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Inverse Adaptation of Hex-dominant Mesh for Large Deformation Finite Element Analysis

  • Arbtip Dheeravongkit
  • Kenji Shimada
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4077)

Abstract

In the finite element analysis of metal forming processes, many mesh elements are usually deformed severely in the later stage of the analysis because of the large deformation of the geometry. Such highly distorted elements are undesirable in finite element analysis because they introduce error into the analysis results and, in the worst case, inverted elements can cause the analysis to terminate prematurely. This paper proposes an inverse adaptation method that reduces or eliminates the number of inverted mesh elements created in the later stage of finite element analysis, thereby lessening the chance of early termination and improving the accuracy of the analysis results. By this method, a simple uniform mesh is created initially, and a pre-analysis is run in order to observe the deformation behavior of the elements. Next, an input hex-dominant mesh is generated in which each element is “inversely adapted,” or pre-deformed in such a way that it has approximately the opposite shape of the final shape that normal analysis would deform it into. Thus, when finite element analysis is performed, the analysis starts with an input mesh of inversely adapted elements whose shapes are not ideal. As the analysis continues, the element shape quality improves to almost ideal and then, toward the final stage of analysis, degrades again, but much less than would be the case without inverse adaptation. This method permits analysis to run to the end, or to a further stage, with few or no inverted elements. Besides pre-skewing the element shape, the proposed method is also capable of controlling the element size according to the equivalent plastic strain information collected from the pre-analysis. The method can be repeated iteratively until reaching the final stage of deformation.

