Korean Journal of Computational Design and Engineering (한국CDE학회논문집)

Society for Computational Design and Engineering (한국CDE학회)
권호 표지

Mesh Reconstruction Using Redistibution of Nodes in Sub-domains and Its Application to the Analyses of Metal Forming Problems

영역별 절점재구성을 통한 격자재구성 및 소성가공해석

  • 홍진태 (한국과학기술원 기계공학과) ;
  • 양동열 (한국과학기술원 기계공학과)
  • Published : 2007.08.31
Download PDF
⟨ Previous Next ⟩

Abstract

In the finite element analysis of forming process, objects are described with a finite number of elements and nodes and the approximated solutions can be obtained by the variational principle. One of the shortcomings of a finite element analysis is that the structure of mesh has become inefficient and unusable because discretization error increases as deformation proceeds due to severe distortion of elements. If the state of current mesh satisfies a certain remeshing criterion, analysis is stopped instantly and resumed with a reconstructed mesh. In the study, a new remeshing algorithm using tetrahedral elements has been developed, which is adapted to the desired mesh density. In order to reduce the discretization error, desired mesh sizes in each lesion of the workpiece are calculated using the Zinkiewicz and Zhu's a-posteriori error estimation scheme. The pre-constructed mesh is constructed based on the modified point insertion technique which is adapted to the density function. The object domain is divided into uniformly-sized sub-domains and the numbers of nodes in each sub-domain are redistributed, respectively. After finishing the redistribution process of nodes, a tetrahedral mesh is reconstructed with the redistributed nodes, which is adapted to the density map and resulting in good mesh quality. A goodness and adaptability of the constructed mesh is verified with a testing measure. The proposed remeshing technique is applied to the finite element analyses of forging processes.

Keywords

References

  1. Zienkiewicz, O. C. and Zhu, J. Z., 'A Simple Error Estimate and Adaptive Procedure for Practical Engineering Analysis', International Journal for Numerical Methods in Engineering, Vol. 24, pp. 337-357, 1987 https://doi.org/10.1002/nme.1620240206
  2. 홍진태, 이석렬, 박철현, 양동열, '오차 예측과 격자밀도 지도를 이용한 적용 Delaunay 격자생성방법', 한국소성가공학회지, Vol. 13, No. 4, pp. 334-341, 2004
  3. Yoon, J. H. and Yang, D. Y., 'Rigid-plastic Finite Element Analysis of Three-dimensional Forging by Considering Friction on Continuous Curved Dies with Initial Guess Generation', International Journal of Mechanical Science, Vol. 30, pp. 887-898, 1988 https://doi.org/10.1016/0020-7403(88)90072-0
  4. Zienkiewicz, O. C. and Zhu, J. Z., 'The Superconvergent Patch Recovery and a Posteriori Error Estimates. Part 1: The Recovery Technique,' International Journal for Numerical Methods in Engineering, Vol. 33, pp. 1331-1364, 1992 https://doi.org/10.1002/nme.1620330702
  5. Piegl, L. A. and Tiller, W., 'Geometry-based Triangulation of Trimmed NURBS Surface', Computer-Aided Design, Vol. 30, pp. 11-18, 1998 https://doi.org/10.1016/S0010-4485(97)00047-X
  6. 이재영, '원시곡면 위의 유한요소망 자동생성 기법', 한국 CAD/CAM학회, Vol. 1, No.4, pp.189-202, 1996
  7. Chew, P., Constrained Delaunay triangulation, ACM, New York, 1987
  8. Bowyer, A., 'Computing Dirichlet Tessellations,' Computational Journal, Vol. 24, No.2, pp. 162-166, 1981 https://doi.org/10.1093/comjnl/24.2.162
  9. Watson, D. F., 'Computing the n-dimensional Delaunay Tessellation with Application to Voromoi Polytopes,' Computational Journal, Vol. 24, No.2, pp. 167-172, 1981 https://doi.org/10.1093/comjnl/24.2.167
  10. Brackbill, J. and Saltzman, J., 'Adaptive Zoning for Singular Problems in Two Dimensions', Journal of Computational Physics, Vol. 46, pp. 342-368, 1982 https://doi.org/10.1016/0021-9991(82)90020-1
  11. 홍진태, 이석렬, 양동열, '격자압축을 이용하여 구성된 격자의 효과적인 격자유연화 방법', 한국소성가공학회지, Vol. 12, No. 4, pp. 340-347, 2003
  12. Ruppert, J., 'A Delaunay Refinement Algorithm for Quality 2-dimensional Mesh Generation', Journal of Algorithm., Vol. 18, pp. 548-585, 1995 https://doi.org/10.1006/jagm.1995.1021
  13. Knupp, P. M., 'Algebraic Mesh Quality Metrics for Unstructured Initial Meshes', Finite Element in Analysis and Design, Vol. 39, pp. 217-241, 2003 https://doi.org/10.1016/S0168-874X(02)00070-7
  14. Weatherill, N. P. and Hassan, O., 'Efficient Threedimensional Delaunay Triangulation with Automatic Point Creation and Imposed Boundary Constraints', International Journal for Numerical Methods in Engineering, Vol. 37, No. 12, pp. 2005-2039, 1994 https://doi.org/10.1002/nme.1620371203
  15. Du, Q. and Wang, D., 'Tetrahedral Mesh Generation and Optimization based on Centroidal Voronoi Tessellations', International Journal for Numerical Methods in Engineering, Vol. 56, pp. 1355-1373, 2003 https://doi.org/10.1002/nme.616