For structure analysis with the finite element method (FEM), the hexahedral element is preferable to the tetrahedral one from the viewpoint of accuracy. Previously, we had introduced a label-driven subdivision method for a two-dimensional mesh and showed that the meshes generated by our method were useful for structural analyses. In this study, we extend our two-dimensional algorithm to three-dimensions and verify that the meshes generated by the proposed mesh-subdivision algorithm are useful for structural analyses.

1. [1] B. Liu, K. T. Miura, and S. Usuki, “Structure Analysis with 2D Quadrilateral Meshes Generated by a Label-Driven Subdivision,” Int. J. of Automation Technology, Vol.10, No.2, 2016.
2. [2] R. Schneiders, “Refining Quadrilateral and Hexahedral Element Meshes,” In: Handbook of Grid Generation, CRC Press, DOI.10.1201.9781420050349.ch21, 1998.
3. [3] W. F. Gordon and C. A. Hall, “Construction of Curvilinear Coordinate Systems and Applications to Mesh Generation,” Int. J. Num. Meth. Eng., Vol.7, p. 461, 1973.
4. [4] R. H. Harber, M. S. Shephard, J. F. Abel, R. H. Gallagher, and D. P. Greenberg, “A General Two-dimensional Finite Element Preprocessor Utilizing Discrete Transfinite Mappings,” Int. J. Num. Meth. Eng., Vol.17, p. 1015, 1981.
5. [5] S. Lai and F. Cheng, “Similarity based Interpolation using Catmull-Clark Subdivision Surfaces,” Vis. Comput. 2006, Vol.22, No.9, pp. 865-873, 2006.
6. [6] F. Cheng, F. Fan, S. Lai, C. Huang, J. Wang, and J. Yong, “Loop Subdivision Surface based Progressive Interpolation,” J. Comput. Sci. Tech., Vol.24, No.1, pp. 39-46, 2009.
7. [7] Z. Chen, X. Luo, L. Tan, B. Ye, and J. Chen, “Progressive Interpolation based on Catmull-Clark Subdivision Surfaces,” Comput. Graph. Forum, Vol.27, No.7, pp. 1823-1827, 2008.
8. [8] T. Maekawa, Y. Matsumoto, and K. Namiki, “Interpolation by Geometric Algorithm,” Comput-Aided Des., Vol.39, pp. 313-323, 2007.
9. [9] M.-C. Rivara, “A Grid Generator Based on 4-triangles Conforming Mesh-refinement Algorithms,” Int. J. Num. Meth. Eng., Vol.24, p. 1343, 1987.
10. [10] E. A. Sadek, “A Scheme for the Automatic Generation of Triangular Finite Elements,” Int. J. for Numerical Methods in Engineering, Vol.15, p. 1813, 1980.
11. [11] B. Wu and S. Wang, “Automatic Triangulation over Three-dimensional Parametric Surfaces based on Advancing Front Method,” Finite Elements in Analysis and Design, Vol.41, Issues 9-10, pp. 892-910, May 2005.
12. [12] L. Sun, G.-T. Yeh, F.-P. Lin, and G. Zhao, “An Automatic Delaunay Triangular Mesh Generation Method based On Point Spacing,” Int. J. of Engineering and Innovative Technology (IJEIT), Vol.3, Issue 3, p. 134, September 2013.
13. [13] P. L. Baehmann, S. L. Wittchen, M. A. Shephard, K. R. Grice, and M. A. Yerry, “Robust, Geometrically based, Automatic Two-dimensional Mesh Generation,” Int. J. Num. Meth. Eng., Vol.24, p. 1043, 1987.
14. [14] J. Papac, A. Helgadottir, C. Ratsch, and F. Gibou, “A Level Set Approach for Diffusion and Stefan-type Problems with Robin Boundary Conditions on Quadtree/Octree Adaptive Cartesian Grids,” J. of Computational Physics, Vol.233, No.15, pp. 241-261, January 2013.
15. [15] Y. T. Lee, A. De Pennington, and N. K. Shaw, “Automatic Finite-Element Mesh Generation from Geometric Models – A Point Based Approach,” ACM Trans. Graphics, Vol.3, p. 287, 1984.
16. [16] A. Pandey, R. Datta, and B. Bhattacharya, “Topology Optimization of Compliant Structures and Mechanisms using Constructive Solid Geometry for 2-d and 3-d Applications,” Methodologies and Application Soft Computing, First online: September 04, 2015.
17. [17] J.-F. Remacle, C. Geuzaine, G. Compere, and E. Marchandise, “High Quality Surface Remeshing Using Harmonic Maps,” Int. J. Numer. Meth. Engng. Vol.83, Issue 4, pp. 403-425, July 23, 2010.
18. [18] N. Harris, “Conformal Refinement of All-Hexahedral Finite Element Meshes,” Master’s Thesis, Brigham Young University, Provo, 2004.
19. [19] M. Parrish, M. Borden, M. L. Staten, and S. E. Benzley, “A Selective Approach to Conformal Refinement of Unstructured Hexahedral Finite Element Meshes,” Proc. of 16th Int. Meshing Roundtable, pp. 251-268, 2007.
20. [20] M. W. Dewey, “Automated Quadrilateral Coarsening by Ring Collapse,” Master’s Thesis, Brigham Young University, Provo, 2008.
21. [21] F. Cheng, J. W. Jaromczyk, J.-R. Lin, S.-S. Chang, and J.-Y. Lu, “A Parallel Mesh Generation Algorithm Based on the Vertex Label Assignment Scheme,” Int. J. Num. Meth. Eng., Vol.28, p. 1429, 1989.