Quad-Layer: Layered Quadrilateral Meshing of Narrow Two-Dimensional Domain by Bubble Packing and Chordal Axis Transformation

This paper presents a new computational method for quadrilateral meshing of a thin, or narrow, two-dimensional domain. An output mesh of our method is well-shaped and either single-layered, multi-layered, or partially multi-layered. Element sizes can be uniform or graded. A high quality, layered quadrilateral mesh is often required for finite element analyses of a narrow two-dimensional domain with a large deformation such as the analysis of rubber deformation or sheet metal forming. Our method consists of two steps: (1) extraction of the skeleton of a given domain by the discrete chordal axis transformation, and (2) discretization of the chordal axis into a set of line segments and conversion of each of the line segments to a single quadrilateral element or multiple layers of quadrilateral elements. In both steps we use a physically-based computational method called bubble packing to discretize a curve into a set of line segments of specified sizes. Experiments show that the accuracy of a large-deformation FEM analysis can be significantly improved by using a well-shaped quadrilateral mesh created by the proposed method.