Journal of Computational Design and Engineering

Society for Computational Design and Engineering (한국CDE학회)
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Quadrilateral mesh fitting that preserves sharp features based on multi-normals for Laplacian energy

  • Received : 2013.09.16
  • Accepted : 2013.11.01
  • Published : 2014.04.01
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Abstract

Because the cost of performance testing using actual products is expensive, manufacturers use lower-cost computer-aided design simulations for this function. In this paper, we propose using hexahedral meshes, which are more accurate than tetrahedral meshes, for finite element analysis. We propose automatic hexahedral mesh generation with sharp features to precisely represent the corresponding features of a target shape. Our hexahedral mesh is generated using a voxel-based algorithm. In our previous works, we fit the surface of the voxels to the target surface using Laplacian energy minimization. We used normal vectors in the fitting to preserve sharp features. However, this method could not represent concave sharp features precisely. In this proposal, we improve our previous Laplacian energy minimization by adding a term that depends on multi-normal vectors instead of using normal vectors. Furthermore, we accentuate a convex/concave surface subset to represent concave sharp features.

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References

  1. Kawaharada H, Hiraoka H. Boundary stencils of volume subdivision for simulations. In: Proceedings of the ACDDE; 2011 Aug 27-29; Shanghai, China; p. 3-8.
  2. Kawaharada H, Sugihara K. Hexahedral mesh generation using subdivision. Computational Engineering. 2011; 16(2): 12-15.
  3. Schneiders R, Schindler R, Weiler F. Octree-based generation of hexahedral element meshes. In: The 5th International Meshing Roundtable; 1996 Oct 10-11; Pittsburgh, PA; p. 205-215.
  4. Loic M. A new approach to octree-based hexahedral meshing. In: The 10th International Meshing Roundtable; 2001 Oct 10- 11; Newport Beach, CA; p. 209-221.
  5. Saten ML, Owen SJ, Blacker TD. Unconstrained paving and plastering: A new idea for all hexahedral mesh generation. In: The 14th International Meshing Roundtable; 2005 Sep 11-14; San Diego, CA; p. 399-416.
  6. Wada Y, Yoshimura S, Yagawa G. Automatic mesh generation method using intelligent local approach 2nd report its extension to hexahedral mesh generation. Journal of Transactions of the Japan Society of Mechanical Engineers Series. 2001; 67(655): 496-502. https://doi.org/10.1299/kikaia.67.496
  7. Blacker TD, Meyers RJ. Seams and wedges in plastering: A 3d hexahedral mesh generation algorithm. Engineering with Computers. 1993; 2(9): 83-93.
  8. Tautges TJ, Blacker T, Mitchell SA. The whisker weaving algorithm: A connectivity-based method for constructing allhexahedral finite element meshes. International Journal for Numerical Methods in Engineering. 1996; 39: 3327-3349. https://doi.org/10.1002/(SICI)1097-0207(19961015)39:19<3327::AID-NME2>3.0.CO;2-H
  9. Muller-Hannemann M. Hexahedral mesh generation by successive dual cycle elimination. In: The 7th International Meshing Roundtable; 1998 Oct 26-28; Dearborn, MI; p. 365-378.
  10. Sheffer A, Etzion M, Rappoport A, Bercovier M. Hexahedral mesh generation using the embedded Voronoi graph. In: The 7th International Meshing Roundtable; 1998 Oct 26-28; Dearborn, MI; p. 347-364.
  11. Jason S, Mitchell SA, Knupp P, White D. Methods for multisweep automation. In: The 9th International Meshing Roundtable; 2000 Oct 2-5; New Orleans, CA; p. 77-87.
  12. Xevi R, Sarrate J. An automatic and general least-squares projection procedure for sweep meshing. In: The 15th International Meshing Roundtable; 2006 Sep 17-20; Birmingham, AB; p. 487-506.
  13. Moriya S, Hiraoka H, Kawaharada H. Replication of sharp features hexahedral meshes using modified Laplacian energy minimization. In: Proceedings of the 3rd Asian Conference on Design and Digital Engineering; 2012 Dec 6-8; Hokkaido, JAPAN; Paper No. 100062.
  14. Aim@Shape Project [Internet]. Darmstadt: Germany; [cited 2012 Jul 11]. Available from: http://shapes.aimatshape.net/
  15. Polymender [Internet]. Seattle; [cited 2012 Jul 11]. Available from: http://www1.cse.wustl.edu/-taoju/code/polymender.htm
  16. Mehra R, Zhou Q, Long J, Sheffer A, Gooch A, Mitra NJ. Abstraction of man-made shapes. ACM Transactions on Graphics. 2009; 28(5): 1-10.