DOI QR코드

DOI QR Code

(4+n)-noded Moving Least Square(MLS)-based finite elements for mesh gradation

  • Lim, Jae Hyuk (Department of Mechanical Engineering, Korea Advanced Institute of Science and Technology (KAIST)) ;
  • Im, Seyoung (Department of Mechanical Engineering, Korea Advanced Institute of Science and Technology (KAIST))
  • 투고 : 2006.05.23
  • 심사 : 2006.08.16
  • 발행 : 2007.01.10

초록

A new class of finite elements is described for dealing with mesh gradation. The approach employs the moving least square (MLS) scheme to devise a class of elements with an arbitrary number of nodal points on the parental domain. This approach generally leads to elements with rational shape functions, which significantly extends the function space of the conventional finite element method. With a special choice of the nodal points and the base functions, the method results in useful elements with polynomial shape functions for which the $C^1$ continuity breaks down across the boundaries between the subdomains comprising one element. Among those, (4 + n)-noded MLS based finite elements possess the generality to be connected with an arbitrary number of linear elements at a side of a given element. It enables us to connect one finite element with a few finite elements without complex remeshing. The effectiveness of the new elements is demonstrated via appropriate numerical examples.

키워드

과제정보

연구 과제 주관 기관 : Ministry of Science and Technology

참고문헌

  1. Aminpour, M.A., Ransom, J.B. and McCleary, S.L. (1995), 'A coupled analysis method for structures with independently modeled finite element sub-domains', Int. J. Numer. Meth. Eng., 38, 3695-3718 https://doi.org/10.1002/nme.1620382109
  2. Aminpour, M.A., Krishnamurthy, T. and Fadale, T.D. (1998), 'Coupling of independently modeled three-dimensional finite element meshes with arbitrary shape interface boundaries', AIAA paper, 98-2060
  3. Cho, Y.-S., Jun, S., Im, S. and Kim, H.-G. (2005), 'An improved interface element with variable nodes for nonmatching finite element meshes', Comput. Meth. Appl. Mech. Eng., 194, 3022-3046 https://doi.org/10.1016/j.cma.2004.08.002
  4. Cho, Y.-S. and Im, S. (2006), 'MLS-based variable-node elements compatible with quadratic interpolation. Part 1: Formulation and application for non-matching meshes', Int. J. Numer. Meth. Eng., 65, 494-516 https://doi.org/10.1002/nme.1453
  5. Cho, Y.-S. and Im, S. (2006), 'MLS-based variable-node elements compatible with quadratic interpolation. Part II: application for finite crack element', Int. J. Numer. Meth. Eng., 65, 517-547 https://doi.org/10.1002/nme.1452
  6. Choi, C.K. and Lee, N.-H. (1996), 'A 3-D adaptive mesh refinement using variable-node solid transition element', Int. J. Numer. Meth. Eng., 39, 1585-1606 https://doi.org/10.1002/(SICI)1097-0207(19960515)39:9<1585::AID-NME918>3.0.CO;2-D
  7. Choi, C.K. and Lee, N.-H. (1993), 'Three dimensional transition solid elements for adaptive mesh gradation', Struct. Eng. Mech., 1, 61-74 https://doi.org/10.12989/sem.1993.1.1.061
  8. Choi, C.K. and Park, Y.M. (1989), 'A nonconforming transition plate bending elements with variable mid-side nodes', Comput. Struct., 32, 295-304 https://doi.org/10.1016/0045-7949(89)90041-2
  9. Choi, C.K. and Park, Y.M. (1997), 'Conforming and nonconforming transition plate bending elements for an adaptive h-refmement', Thin-Walled Struct., 28, 1-20 https://doi.org/10.1016/S0263-8231(97)00007-4
  10. Farhat, C. and Roux, F.X. (1991), 'A method of finite element tearing and interconnecting and its parallel solution algorithm', Int. J. Numer. Meth. Eng., 32, 1205-1227 https://doi.org/10.1002/nme.1620320604
  11. Gupta, A.K. (1978), 'A finite element for transition from a fine to a coarse grid', Int. J. Numer. Meth. Eng., 12, 35-45 https://doi.org/10.1002/nme.1620120104
  12. Han, W. and Meng, X. (2001), 'Error analysis of the reproducing kernel particle method', Comput. Meth. Appl. Mech. Eng., 190, 6157-6181 https://doi.org/10.1016/S0045-7825(01)00214-6
  13. Hinton, E. and Campbell, J.S. (1974), 'Local and global stress smoothing of discontinuous finite element functions using a least square method', Int. J. Numer. Meth. Eng., 8, 461-480 https://doi.org/10.1002/nme.1620080303
  14. Jin, X., Li, G. and Alum, R.N. (2001), 'On the equivalence between least square and kernel approximations in meshless methods', Comput. Model. Eng. Sci., 2, 341-350
  15. Kim, H.-G. (2002), 'Interface Element Method (IEM) for a partitioned system with non-matching interfaces', Comput. Meth. Appl. Mech. Eng., 191, 3165-3194 https://doi.org/10.1016/S0045-7825(02)00255-4
  16. Lancaster, P. and Salkauskas, K. (1981), 'Surface generated by moving least squares method', Math. Comp., 37, 141-158 https://doi.org/10.2307/2007507
  17. Lim, J.H., Im, S. and Cho, Y.-S., 'MLS(Moving Least Square)-based finite elements for complex domains and discontinuities', Int. J. Numer. Meth. Eng., Accepted for Publication
  18. Lim, J.H., Im, S. and Cho, Y.-S., 'MLS (Moving Least Square)-based finite elements for three-dimensional nonmatching meshes and adaptive mesh refinement', Comput. Meth. Appl. Mech. Eng., Accepted for Publication
  19. Liu, G.R., Gu, Y.T. and Dai, K.Y. (2004), 'Assessment and applications of point interpolation methods for computational mechanics', Int. J. Numer. Meth. Eng., 59, 1373-1397 https://doi.org/10.1002/nme.925
  20. Liu, W.K., Jun, S. and Zhang, Y.F. (1995), 'Reproducing kernel particle methods', Int. J. Numer. Meth. Fluids, 20, 1081-1106 https://doi.org/10.1002/fld.1650200824
  21. Pantano, A. and Averill, R.C. (2002), 'A penalty-based finite element interface technology', Comput. Struct., 80, 1725-1748 https://doi.org/10.1016/S0045-7949(02)00056-1
  22. Park, K.C., Felippa, C.A. and Rebel, G. (2002), 'A simple algorithm for localized construction of non-matching structural interfaces', Int. J. Numer. Meth. Eng., 53, 2117-2142 https://doi.org/10.1002/nme.374
  23. Quiroz, L. and Beckers, P. (1995), 'Non-conforming mesh gluing in the finite elements methods', Int. J. Numer. Meth. Eng., 38, 2165-2184 https://doi.org/10.1002/nme.1620381303
  24. Timoshenko, S.P. and Goodier, J.N. (1970), Theory of Elasticity(3rd edn). McGraw-Hill, New York

