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An improved non-singular method of fundamental solutions (INMFS), where the sources are located on the domain boundary, is developed for 3D linear elasticity problems. To circumvent the singularities of the kernel in Fundamental Solution (FS) these are substituted by the volume integral of the FS over a small sphere. The normalized volume integral is used when the sources and collocation points are coincident. The desingularization of the fundamental traction is achieved by assuming the balance of the forces for complying with the mechanical equilibrium, calculated through meshless boundary patches coinciding with the boundary nodes. This improved approach avoids any need to solve the problem three times, as in the recently developed Non-singular Method of Fundamental Solutions (NMFS) by Liu and Šarler in 2018. The INMFS, NMFS and MFS solutions as well as the analytical solutions for a pair of single and one bi-material elasticity problems are employed to evaluate the viability and correctness of the new method in 3D. The INMFS results are reasonably accurate and converge uniformly to the analytical solution. The absence of an artificial boundary, trivial coding, and the straightforward use of the INMFS in problems with different materials in contact are demonstrated in this paper. [ABSTRACT FROM AUTHOR]

Abstract In this paper, the Non-singular Method of Fundamental Solutions (NMFS) is extended to three-dimensional (3D) isotropic linear elasticity problems. In order to avoid the singularities in the classical Method of Fundamental Solutions (MFS), are the source points outside the problem domain replaced by normalizing the volume integral of the fundamental solutions over the sphere around the singularity on the physical boundary. The derivatives of the fundamental solutions at the singularity, required in the traction boundary conditions, are calculated from three reference solutions of the linearly varying simple displacement fields. The artificial boundary appearing in MFS is with this operations removed in NMFS. A comparison between NMFS and MFS solutions and analytical solutions for two single and two bi-material elasticity problems is used to assess the feasibility and the accuracy of the newly developed 3D method. Although NMFS results are slightly less accurate than MFS results in all spectra of performed tests, all NMFS results converge to the analytical solution. The lack of artificial boundary is particularly advantageous when using NMFS in multibody problems. The developments describe a first use of NMFS for 3D solid mechanics problems. [ABSTRACT FROM AUTHOR]