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

摘要

In this paper, the application of the natural element method (NEM) to the numerical analysis of two- and three-dimensional piece-wise homogeneous domains is presented. The NEM differs from other meshless methods in its capability to accurately reproduce essential boundary conditions along convex boundaries. The α-shape-based extension of this method (α-NEM) generalizes this behaviour to non-convex 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 effective algorithms are presented for the construction of α-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.