A natural neighbour‐based moving least‐squares approach for the element‐free Galerkin method

The element‐free Galerkin method (EFG) and the natural element method (NEM) are two well known and widely used meshless methods. Whereas the EFG method can represent moving boundaries like cracks only by modifying the weighting functions the NEM requires an adaptation of the nodal set‐up. But on the other hand the NEM is computationally more efficient than EFG. In this paper a new concept for the automatic adjustment of nodal influence domains in the EFG method is presented in order to obtain an efficiency similar to the NEM. This concept is based on the definition of natural neighbours for each meshless node which can be determined from a Voronoi diagram of the nodal set‐up. In this approach adapted nodal influence domains are obtained by interpolating the distances to the natural neighbours depending on the direction. In the paper we show that this concept leads, especially for problems with grading node density, to a reduced number of influencing nodes at the interpolation points and consequently a significant reduction of the numerical effort.