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Evaluation of grid-based hex meshes for solid mechanics

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Abstract

Grid-based methods for generating all-hex meshes show tremendous promise in automating and speeding up turnaround for computational simulations for solid mechanics. Recognizing some of the inherent weaknesses of grid-based methods, there has been hesitancy in accepting this technology as a viable option for critical FEA. The authors extend previous work on a grid-based method known as sculpt, and evaluate its effectiveness in practice. This study attempts to compare meshes generated with traditional manual pave-and-sweep technologies with those generated with sculpt’s automatic overlay grid method. We use a simple torsion pin analysis to understand both linear-elastic and non-linear elastic–plastic responses with grid-based meshes. We also introduce improvements to the sculpt grid-based procedure, including adaptive optimization-based smoothing, hex-dominant and pillowing to capture curve features as proposed techniques for improving mesh quality. This study demonstrates that in the cases tested, equivalent or superior results were achieved with grid-based meshes when compared to pave-and-sweep meshes.

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References

  1. Ansys ICEM CFD Mesh Generation Software (2014) http://www.ansys.com/Products/Other+Products/ANSYS+ICEM+CFD. Accessed July 2014

  2. Blacker TD, Meyers RJ (1993) Seams and wedges in plastering: a 3D hexahedral mesh generation algorithm. Eng Comput 2(9):83–93

    Article  Google Scholar 

  3. Brewer M, Freitag-Diachin L, Knupp PM, Leurent T, Melander D (2003) The mesquite mesh quality improvement toolkit, In: Proceedings, 12th International Meshing Roundtable 239–250

  4. Canann SA, Tristano JR, Staten ML (1998) An approach to combined laplacian and optimization-based smoothing for triangular, quadrilateral, and quad-dominant meshes, In: Proceedings, 7th International Meshing Roundtable p. 479–494

  5. Cook WA, Oakes WR (1982) Mapping methods for generating three-dimensional meshes, Comput Mech Eng, Aug, p. 67–72

  6. Cubit, Geometry and Meshing Toolkit (2014) http://cubit.sandia.gov. Accessed July 2014

  7. Freitag LA, Jones M, Plassmann PE (1995) An efficient parallel algorithm for mesh smoothing, In: Proceedings, 4th International Meshing Roundtable p. 47–58

  8. GHS3D: A powerful isotropic tet-mesher (2014) http://www-roc.inria.fr/gamma/gamma/ghs3d. Accessed July 2014

  9. Gridgen, Reliable CFD Meshing Software (2014) http://www.pointwise.com/gridgen. Accessed July 2014

  10. GridPro, Superior Engineering Solutions (2014) http://www.gridpro.com. Accessed July 2014

  11. Ito Y, Shih AM, Soni BK (2009) Octree-based reasonable-quality hexahedral mesh generation using a new set of refinement templates. Int J Numer Methods Eng 77(13):1809–1833

    Article  MATH  MathSciNet  Google Scholar 

  12. Knupp PM (2000) Achieving finite element mesh quality via optimization of the Jacobian matrix norm and associated quantities. Part II: A framework for volume mesh optimization and the condition number of the Jacobian matrix, Int J Numer Methods Eng 48:1165–1185

    Article  MATH  Google Scholar 

  13. Knupp PM (2001) Hexahedral and tetrahedral mesh untangling. Eng Comput 17:261–268

    Article  MATH  Google Scholar 

  14. Knupp PM (2003) A method for hexahedral mesh shape optimization. Int J Numer Methods Eng 58:319–332

    Article  MATH  Google Scholar 

  15. Owen SJ (2012) Parallel Smoothing for Grid-Based Methods, 21st Int. Meshing Roundtable, Research Note

  16. Owen SJ, Staten ML, Sorensen MC (2011) Parallel hex meshing from volume fractions, Proc. 20th Int. Meshing Roundtable, p. 161–178

  17. Owen SJ, Shepherd JF (2009) Embedding features in a cartesian grid, Proc. 18th Int. Meshing Roundtable, p. 117–138

  18. Owen SJ, Saigal S (2001) Formation of pyramid elements for hexahedra to tetrahedra transitions. Comput Methods in Applied Mechanics and Eng. 190(34):4505–4518

    Article  MathSciNet  Google Scholar 

  19. Richardson LF (1911) The approximate arithmetical solution by finite differences of physical problems including differential equations, with an application to the stresses in a masonry dam. Philos Transactions Royal Soc Lond Ser A 210(459–470):307–357

    Article  MATH  Google Scholar 

  20. Schneiders R, Schindler F, Weiler F (1996) Octree-based generation of hexahedral element meshes, Proc. 5th Int. Meshing Roundtable, p. 205–216

  21. Shelton TR, Crane NK, Cox JV (2013) An exploration of accuracy and convergence of the degenerate uniform strain hexahedral element, Proc. ASME 2013 Int. Mechanical Eng. Congress and Exposition (To appear)

  22. Sierra Solid Mechanics Team (2011) Adagio 4.22 User’s Guide, Sandia National Laboratories, Sandia Report SAND2011-7597

  23. Staten ML, Canann SA, Owen SJ (1998) BMSWEEP: Locating Interior Nodes During Sweeping, Proc. 7th Int. Meshing Roundtable p. 7–18

  24. Staten ML, Kerr RA, Kerr, Owen SJ, Blacker TD (2006) Unconstrained Paving and Plastering: Progress Update, Proc., 15th Int. Meshing Roundtable p. 469–486

  25. Tam TKH, Armstrong CG (1991) 2D Finite Element Mesh Generation by Medial Axis Subdivision, Adv Eng Softw 13:313–324

    MATH  Google Scholar 

  26. Tautges TJ, Blacker TD, Mitchell SA (1996) The Whisker Weaving Algorithm: A Connectivity-Based Method for Constructing All-Hex Meshes. Int J Numer Methods Eng 39:3327–3349

    Article  MATH  MathSciNet  Google Scholar 

  27. TrueGrid by XYZ Scientific Applications, Inc. (2013) A Mesh Generator and Pre-processor for FEA and CFD Analysis, http://www.truegrid.com. Accessed July 2014

  28. Zhang Y, Bajaj CL (2006) Adaptive and Quality Quadrilateral/Hexahedral Meshing from Volumetric Data. Comput Methods Appl Mech Eng 195:942–960

    Article  MATH  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Simulation Modeling Sciences, Sandia National Laboratories, Albuquerque, NM, USA

    Steven J. Owen

  2. Computational Solid Mechanics and Structural Dynamics, Sandia National Laboratories, Albuquerque, NM, USA

    Tim R. Shelton

Authors
  1. Steven J. Owen
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  2. Tim R. Shelton
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Correspondence to Steven J. Owen.

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Sandia is a multiprogram laboratory operated by Sandia Corporation, a Lockheed Martin Company for the United States Department of Energy’s National Nuclear Security Administration under contract DE-AC04-94AL85000.

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Owen, S.J., Shelton, T.R. Evaluation of grid-based hex meshes for solid mechanics. Engineering with Computers 31, 529–543 (2015). https://doi.org/10.1007/s00366-014-0368-8

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  • DOI: https://doi.org/10.1007/s00366-014-0368-8

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