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The natural radial element method
Author(s) -
Belinha J.,
Dinis L.M.J.S.,
Natal Jorge R.M.
Publication year - 2013
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.4427
Subject(s) - delaunay triangulation , interpolation (computer graphics) , finite element method , mathematics , mathematical optimization , partial differential equation , cardinal point , benchmark (surveying) , triangulation , function (biology) , computer science , algorithm , topology (electrical circuits) , mathematical analysis , geometry , structural engineering , animation , physics , computer graphics (images) , optics , geodesy , combinatorics , evolutionary biology , geography , engineering , biology
SUMMARY In this work an innovative numerical approach is proposed, which combines the simplicity of low‐order finite elements connectivity with the geometric flexibility of meshless methods. The natural neighbour concept is applied to enforce the nodal connectivity. Resorting to the Delaunay triangulation a background integration mesh is constructed, completely dependent on the nodal mesh. The nodal connectivity is imposed through nodal sets with reduce size, reducing significantly the test function construction cost. The interpolations functions, constructed using Euclidian norms, are easily obtained. To prove the good behaviour of the proposed interpolation function several data‐fitting examples and first‐order partial differential equations are solved. The proposed numerical method is also extended to the elastostatic analysis, where classic solid mechanics benchmark examples are solved. Copyright © 2013 John Wiley & Sons, Ltd.