Comparative Study of Unstructured Meshes Made of Triangles and Quadrilaterals

Proceedings, 6th International Meshing Roundtable, Sandia National Laboratories, pp.437-447, October 1997

MESHING
RESEARCH
CORNER

Anish Malanthara and Walter Gerstle
anishm@arc.unm.edu gerstle@unm.edu
Department of Civil Engineering, University of New Mexico

Abstract
Extensive studies have been conducted on the generation of unstructured meshes of triangles for the purpose of finite element analysis. Delaunay triangulation has been the basis of several such methods, and has lead to algorithms that can produce unstructured meshes of triangles for any planar domain. However, there have not been many robust methods for producing unstructured meshes of quadrilaterals. This is unfortunate, because for plain stress and plain strain problems solved using finite element analysis, 4-noded quadrilateral elements perform much better than 3-noded triangular elements, especially when the discretisation is not dense.

In this paper, we present an extremely simple and guaranteed method to generate meshes of quadrilaterals from meshes of triangles generated using a robust Delaunay triangulation algorithm. The elements thus obtained have less than optimal aspect ratios. In order to determine if the less than optimal aspect ratios of the elements affect the quality of results when these meshes are used for finite element modeling, we applied these meshes to the solution of a problem. We are of the opinion that a mesh of quadrilaterals generated in the inexpensive manner presented in this paper produces results that compare well even with those from mapped meshes. Thus, the presented method provides an efficient, simple and effective way to generate unstructured meshes of quadrilaterals of reasonable quality.