Modelling three-dimensional piece-wise homogeneous domains using the -shape-based natural element method

In this paper, the application of the natural element method (NEM) to the numerical analysis of twoand three-dimensional piece-wise homogeneous domains is presented. The NEM di ers from other meshless methods in its capability to accurately reproduce essential boundary conditions along convex boundaries. The -shape-based extension of this method ( -NEM) generalizes this behaviour to nonconvex domains, enables us to construct models entirely in terms of the initial cloud of points and allows us to simulate material discontinuities in a straightforward manner. In the following sections, simple and e ective algorithms are presented for the construction of -shapes in domains composed of various materials. Examples are presented in two- and three-dimensional cases in the context of linear elastostatics showing good performance even with the simple numerical quadrature used