted and unwetted regions of porous media. A non-singular version of the method of fundamental solutions (MFS), termed the boundary distributed source method (BDS), is applied. Darcy flow and homogenous isotropic porous media is assumed. The solution is represented in terms of the fundamental solution of the Laplace equation in two-dimensional Cartesian coordinates. The desingularisation is achieved through boundary distributed sources of the fundamental solution and indirect calculation of the derivatives of the fundamental solution. Respectively, the artificial boundary, characteristic for the classical, singular MFS is not present. The novel BDS is compared with the MFS and the analytical solutions for several numerical examples with excellent agreement. A sensitivity study of the solution, regarding the discretization and the free parameters is performed. The main contributions of the study are the application of the BDS to free and moving boundary problems and the comparison of BDS with MFS for these types of problems. The developed model can be applied to various geohydrological problems.

COBISS.SI-ID: 2412539