Generating quadrilateral elements on plane and over curved surfaces

Abstract

An algorithm is proposed to generate quadrilateral elements over a triangular element mesh by selectively removing diagonals between triangles. The quality (shape) of a triangular element can be measured by the dimensionless α value (area/sum of squares of sides). As for quadrilateral elements, a new distortion coefficient β has to be introduced, with which the quality of a quadrilateral can be compared to those of the two triangles arising from a cut along either diagonal. A parameter γ can be specified by the user to give higher preference either to triangles or to quadrilaterals. Hence a careful selection of γ would lead to an optimized hybrid mesh consisting of both triangular and quadrilateral elements. Since a quadrilateral can always be divided into two triangles, the method can be considered as a general approach for the generation of quadrilateral elements both on plane and over curved surfaces. As shown by the examples, regular quadrilateral finite element meshes and quadrilateral elements at the interior part of a region are easily recovered by the algorithm.