Periodic boundary conditions in element free Galerkin method

The purpose of this paper is to introduce a new methodology to implement periodic and anti‐periodic boundary conditions in the element free Galerkin method (EFGM).

This paper makes use of the interpolating moving least squares (IMLS) in the EFGM to implement periodic and anti‐periodic boundary conditions. This fact allows imposing periodic and anti‐periodic boundary conditions in a way similar to the one used by the finite element method.

EFGM generally uses the moving least squares to obtain its shape functions. So, these functions do not possess the Kronecker delta property. As a consequence, the imposition of essential, as well as periodic and anti‐periodic boundary conditions needs other techniques to do it. When EFGM makes use of IMLS the shape functions satisfy the Kronecker delta property. As consequence the periodic boundary conditions implementation can be done in a direct way, similar to the FEM.

IMLS provides a new way of periodic boundary conditions implementation in EFGM. This kind of implementation provides an easy and direct way in comparison to usual existing methods. With this technique EFGM can now easily take advantage of electrical machines symmetry.