Structural Engineering and Mechanics

  • 제17권5호
  • /
  • Pages.671-690
  • /
  • 2004
  • /
  • 1225-4568(pISSN)
  • /
  • 1598-6217(eISSN)
테크노프레스 (Techno-Press)
권호 표지
DOI QR코드

DOI QR Code

Development of a meshless finite mixture (MFM) method

  • Cheng, J.Q. (Institute of High Performance Computing) ;
  • Lee, H.P. (Institute of High Performance Computing) ;
  • Li, Hua (Institute of High Performance Computing)
  • 투고 : 2003.07.18
  • 심사 : 2003.12.22
  • 발행 : 2004.05.25
⟨ 이전 논문 다음 논문 ⟩

초록

A meshless method with novel variation of point collocation by finite mixture approximation is developed in this paper, termed the meshless finite mixture (MFM) method. It is based on the finite mixture theorem and consists of two or more existing meshless techniques for exploitation of their respective merits for the numerical solution of partial differential boundary value (PDBV) problems. In this representation, the classical reproducing kernel particle and differential quadrature techniques are mixed in a point collocation framework. The least-square method is used to optimize the value of the weight coefficient to construct the final finite mixture approximation with higher accuracy and numerical stability. In order to validate the developed MFM method, several one- and two-dimensional PDBV problems are studied with different mixed boundary conditions. From the numerical results, it is observed that the optimized MFM weight coefficient can improve significantly the numerical stability and accuracy of the newly developed MFM method for the various PDBV problems.

키워드

참고문헌

  1. Belytschko, T., Lu, Y.Y. and Gu, L. (1994), "Element free Galerkin methods", Int. J. Numer. Meth. Eng., 37,229-256. https://doi.org/10.1002/nme.1620370205
  2. Cheng, M. and Liu, G.R. (2002), "A novel finite point method for flow simulation", Int. J. Numer. Meth. Fluid,39(12), 1161-1178. https://doi.org/10.1002/fld.365
  3. Cheng, J.Q., Li, H., Lam, K.Y., Ng, T.Y. and Yew, Y.K. (2002), "A new hybrid meshless-differential orderreduction (hM-DOR) method for deformation control of smart circular plate by distributed sensors/actuators",Advances in Meshfree and X-FEM Methods, Liu GR Editor, World Scientific Singapore, 49-54.
  4. Duarte, C.A. and Oden, J.T. (1996), "An h-p adaptive method using clouds", Comput. Meth. Appl. Mech. Eng.,139, 237-262. https://doi.org/10.1016/S0045-7825(96)01085-7
  5. Gingold, R.A. and Moraghan, J.J. (1977), "Smoothed particle hydrodynamics: theory and applications to nonsphericalstars", Monthly Notices of the Astronomical Society, 181, 375-389. https://doi.org/10.1093/mnras/181.3.375
  6. Gosz, J. and Liu, W.K. (1996), "Admissible approximations for essential boundary conditions in the reproducingkernel particle method", Comput. Mech., 19, 120-135. https://doi.org/10.1007/BF02824850
  7. Gunther, F.C. and Liu, W.K. (1998), "Implementation of boundary conditions for meshless methods", Comput.Meth. Appl. Mech. Eng., 63, 205-230.
  8. Hegen, D. (1996), "Element-free Galerkin methods in combination with finite element approaches", Comput.Meth. Appl. Mech. Eng., 135, 143-166. https://doi.org/10.1016/0045-7825(96)00994-2
  9. Krongauz, Y. and Belytschko, T. (1996), "Enforcement of essential boundary conditions in meshlessapproximation using finite elements", Comput. Meth. Appl. Mech. Eng., 131, 133-145. https://doi.org/10.1016/0045-7825(95)00954-X
  10. Liszka, T.J., Duarte, C.A.M. and Tworzydlo, W.W. (1996), "hp-meshless cloud method", Comput. Meth. Appl.Mech. Eng., 139, 263-288. https://doi.org/10.1016/S0045-7825(96)01086-9
  11. Liu, G.R. (2002), Mesh Free Methods - Moving Beyond the Finite Element Method, CRC Press.
  12. Liu, G.R. and Wu, T.Y. (2001), "Application of generalized differential quadrature rule in Blasius and Onsagerequation", Int. J. Numer. Meth. Eng., 52(9), 1013-1027. https://doi.org/10.1002/nme.251
  13. Liu, W.K., Chen, Y., Chang, C.T. and Belytschko, T. (1996), "Advances in multiple scale kernel particlemethods", Comput. Mech., 18, 73-111. https://doi.org/10.1007/BF00350529
  14. Liu, W.K., Jun, S. and Zhang, Y.F. (1995), "Reproducing kernel particle methods", Int. J. Numer. Meth. Eng., 20,1081-1106. https://doi.org/10.1002/fld.1650200824
  15. Liu, W.K., Jun, S., Li, S., Adde, J. and Belytschko, T. (1995), "Reproducing kernel particle methods forstructural dynamics", Int. J. Numer. Meth. Eng., 38, 1665-1679.
  16. Lu, Y.Y., Belytschko, T. and Gu, L. (1994), "A new implementation of the element free Galerkin method",Comput. Meth. Appl. Mech. Eng., 113, 397-414. https://doi.org/10.1016/0045-7825(94)90056-6
  17. Mukherjee, Y.X. and Mukherjee, S. (1997), "On boundary conditions in the element free Galerkin method",Comput. Mech., 19, 267-270.
  18. Ng, T.Y., Li, H., Cheng, J.Q. and Lam, K.Y. (2003), "A new hybrid meshless-differential order reduction (hMDOR)method with applications to shape control of smart structures via distributed sensors/actuators", Eng.Struct., 25(2), 141-154. https://doi.org/10.1016/S0141-0296(02)00116-5
  19. Onate, E., Idelsohn, S., Zienkiewicz, O.C. and Taylor, R.L. (1990), "A finite point method in computationalmechanics: applications to convective transport and fluid flow", Int. J. Numer. Meth. Eng., 39, 3839-3866. https://doi.org/10.1002/(SICI)1097-0207(19961130)39:22<3839::AID-NME27>3.0.CO;2-R
  20. Shu, C. (2000), Differential Quadrature and Its Application in Engineering, Springer, Great Britain.
  21. Tarter, M.E. and Lock, M.D. (1994), Model-free Curve Estimation, Chapman & Hall, New York.
  22. Zhu, T. and Atluri, S.N. (1998), "Modified collocation method and a penalty formulation for enforcing theessential boundary conditions in the element free Galerkin method", Comput. Mech., 21, 211-222. https://doi.org/10.1007/s004660050296
  23. Zong, Z. and Lam, K.Y. (2002), "A localized differential quadrature (LDQ) method and its application to the 2Dwave equation", Comput. Mech., 29, 382-391. https://doi.org/10.1007/s00466-002-0349-4

피인용 문헌

  1. Micromechanical failure analysis of composite materials subjected to biaxial and off-axis loading vol.62, pp.1, 2017, https://doi.org/10.12989/sem.2017.62.1.043