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Modelling three‐dimensional piece‐wise homogeneous domains using the α ‐shape‐based natural element method
Author(s) -
Cueto E.,
Calvo B.,
Doblaré M.
Publication year - 2002
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.452
Subject(s) - classification of discontinuities , quadrature (astronomy) , simple (philosophy) , regular polygon , boundary element method , homogeneous , mathematics , context (archaeology) , meshfree methods , computer science , boundary (topology) , finite element method , mathematical optimization , algorithm , geometry , mathematical analysis , structural engineering , engineering , paleontology , philosophy , electrical engineering , epistemology , combinatorics , biology
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. Copyright © 2002 John Wiley & Sons, Ltd.