Slices based Element Free Galerkin formulation

The solution of problems with multiscale geometry as well as those with complex, arbitrary three dimensional configuration with the Element Free Galerkin (EFG) method is presented in this paper. Multiscale geometries, where one or more dimensions of the object are of a scale larger than the rest, are treated by the use of directionally biased domains of influence for the nodal locations and corresponding directionally biased weight functions. The bias in these quantities is similar to the scale bias of the problem geometry. A method of slices is next introduced to allow for a direct distribution of EFG nodal points in the domain of the object. Nodal distributions are provided for a number of two dimensional sections or slices of the object which are then directly employed in EFG computations. The validity of these developments is demonstrated through the solution of various example problems and their verification against known or alternate numerical solutions.