A close look at valences in hexahedral element meshes

Abstract

SUMMARYThis 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.