DOI QR코드

DOI QR Code

Shape Function Modification for the Imposition of EFGM Essential Boundary Conditions

EFGM에서 필수경계조건 처리를 위한 형상함수 수정법

Seok, Byeong-Ho;Song, Tae-Han;Im, Jang-Geun
석병호;송태한;임장근

  • Published : 2000.03.01

Abstract

For the effective analysis of an engineering problem, meshless methods which require only positioning finite points without the element meshing recently have been proposed and being studied extensively. Meshless methods have difficulty in imposing essential boundary conditions directly, because non-interpolate shape functions originated from an approximation process are used. So some techniques, which are Lagrange multiplier method, modified variational principles and coupling with finite elements and so on, were introduced in order to impose essential boundary conditions. In spite of these methods, imposition of essential boundary conditions have still many problems like as non-positive definiteness, inaccuracy and negation of meshless characteristics. In this paper, we propose a new method which modifies shape function. Through numerical tests, convergence, accuracy and validity of this method are compared with the standard EFGM which uses Lagrange multiplier method or modified variational principles. According to this study, the proposed method shows the comparable accuracy and efficiency.

Keywords

Element Free Galerkin Method(EFGM);Meshless Method;Essential Boundary Conditions;Interpolation Characteristics;Shape Function

References

  1. Belytschko, T., Organ, D. J. and Krongauz, Y, 1995, 'A Coupled Finite Element-Element-Free Galerkin Method,' Computational Mechnics , Vol. 17, pp. 186-195 https://doi.org/10.1007/BF00364080
  2. Krongauz, Y. and Belytschko, T., 1996, 'Enforcement of Essential Boundary Conditions in Meshless Approximations Using Finite Elements,' Computer Methods in Applied Mechanics and Engineering , Vol. 131, pp. 133-145 https://doi.org/10.1016/0045-7825(95)00954-X
  3. Kaljevic, I. and Saigal, S., 1997, 'An Improved Element-Free Galerkin Formulation,' International Journal for Numerical Methods in Engineering, Vol. 40, pp. 2953-2974
  4. Belytschko, T., Krongauz, Y., Organ, D., Fleming, M. and Krysl, P., 1996, 'Meshless Methods: An Overview and Recent Developments,' Computer Methods in Applied Mechanics and Engineering , Vol. 139, pp. 3-47 https://doi.org/10.1016/S0045-7825(96)01078-X
  5. Dolbow, J. and Belytschko, T., 1998, 'An Introduction to Programming the Meshless Element Free Galerkin Method,' Computational Mechanics, Vol. 5, No. 3, pp. 207-241
  6. 석병호, 임장근, 1998, '갤러킨 정식화를 사용한 무요소법의 구성과 그 특성,' 대한기계학회 '98년도 춘계학술대회 논문집, pp.396-401
  7. 석병호, 임장근,1999, '갤러킨 정식화를 사용한 무요소법의 구성과 그 특성,' 전산구조공학회논문집 , 제12권, 제1호, pp.47-56
  8. 송태한, 엄장큰, 1999, 'RKPM의 새로운 구성법,' 대한기계학회 '99 년도 춘계학술대회논문집, pp.833-837
  9. 석병호, 임장근, 1999, 'EFGM에서 필수경계조건을 위한 형상함수 수정법,' 대한기계학회 '99년도 춘계학술대회논문집, pp. 838-842
  10. Nayroles, B., Touzot, G. and Villon P., 1992, 'Generalizing the Finite Element Method: Diffuse Approximation and Diffuse Elements,' Computational Mechanics , Vol. 10, pp. 307-318 https://doi.org/10.1007/BF00364252
  11. Belytschko, T., Lu, Y. Y. and Gu L., 1994, 'Element-Free Galerkin Methods,' International Journal for Numerical Methods in Engineering , Vol. 37, pp. 229-256 https://doi.org/10.1002/nme.1620370205
  12. Lu, Y. Y., Belytschko, T. and Gu, L., 1994, 'A New Implementation of the Element-Free Galerkin Method,' Computer Methods in Applied Mechanics and Engineering , Vol. 113, pp. 397-414 https://doi.org/10.1016/0045-7825(94)90056-6
  13. Liu, W. K., Jun, S. and Zhang, Y. F., 1995, 'Reproducing Kernel Particle Methods,' International Journal for Numerical Methods in Fluids, Vol. 20, pp. 1081-1106 https://doi.org/10.1002/fld.1650200824
  14. Duarte, C. A. and Oden, J. T., 1996, 'An h-p Adaptive Method Using Clouds,' Computer Methods in Applied Mechanics and Engineering, Vol. 139, pp. 237-262 https://doi.org/10.1016/S0045-7825(96)01085-7
  15. Babuska, I. and Melenk, J. M., 1997, 'The Partition of Unity,' International Journal for Numerical Methods in Engineering, Vol. 40, pp. 727-758 https://doi.org/10.1002/(SICI)1097-0207(19970228)40:4<727::AID-NME86>3.0.CO;2-N
  16. 송태한, 임장근, 1998, 'RKPM 에서의 변위 경계조건 처리법,' 대한기계학회 '98년도 춘계학술대회논문집,pp.391-395