A modified advancing layers mesh generation for thin three-dimensional objects with variable thickness

Abstract

A method of generating modified advancing layers mesh is proposed. In this paper the mesh generation process of semi-unstructured prismatic/tetrahedral mesh is presented for relatively thin three-dimensional geometries with variable thickness, as in the case of injection molding analysis. Prismatic meshes are generated by offsetting initial surface triangular meshes. During the mesh generation process, mesh quality is efficiently improved with the use of a new node relocation method. Finally, tetrahedral meshes are automatically generated in the rest of the domain. The mesh generating capability of the proposed algorithm is demonstrated with the several practical test cases.

Introduction

Recent advances in injection molding technology require high accuracy and good mechanical properties of injection molded parts. Computer-aided analysis has been widely employed for injection mold design to meet such requirements. In computational fluid dynamics involving plastic injection mold components with variable thickness, which is a major concern in this paper, multiple layers of meshes are employed even for the regions of thin part for obtaining accurate simulation results. There are numerous mesh generation algorithms developed so far and most of them are concentrated on mesh generation for structural analysis. Conventional mesh generation methods for structural analysis usually generate regular elements as close as possible to equilateral tetrahedral or prismatic elements, so they are not suitable for injection molding analysis. Relatively few meshing algorithms have been developed for computational fluid dynamics analysis, especially for boundary layer flow analysis such as injection molding application [1], [2], [3], [4], [5], [6]. In this method three-dimensional (3-D) boundary layer meshes are generated by offsetting from surface triangular meshes. Most of the research works have been focused on mesh generation for computational fluid dynamics analysis, in which the outside space of 3-D object has been usually the analysis domain. In these applications offsetting thickness was usually uniform because the analysis domain was outside open space of 3-D object. However, these methods are not efficient in their application to objects with variable thickness such as in injection molding application.

This paper describes a mesh generation process of semi-unstructured prismatic/tetrahedral meshes for relatively thin 3-D geometries with variable thickness. Fig. 1 shows an example of a sectional view of boundary layer meshes constructed in a rectangular hexahedron with a two-dimensional (2-D) illustration. In the sectional view, quadrilaterals represent prismatic elements and triangles represent tetrahedral elements. In order to generate a compatible mesh throughout the domain, tetrahedral elements are generated inside the inner triangular surfaces of prismatic elements.

In case of applying offset, it is not appropriate to use uniform offset depth that is determined by the thickness of thin parts of a model, especially for a model with both thin and thick parts as shown in Fig. 2(a). It would be more appropriate to use different offset depths for regions with different thickness, and thus offset depths should be properly adjusted according to the thickness of the corresponding part of a model as shown in Fig. 2(b). Fig. 2(a) represents a meshing result by previous advancing layers method (ALM), while Fig. 2(b) represents a meshing result by the modified advancing layers method (MALM) presented in this paper. A part of the proposed algorithm has been presented in the authors’ previous paper [7]. The main characteristic of the new approach is that the thickness of the layers near the boundary can be controlled with a parameter called bias level and the new approach is focused on relatively thin geometries with variable thickness as in the case of injection molding analysis. After offsetting boundary layers, some layers of thin parts may intersect with each other, or too close to each other so that further mesh generation is not possible for the remaining domain. Nodes connected to the intersecting layers should be properly relocated to resolve this problem. Previous works used uniform relocation of nodes toward the boundary and thus resulted in thin layers of meshes near the boundary. Moreover, previously suggested relocation process is in itself an iterative process [2]. In this paper an efficient nodes relocation method that can improve the quality of intersecting mesh has been presented, in which the resulting boundary layer thicknesses are adjusted according to the overall shape and thickness of the local region. In our approach node relocation process is completed in one step of relocation process.