Keywords

Equivalent Plastic Strain Inverted Element Tetrahedral Mesh Original Mesh Input Mesh 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    ABAQUS 6.4.: Getting Started with ABAQUS/Explicit. In: Quasi-Static Analysis ch. 7. Hibbitt, Karlsson & Sorensen, Inc. (2003)Google Scholar
  2. 2.
    ABAQUS 6.4.: Analysis User’s Manual. Hibbitt, Karlsson & Sorensen, Inc. (2003)Google Scholar
  3. 3.
    ABAQUS 6.4.: Example Problems Manual. In: Forging with Sinusoidal Die ch. 1.3.9. Hibbitt, Karlsson & Sorensen, Inc. (2003)Google Scholar
  4. 4.
    Coupez, T.: Automatic Remeshing in Three-dimensional Moving Mesh Finite Element Analysis of Industrial Forming. Simulation of Material Processing: Theory, Practice, Methods and Applications, 407–412 (1995)Google Scholar
  5. 5.
    Dheeravongkit, A., Shimada, K.: Inverse Pre-deformation of Finite Element Mesh for Large Deformation Analysis. In: Proceedings of 13th International Meshing Roundtable, pp. 81–94 (2004)Google Scholar
  6. 6.
    Dheeravongkit, A., Shimada, K.: Inverse Pre-deformation of Finite Element Mesh for Large Deformation Analysis. Journal of Computing and Information Science in Engineering 5(4), 338–347 (2004)CrossRefGoogle Scholar
  7. 7.
    Dheeravongkit, A., Shimada, K.: Inverse Pre-deformation of the Tetrahedral Mesh for Large Deformation Finite Element Analysis. Computer-Aided Design and Applications 2(6), 805–814 (2005)Google Scholar
  8. 8.
    Gadala, M.S., Wang, J.: Simulation of Metal Forming Processes with Finite Element Methods. International Journal for Numerical Method in Engineering 44, 1397–1428 (1999)MATHCrossRefGoogle Scholar
  9. 9.
    Hattangady, N.V.: Automatic Remeshing in 3-D Analysis of Forming Processes. International Journal for Numerical Methods in Engineering 45, 553–568 (1999)MATHCrossRefGoogle Scholar
  10. 10.
    Hattangady, N.V.: Automated Modeling and Remeshing in Metal Forming Simulation. Ph.D. Thesis. Rensselaer Polytechnic Institute (2003)Google Scholar
  11. 11.
    Joun, M.S., Lee, M.C.: Quadrilateral Finite-Element Generation and Mesh Quality Control for Metal Forming Simulation. International Journal for Numerical Methods in Engineering 40, 4059–4075 (1997)MATHCrossRefGoogle Scholar
  12. 12.
    Khoei, A.R., Lewis, R.W.: Adaptive Finite Element Remeshing in a Large Deformation Analysis of Metal Powder Forming. International Journal for Numerical Methods in Engineering 45(7), 801–820 (1999)MATHCrossRefGoogle Scholar
  13. 13.
    Kraft, P.: Automatic Remeshing With Hexahedral Elements: Problems, Solutions and Applications. In: Proceedings of 8th International Meshing Roundtable, pp. 357–367 (1999)Google Scholar
  14. 14.
    Kwak, D.Y., Cheon, J.S., Im, Y.T.: Remeshing for Metal Forming Simulations–Part I: Two-dimensional Quadrilateral Remeshing. International Journal for Numerical Methods in Engineering 53(11), 2463–2500 (2002)MATHCrossRefGoogle Scholar
  15. 15.
    Kwak, D.Y., Im, Y.T.: Remeshing for metal forming simulations–Part II: Three-dimensional hexahedral mesh generation. International Journal for Numerical Methods in Engineering 53(11), 2501–2528 (2002)MATHCrossRefGoogle Scholar
  16. 16.
    Lee, Y.K., Yang, D.Y.: Development of a Grid-based Mesh Generation Technique and its Application to Remeshing during the Finite Element Simulation of a Metal Forming Process. Engineering Computations 16(3), 316–339 (1999)MATHCrossRefGoogle Scholar
  17. 17.
    Meinders, T.: Simulation of Sheet Metal Forming Processes. In: Adaptive Remeshing ch. 5 (1999)Google Scholar
  18. 18.
    Merrouche, A., Selman, A., Knoff-Lenoir, C.: 3D Adaptive Mesh Refinement. Communications in Numerical Methods in Engineering 14, 397–407 (1998)MATHCrossRefMathSciNetGoogle Scholar
  19. 19.
    Petersen, S.B., Martins, P.A.F.: Finite Element Remeshing: A Metal Forming Approach for Quadrilateral Mesh Generation and Refinement. International Journal for Numerical Methods in Engineering 40, 1449–1464 (1997)CrossRefGoogle Scholar
  20. 20.
    Souli, M.: An Eulerian and Fluid-Structure Coupling Algorithm in LS-DYNA. In: 5th International LS-Dyna Users Conference (1999)Google Scholar
  21. 21.
    Souli, M., Olovsson, L.: ALE and Fluid-Structure Interaction Capabilities in LS-DYNA. In: 6th International LS-Dyna Users Conference, 15-37-14-45 (2000)Google Scholar
  22. 22.
    Souli, M., Olovsson, L., Do, I.: ALE and Fluid-Structure Interaction Capabilities in LS-DYNA. In: 7th International LS-Dyna Users Conference, 10-27-10-36 (2002)Google Scholar
  23. 23.
    Stoker, H.C.: Developments of Arbitrary Lagrangian-Eulerian Method in Non-Linear Solid Mechanics. PhD thesis. University of Twente (1999)Google Scholar
  24. 24.
    Vallinkoski, I.: The design and implementation of a color management application. Chapter 6 Gamut Mapping Algorithm. MS Thesis. Helsinki University of Technology (1998)Google Scholar
  25. 25.
    Wagoner, R.H., Chenot, J.-L.: Forging Analysis. In: ch. 10 Metal Forming Analysis (2001) ISBN 0-521-64267-1Google Scholar
  26. 26.
    Wan, J., Kocak, S., Shephard, M.S.: Automated Adaptive Forming Simulations. In: Proceedings of 12th Interational Meshing Roundtable, pp. 323–334 (2003)Google Scholar
  27. 27.
    Yamakawa, S., Shimada, K.: Hex-Dominant Mesh Generation with Directionality Control via Packing Rectangular Solid Cells. IEEE Geometric Modeling and Processing - Theory and Applications (2002)Google Scholar
  28. 28.
    Yamakawa, S., Shimada, K.: Fully-Automated Hex-Dominant Mesh Generation with Directionality Control via Packing Rectangular Solid Cells. International Journal for Numerical Methods in Engineering 57, 2099–2129 (2003)MATHCrossRefMathSciNetGoogle Scholar
  29. 29.
    Yamakawa, S., Shimada, K.: Increasing the number and volume of hexahedral and prism elements in a hex-dominant mesh by topological transformations. In: Proceedings of 12th International Meshing Roundtable, pp. 403–413 (2003)Google Scholar
  30. 30.
    Zienkiewicz, O.C., Zhu, J.Z.: The Superconvergent Patch Recovery and A Posteriori Error Estimates. Part 1: The Recovery Technique. International Journal for Numerical Methods in Engineering 33, 1331–1364 (1992)MATHCrossRefMathSciNetGoogle Scholar
  31. 31.
    Zienkiewicz, O.C., Zhu, J.Z.: The Superconvergent Patch Recovery and a Posteriori Error Estimates. Part 2: Error Estimates and Adaptivity. International Journal for Numerical Methods in Engineering 33, 1365–1382 (1992)MATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Arbtip Dheeravongkit
    • 1
  • Kenji Shimada
    • 1
  1. 1.Carnegie Mellon UniversityPittsburghUSA

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