피인용 문헌

  1. A new computational approach to contact mechanics using variable-node finite elements vol.73, pp.13, 2008, https://doi.org/10.1002/nme.2162
  2. Finite element analysis of quasistatic crack propagation in brittle media with voids or inclusions vol.230, pp.17, 2011, https://doi.org/10.1016/j.jcp.2011.05.016
  3. A new three-dimensional variable-node finite element and its application for fluid–solid interaction problems vol.281, 2014, https://doi.org/10.1016/j.cma.2014.07.026
  4. An efficient three-dimensional adaptive quasicontinuum method using variable-node elements vol.228, pp.13, 2009, https://doi.org/10.1016/j.jcp.2009.03.028
  5. A sliding mesh technique for the finite element simulation of fluid–solid interaction problems by using variable-node elements vol.130, 2014, https://doi.org/10.1016/j.compstruc.2013.10.003
  6. A node-to-node scheme with the aid of variable-node elements for elasto-plastic contact analysis vol.102, pp.12, 2015, https://doi.org/10.1002/nme.4862
  7. Variable-node finite elements with smoothed integration techniques and their applications for multiscale mechanics problems vol.88, pp.7-8, 2010, https://doi.org/10.1016/j.compstruc.2009.12.004
  8. Three-dimensional variable-node elements based upon CS-FEM for elastic–plastic analysis vol.158, 2015, https://doi.org/10.1016/j.compstruc.2015.06.005
  9. MULTISCALE FINITE ELEMENT METHOD FOR HETEROGENEOUS MEDIA WITH MICROSTRUCTURES: CRACK PROPAGATION IN A POROUS MEDIUM vol.01, pp.01, 2009, https://doi.org/10.1142/S1756973709000086
  10. Variable-node element families for mesh connection and adaptive mesh computation vol.43, pp.3, 2012, https://doi.org/10.12989/sem.2012.43.3.349