Automatic mesh generation of quadrilateral elements using intelligent local approach

Abstract

This paper describes a new automated mesh generation method named Intelligent Local Approach (ILA), which well controls both size and aspect ratio of quadrilateral element in a two-dimensional plane. The ILA can be straightforwardly extended to hexahedral elements in a three-dimensional solid. Here elements are created sequentially, considering local information on geometrical constraints and user's demand on quality of elements. A user can specify the following two numerical fields, (a) a field of element size and (b) that of element aspect ratio. A field of priority of element creation is also specified within the ILA. To efficiently deal with various complicated geometrical constraints for high quality quadrilateral elements, a fuzzy knowledge processing technique is effectively utilized. The ILA is implemented using an object-oriented technique. Fundamental performances of the ILA are demonstrated in detail through generating several quadrilateral meshes.

Introduction

Unstructured mesh generation for the finite element method (FEM) and the finite difference method (FDM) are in general very labor-intensive and time-consuming. Numerous research activities have been devoted into the development of automatic mesh generation techniques. The Delaunay method, which automatically generates triangular elements for two-dimensional (2-D) case or tetrahedral elements for three-dimensional (3-D) case for a given set of nodes, has been well studied and utilized [1], [2], [3], [4]. The Quadtree/Octree methods have been also popularly utilized to generate triangular/tetrahedral meshes, respectively [5], [6], [7]. The present authors have developed a fully automatic mesh generation system for triangular or quadrilateral elements for 2-D plane and 3-D shell, and tetrahedral elements for 3-D solid using the fuzzy knowledge processing and some computational geometry techniques such as the Bucketing method and the Delaunay method [8], [9], [10]. This FuzzyMesh method has been implemented in CAE systems for car body modeling in several Japanese automobile companies [11], [12], [13], and in one commercial pre/post processors [14], [15]. Thus, we can conclude that fully automatic mesh generation techniques for triangular elements and tetrahedral elements have already been established. On the other hand, the automatic mesh generation of hexahedral elements for 3-D solid is still an open problem, though this element is strongly demanded for some kinds of analyses.

There are two main reasons for such strong demand on hexahedral elements. Firstly, compared with tetrahedral elements, hexahedral elements are more suitable to strongly nonlinear problems such as deformation of tires and metal forming. Secondly hexahedral elements with large aspect ratio are good at modeling thinner 3-D solid and boundary layers in fluid dynamics. There have been some attempts to develop automatic mesh generation systems for hexahedral elements such as HEXAR [16] and Whisker Waving method [17]. However, these systems are not always stable, and cannot control element size and aspect ratio as human does manually or as human desires.

To solve such difficulties, this paper proposes a new automatic mesh generation algorithm named Intelligent Local Approach (ILA), which can control both size and aspect ratio of quadrilateral element for 2-D plane and hexahedral elements for 3-D solid. As for quadrilateral elements, it is possible to create them from triangular elements. However, such an approach cannot be extended to mesh generation of hexahedral meshes. The ILA can be straightforwardly extended from quadrilateral meshes to hexahedral ones. The present paper demonstrates the validity of the ILA through the generation of quadrilateral elements. The ILA will be extended to hexahedral meshes in the next step, which is not given in the present paper.