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A close look at valences in hexahedral element meshes
Author(s) -
Staten Matthew L.,
Shimada Kenji
Publication year - 2010
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.2876
Subject(s) - hexahedron , quadrilateral , topology (electrical circuits) , polygon mesh , topology optimization , element (criminal law) , mathematics , tetrahedron , finite element method , computer science , geometry , combinatorics , engineering , structural engineering , political science , law
This paper discusses using valences in objective functions for topological modification of 3D hexahedral meshes. For topological optimization of 2D quadrilateral meshes, node valence (i.e. number of element edges attached to each node) is used to maximize the number of regular nodes (i.e. nodes with four attached edges). Difficulties in developing 3D hexahedral local topology modifications have limited the success of hexahedral topology optimization, although published literature suggests using an object function based on node valence. However, in this paper, we show that node valence is not a consistent measure of good hexahedral element topology, and objective functions based on node valence can lead to element topology, which will only admit concave element shapes. Instead, we propose that objective functions based on edge valence (i.e. number of quadrilateral faces attached to each element edge) will provide a consistent measure of element topology. Copyright © 2010 John Wiley & Sons, Ltd.