A Connectivity Based Method for Representing and Constructing All-Hexahedral Finite Element Meshes

, 1995

MESHING
RESEARCH
CORNER

Brigham Young University
Sandia National Laboratory
Abstract
This paper presents a dual representation of a hexahedral mesh, the "Spatial Twist Continuum" that provides a means of quantifying Connectivity constraints for hexahedral finite element meshes. We begin by describing the two-dimensional analog of the method for the representation of all quadrilateral elements on surfaces. For the two-dimensional case, quadrilateral elements are represented with a series of chords that pass through opposing element faces and intersect at the element's centroid. The power of the method is displayed in the three- dimensional representation where the chords seen in the two-dimensional analog are actually edges of two-dimensional twist planes and hexahedral elements are defined by the intersection of three of these twist planes. The twist planes. and how they are forced to twist through a continuum to define hexahedral elements, are the basis of the spatial twist continuum.