Searching Algorithm for Finite Element Analysis of 2-D Contact Problems

2차원 접촉문제의 유한요소 해석을 위한 탐색알고리즘

  • 장동환 (인하대학교 자동화공학과) ;
  • 최호준 (인하대학교 자동화공학과) ;
  • 고병두 (인하대학교 자동화공학과) ;
  • 조승한 (인하대학교 자동화공학과) ;
  • 황병복 (인하대학교 자동화공학과)
  • Published : 2003.12.01

Abstract

In this paper, efficient and accurate contact search algorithm is proposed for the contact problems by the finite element method. A slave node and a maser contact segment is defined using the side of a finite element on the contact surface. The specific goal is to develop techniques of reducing the nonsmoothness of the contact interactions arising from the finite element discretization of the contact surface. Contact detection is accomplished by monitoring the territory of the slave nodes throughout the calculation for possible penetration of a master surface. To establish the validity of the proposed algorithm, some different process and geometries examples were simulated. Efforts are focused on the error rate that is based on the penetrated area through the simulations fur large deformation with contact surface between deformable bodies. A proposed algorithm offers improvements in contact detection from the simulation results.

Keywords

References

  1. I. Paczelt, B.A. Szabo and T. Szabo, 'Solution of contact problem using the hp-version of the finite element method,' Int. J. Computers & Mathematics with Appl. Vol. 38, pp. 49-69, 1999 https://doi.org/10.1016/S0898-1221(99)00261-8
  2. S.S. Cho, S.Y. Lee and Y.K. Ryu, 'Determination of flexible tool path in curved surface finishing based on contact analysis,' J. KSPE, Vol. 17, No. 11, pp. 69-74, 2000
  3. P. Wriggers, 'Finite element methods for contact problems with friction,' Tribology International, Vol. 29, No. 8, pp. 651-658, 1996 https://doi.org/10.1016/0301-679X(96)00011-4
  4. S.P. Timoshenko and J.N. Foodier, 'Theory of Elasticity,' 3rd edition (McGraw-Hill, Toronto), pp. 403-422, 1970
  5. K.L. Johnson, 'Tribology group nominated lecture: One hundred years of Hertz contact,' Proc. Inst. Mech. Engrs. 196, pp. 363-378, 1982
  6. V. Padmanabhan and T.A. Laursen, 'A framework for development of surface smoothing procedures in large deformation frictional contact analysis,' Finite Elements in Analysis and Design, Vol. 37, pp. 173-198, 2001 https://doi.org/10.1016/S0168-874X(00)00029-9
  7. H.C.J. Bruneel and I.D. Rycke, 'QuickTrace: a fast algorithm to detect contact,' Int. J. for Numer. Meth. Engng., Vol. 54, pp. 299-316, 2002 https://doi.org/10.1002/nme.428
  8. W. R. C. Underhill, M. A. Dokainish, G. E. Oravas, 'A method for contact problems using virtual elements,' Comp. Methods Appl. Mech. Engrg., Vol. 143, pp. 229-247, 1997 https://doi.org/10.1016/S0045-7825(94)00764-0
  9. A, Santos, A. Makinouchi, 'Contact strategies to deal with different tool descriptions in static explicit FEM of 3-D sheet metal forming simulation,' NUMISHEET'93, Makinouchi et al.(eds), Japan, pp. 261-270, 1993
  10. E. Nakamachi, 'Computer aided simulation fo sheet metal forming procedures by thin shell finite element analysis,' Advancde Technology of Plasticity, Kyoto, pp. 1475-1750, 1990
  11. L. Nilsson, Z.H. Zhong, M. Oldenburg., 'Analysis of shell structures subjected to contact-impacts,' In Symposium on Analytical and Computational Models for Shells, Noor AK(ed.), ASME: San Fransisco, 1989
  12. Z.H. Zhong, 'Finite Element Procedure for Contact-Impact Problems,' Oxford University Press: New York, 1993
