Abstract

In this paper, a novel hexahedral refinement method is introduced which finds the optimal tradeoff between the number of inserted elements and inserted singularities according to user-prescribed weighting. The input of our algorithm is the hexahedral mesh with quads tagged for refinement. The quad sets to be inserted by sheet inflation are determined by solving a integer optimization problem to minimize the number of inserted elements and inserted singularities while maintaining mesh consistency. Finally, we design the optimized sheet structures by selecting the optimal local shrink set at the cross section of intersecting quad sets to ensure the quality of mesh refinement. The refinement scheme can be applied iteratively until the mesh density meets the requirements. Experimental results for some mechanical parts verified the effectiveness of the proposed method.

References

1.
Zhang
,
H.
,
Zhao
,
G.
, and
Ma
,
X.
,
2007
, “
Adaptive Generation of Hexahedral Element Mesh Using An Improved Grid-Based Method
,”
Comput. Aided Des.
,
39
(
10
), pp.
914
928
.
2.
Pietroni
,
N.
,
Campen
,
M.
,
Sheffer
,
A.
,
Cherchi
,
G.
,
Bommes
,
D.
,
Gao
,
X.
,
Scateni
,
R.
,
Ledoux
,
F.
,
Remacle
,
J.-F.
, and
Livesu
,
M.
,
2022
, “
Hex-Mesh Generation and Processing: A Survey
,” arXiv preprint arXiv:2202.12670.
3.
Tchon
,
K.-F.
,
Dompierre
,
J.
, and
Camarero
,
R.
,
2002
, “
Conformal Refinement of All-Quadrilateral and All-Hexahedral Meshes According to An Anisotropic Metric
,”
11th International Meshing Roundtable
,
Ithaca, NY
,
Sept. 15–18
.
4.
Benzley
,
S. E.
,
Harris
,
N. J.
,
Scott
,
M.
,
Borden
,
M.
, and
Owen
,
S. J.
,
2005
, “
Conformal Refinement and Coarsening of Unstructured Hexahedral Meshes
,”
ASME J. Comput. Inf. Sci. Eng.
,
5
(
4
), pp.
330
337
.
5.
Mitchell
,
S. A.
, and
Tautges
,
T. J.
,
1995
, “
Pillowing Doublets: Refining a Mesh to Ensure That Faces Share at Most One Edge
,” Technical Report,
Sandia National Lab.(SNL-NM)
,
Albuquerque, NM
.
6.
Borden
,
M. J.
,
Benzley
,
S. E.
,
Mitchell
,
S. A.
,
White
,
D. R.
, and
Meyers
,
R. J.
,
2000
, “
The Cleave and Fill Tool: An All-Hexahedral Refinement Algorithm for Swept Meshes.
Proceedings of the 9th International Meshing Roundtable
,
New Orleans, LA
,
Oct. 2–5
, IMR, pp.
69
76
.
7.
Tchon
,
K.-F.
, and
Dompierre
,
J.
,
2004
, “
Automated Refinement of Conformal Quadrilateral and Hexahedral Meshes
,”
Int. J. Numer. Methods Eng.
,
59
(
12
), pp.
1539
1562
.
8.
Park
,
C.-H.
, and
Yang
,
D.-Y.
,
2006
, “
Adaptive Refinement of All-Hexahedral Elements for Three-Dimensional Metal Forming Analysis
,”
Finite Elements Anal. Des.
,
43
(
1
), pp.
22
35
.
9.
Shen
,
C.
,
Gao
,
S.
, and
Wang
,
R.
,
2022
, “
Hexahedral Mesh Adaptation Based on Posterior-Error Estimation
,”
Eng. Comput.
10.
Schneiders
,
R.
,
Schindler
,
R.
, and
Weiler
,
F.
,
1996
, “
Octree-Based Generation of Hexahedral Element Meshes
,”
Proceedings of the 5th International Meshing Roundtable
,
Pittsburgh, PA
,
Oct. 10–11
.
11.
Ito
,
Y.
,
Shih
,
A. M.
, and
Soni
,
B. K.
,
2009
, “
Octree-Based Reasonable-Quality Hexahedral Mesh Generation Using a New Set of Refinement Templates
,”
Int. J. Numer. Methods Eng.
,
77
(
13
), pp.
1809
1833
.
12.
Wada
,
Y.
, and
Okuda
,
H.
,
2002
, “
Effective Adaptation Technique for Hexahedral Mesh
,”
Concurr. Comput. Pract. Exp.
,
14
(
6–7
), pp.
451
463
.
13.
Kwak
,
D.-Y.
, and
Im
,
Y.-T.
,
2002
, “
Remeshing for Metal Forming Simulations-Part II: Three-Dimensional Hexahedral Mesh Generation
,”
Int. J. Numer. Methods Eng.
,
53
(
11
), pp.
2501
2528
.
14.
Parrish
,
M.
,
Borden
,
M.
,
Staten
,
M.
, and
Benzley
,
S.
,
2008
, “
A Selective Approach to Conformal Refinement of Unstructured Hexahedral Finite Element Meshes
,”
Proceedings of the 16th International Meshing Roundtable
,
Seattle, WA
,
Oct. 14–17
, Springer, pp.
251
268
.
15.
Zhang
,
Y.
,
Liang
,
X.
, and
Xu
,
G.
,
2013
, “
A Robust 2-Refinement Algorithm in Octree Or Rhombic Dodecahedral Tree Based All-Hexahedral Mesh Generation
,”
Comput. Methods. Appl. Mech. Eng.
,
256
, pp.
88
100
.
16.
Gurobi Optimization
,
2022
,
Gurobi Optimizer Reference Manual
, 9.5 ed.,
6
.
17.
Wang
,
R.
,
Ding
,
M.
,
Wu
,
H.
,
Zheng
,
Z.
, and
Gao
,
S.
,
2020
, “
Optimization Design Method of Complex Sheet Insertion Operation of Hexahedral Mesh
,”
J. Comput. Aided Des. Comput. Graph.
,
32
(
5
), pp.
846
856
.
18.
Melander
,
D. J.
,
Benzley
,
S. E.
, and
Tautges
,
T.
,
1997
, “
Generation of Multi-Million Element Meshes for Solid Model-Based Geometries: The Dicer Algorithm
,” Technical Report,
Sandia National Lab.(SNL-NM)
,
Albuquerque, NM
.
19.
Owen
,
S. J.
,
Shih
,
R. M.
, and
Ernst
,
C. D.
,
2017
, “
A Template-Based Approach for Parallel Hexahedral Two-Refinement
,”
Comput. Aided Des.
,
85
, pp.
34
52
.
20.
Wang
,
R.
,
Shen
,
C.
,
Chen
,
J.
,
Wu
,
H.
, and
Gao
,
S.
,
2017
, “
Sheet Operation Based Block Decomposition of Solid Models for Hex Meshing
,”
Comput. Aided Des.
,
85
, pp.
123
137
.
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