Journal of the Korean Society for Aeronautical & Space Sciences (한국항공우주학회지)

The Korean Society for Aeronautical and Space Sciences (한국항공우주학회)
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Node Activation Technique for Finite Element Model : Ⅰ. Theory

유한요소 모델의 절점 활성화 기법 : Ⅰ. 이론

  • Published : 2003.05.01
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Abstract

In this paper, a novel technique is proposed to arbitrarily activate the nodal points in finite element model through the meshless approximation methods such as MLS(moving least squares method), and theoretical investigations are carried out including the consistency and boundeness of numerical solution to prove the validity of the proposed method. By using the proposed node activation technique, one can activate and handle only the concerned nodes as unknown variables among the large number of nodal points in the finite element model. Therefore, the proposed technique has a great potential in design and reanalysis procedure.

본 논문에서는 이동최소자승 근사법 등의 무요소 근사법을 이용하여 유한요소모델 절점의 연결성과 무관하게 유한요소 절점을 자유로이 활성화시킬 수 있는 절점활성화 기법을 제안하고, 제안된 방법의 타당성을 고찰하기 위해 일관성 조건, 수치해의 유계성 등에 대한 이론적 고찰을 수행한다. 제안된 절점활성화 기법을 이용하면 많은 수의 유한요소 절점 중 관심이 있는 일부 절점만을 선택, 활성화시켜 이들만을 미지수로 이용하여 문제를 해석할 수 있기 때문에 설계 및 재해석을 효율적으로 수행할 수 있다.

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References

  1. Nayroles, B., Touzot, G., and Villon, P., "Generalizing the finite element method : diffuse approximation and diffuse elements," Comp. Mech., Vol. 10, 1992, pp. 307-318. https://doi.org/10.1007/BF00364252
  2. Belytschko, T., Lu, Y.Y., and Gu, L., "Element-free Galerkin methods," Int. J. Num. Meth. Eng., Vol. 37, 1994, pp. 229-256. https://doi.org/10.1002/nme.1620370205
  3. Belytschko, T., Krongauz, Y., and Organ D., "Meshless methods: on overview and recent developments," Comp. Meth. Appl. Mech. Eng. Vol. 139, 1996, pp. 3-47. https://doi.org/10.1016/S0045-7825(96)01078-X
  4. Liu, W.K., Jun, S., Zhang, Y., "Reproducing kernel particle methods," Int. J. Num. Meth. Fluids, Vol. 20, 1995, pp. 1081-1106. https://doi.org/10.1002/fld.1650200824
  5. Liu, W.K., Chen, Y., Chang, C.T., Belytschko, T., "Advances in multiple sclale kernel particle methods," Comp. Mech., Vol. 18, 1996, pp. 73-111. https://doi.org/10.1007/BF00350529
  6. Babuska, I., Melenk, J., "The partition of unity method," Int. J. Num. Meth. Eng., Vol. 40, 1997, pp. 727-758. https://doi.org/10.1002/(SICI)1097-0207(19970228)40:4<727::AID-NME86>3.0.CO;2-N
  7. Duarte, C.A., Orden, J.T., "An h-p adaptive method using clouds," Comp. Meth. Appl. Mech. Eng., Vol. 139, 1996, pp. 237-262. https://doi.org/10.1016/S0045-7825(96)01085-7
  8. Atluri S.N., Cho. J.Y., Kim H.G., "Analysis of thin beams, using the meshless local Petrov- Galerkin method, with generalized moving least squares interpolations," Comp. Mech. Vol. 24, 1999, pp. 334-347. https://doi.org/10.1007/s004660050456
  9. Atluri, S.N., Kim, H.G., Cho, J.Y., "A critical assessment of the truly Meshless Local Petrov-Galerkin (MLPG), and Local Boundary Integral Equation (LBIE) methods," Comp. Mech., Vol. 24, 1999, pp. 348-372. https://doi.org/10.1007/s004660050457
  10. Lancaster, P. and Salkaskas, K., "Surfaces generated by moving least squares methods," Meth. Comp. Vol. 37, 1981, pp. 141-158. https://doi.org/10.2307/2007507
  11. Naylor, A. W., and Sell, G. R., Linear Operator Theory in Engineering and Science, Springer-Verlag, New York, 1982.
  12. Strang, G., and Fix, G. J., An Analysis of the Finite Element Method, Prentice-Hall, Englewood Cliffs, N.J., 1973.
  13. Kim, S. J., Choi, Y. J., "Analysis of Mindlin plate by the element free Galerkin method applying penalty technique", Proceeding of 40th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference and Adaptive Structures Forum, pp.403-410, St.Louis, MO, 12-15 April, 1999
  14. 지영범, 조진연, "무요소법 변위 경계조건의 처리를 위한 이산 벌칙함수법의 적용," 한국항공우주학회 2001년도 추계학술대회 논문집, 2001년 11월, 세종대학교, pp. 817-820.
  15. Cho, J.Y., Jee, Y.B., "Further Investigation of Penalty Method to Efficiently Handle the Essential Boundary Conditions in Meshless Methods," Proceeding of the International Conference on Computational Engineering and Science, Reno, Nevada, July 31-August 2, 2002, CD-ROM