  13. N. Rebelo, J.C. Nagtegaal, L.M. Taylor, R. Passman, 'Comparison of implicit and explicit finite element methods int the simulation of metal forming processes,' Numiform'92, Chenot et al.(eds.), Valbonne, pp. 99-108, 1992
  14. M.W. Heinstein, S.W. Attaway, J.W. Swegle, F.J. Mello, 'A general contact detection algorithm for finite element analysis,' Computational Mechanical Publications, UK, 1993
  15. S.W. Attaway, 'Update of PRONTO2D and PRONTO3D Transient Solid Dynamics Programs,' SAND90-0102, Sandia National Laboratories, Albuquerque, NM 87185, 1990
  16. J.O. Hallquist and D.J. Benson, 'User's Manual for DYNA3D: Nonlinear Dynamics Analysis of Structures,' Rev. 3, UCID-19592, Lawrence Livemore National Laboratories, 1987
  17. Hibbitt, Karlsson and Sorensen, Inc., 'Contact Calculations with ABAQUS-ABAQUS Explicit Users Manual,' Hibbitt, Karlsson and Sorensen, Inc., 1992
  18. Y.W. Hahn and Y.T. Im, 'Finite element analysis forming processes with free surface contact algorithm,' Trans. of Materials Processing, Vol. 4, No. 1, pp. 48-58, 1995
  19. J.O. Hallquist, G.L. Goudreau, Benson DJ, 1985, 'Sliding interfaces with contact-impact in large-scale Lagrangian computation,' Computer Methods in Applied Numerical Methods, Vol. 51, pp. 107-137 https://doi.org/10.1016/0045-7825(85)90030-1
  20. T. Belytschko and W.K. Liu and B. Moran, Nonlinear finite elements for continua and structures, John Wiley & Sons, LTD, England, 2000
  21. D.H. Jang and B.B. Hwang, 'Rigid-plastic FE modelling of frictional contact problems on a penalty method,' Trans. of Meterials Processing, Vol. 12, No. 1, pp. 34-42, 2003
  22. Z.H. Zhong and L. Nillson, 'A contact searching algorithm for contact problems,' Computers & Structures, Vol. 33, No. 1, pp. 197-209, 1989 https://doi.org/10.1016/0045-7949(89)90141-7
  23. M. Bruneel and I. de Rijcke, 'A fast algorithm to detect contact,' Technical Report HBr/9501 OCAS n.v., October, 1995
  24. A.M. Harbraken, J.P. Radu and R. Charlier, 'Numerical approach of contact with friction between two bodies in large deformations,' Contact Mechanics int, Symposium, October 7-9, 1992
  25. Z.H. Zhong and L. Nilsson, 'A unified contact algorithm based on the territory concept,' Comput. Method Appl. Mech. Engrg, Vol. 130, pp. 1-16, 1996 https://doi.org/10.1016/0045-7825(95)00886-1
  26. S. Wang and A. Makinouchi, 'Contact search strategies for FEM simulation of the blow molding process,' Int. J. Numer. Meth. Engng 48, pp. 501-521, 2000 https://doi.org/10.1002/(SICI)1097-0207(20000610)48:4<501::AID-NME887>3.0.CO;2-S
  27. S.P. Wang and E. Nakamachi, 'The inside-outside contact search algorithm for finite element analysis,' Int. J. for Numer. Meth. Engng., Vol. 40, pp. 3665-3685, 1997 https://doi.org/10.1002/(SICI)1097-0207(19971015)40:19<3665::AID-NME234>3.0.CO;2-K
  28. M. Oldenburg and L. Nilsson, 'The position code algorithm for contact searching,' Int. J. for Numer. Meth. Engng., Vol. 37, pp. 359-386, 1994 https://doi.org/10.1002/nme.1620370302
  29. T. Belytschko, W.J.T. Daniel and G. Ventura, 'A monolithic smoothing-gap algorithm for contact-impact based on the signed distance function,' Int. J. for Numer. Meth. Engng., Vol. 55, pp. 101-125, 2002 https://doi.org/10.1002/nme.568
  30. A.M. Habraken and S. Cescotto, 'Contact between deformable solids: The fully coupled approach, Mathl,' Comput. Modelling, Vol. 28, No. 4-8, pp. 153-169, 1998 https://doi.org/10.1016/S0895-7177(98)00115-0
  31. Air Force Material Lavoratory, 'Forming Equipment,' Materials and Practices, Metal and Ceramics Information Center, p. 164, 1973