A New Global-Local Analysis Using MLS(Moving Least Square Variable-Node Finite Elements

이동최소제곱 다절점 유한요소를 이용한 새로운 전역-국부해석

  • Published : 2007.06.30

Abstract

We present a new global-local analysis with the aid of MLS(Moving Least Square) variable-node finite elements which can possess an arbitrary number of nodes on element master domain. It enables us to connect one finite element with a few finite elements without complex remeshing. Compared to other type global-local analysis, it does not require any superimposed mesh or need not solve the equilibrium equation twice. To demonstrate the performance of the proposed scheme, we will show several examples in relation to capturing highly local stress field using global-local analysis.

References

  1. Aminpour, M.A., Ransom, J.B., McCleary, S.L.(1995) A coupled analysis method for structures with independently modeled finite element sub-domains. International Journal for Numerical Methods in Engineering, 38, pp. 3695-3718 https://doi.org/10.1002/nme.1620382109
  2. Cho, Y.S., Im, S.(2006) MLS-based variable-node elements compatible with quadratic interpolation Part II: application for finite crack element. International Journal for Numerical Methods in Engineering, 65, pp. 517-547 https://doi.org/10.1002/nme.1452
  3. Cho, Y.S., Im, S.(2006) MLS-based variable-node elements compatible with quadratic interpolation. Part I: formulation and application for non-matching meshes. International Journal for Numerical Methods in Engineering, 65, pp. 494-516 https://doi.org/10.1002/nme.1453
  4. Cho, Y.S., Jun, S., Im, S., Kim, H.G.(2005) An improved interface element with variable nodes for non-matching finite element meshes. Computer Methods in Applied Mechanics and Engineering, 194, pp. 3022-3046 https://doi.org/10.1016/j.cma.2004.08.002
  5. Choi, C. K., Park, Y. M.(1989) A nonconforming Transition Plate Bending Elements with Variable Mid-side nodes. Computers and Structures, 32, pp. 295-304 https://doi.org/10.1016/0045-7949(89)90041-2
  6. Choi, C.K., Lee, N.-H.(1993) Three dimensional transition solid elements for adaptive mesh gradation. Structural Engineering and Mechanics, 1, pp. 61-74 https://doi.org/10.12989/sem.1993.1.1.061
  7. Choi, C.K., Lee, N.-H.(1996) A 3-D adaptive mesh refinement using variable-node solid transition element. International Journal for Numerical Methods in Engineering, 39, pp. 1585-1606 https://doi.org/10.1002/(SICI)1097-0207(19960515)39:9<1585::AID-NME918>3.0.CO;2-D
  8. Choi, C.K., Park, Y. M.(1997) Conforming and nonconforming transition plate bending elements for an adaptive h-refinement. Thin-Walled Structures, 28, pp. 1-20 https://doi.org/10.1016/S0263-8231(97)00007-4
  9. Fish, J., Guttal, R.(1998) The s-version of finite element method for laminated composites. International Journal for Numerical Methods in Engineering, 39, pp. 3641-3662 https://doi.org/10.1002/(SICI)1097-0207(19961115)39:21<3641::AID-NME17>3.0.CO;2-P
  10. Hughes, T. J. R.(1987) The finite element method: linear static and dynamic finite element analysis. Prentice-Hall, New York
  11. Jin, X., Li, G., Aluru, R.N.(2001) On the equivalence between least square and kernel approximations in meshless methods. Computer Modeling in Engineering and Science, 2, pp. 341-350
  12. Kadowaki, H., Liu, W. K.(2004) Bridging multi-scale method for localization problems. Computer Methods in Applied Mechanics and Engineering, 193, pp. 3267-3302 https://doi.org/10.1016/j.cma.2003.11.014
  13. Kim, H.G. (2002) Interface Element Method (IEM) for a partitioned system with non-matching interfaces. Computer Methods in Applied Mechanics and Engineering, 191. pp. 3165-3194 https://doi.org/10.1016/S0045-7825(02)00255-4
  14. Lancaster, P., Salkauskas, K.(1981) Surface generated by moving least squares method. Mathematics of Computation, 37, pp. 141-158 https://doi.org/10.2307/2007507
  15. Li, S., Liu, W.K.(2004) Meshfree Particle Methods, Springer, New York
  16. Lim, J. H., Im, S.(2007) (4+n)-noded MLS (Moving Least Square)-based finite elements for mesh gradation. Structural Engineering and Mechanics, 25, pp. 91-106 https://doi.org/10.12989/sem.2007.25.1.091
  17. Lim, J. H., Im, S., Cho, Y.-S.(2007) MLS (Moving Least Squarer-based finite elements for three-dimensional non-matching meshes and adaptive mesh refinement. Computer Methods in Applied Mechanics and Engineering, 196, pp. 2216-2228 https://doi.org/10.1016/j.cma.2006.11.014
  18. Lim, J. H., Im, S., Cho, Y.-S.(2007) Variable-node finite elements for non-matching meshes by means of MLS(Moving Least Square) scheme. International Journal Numerical Methods in Engineering, available online
  19. Liu, G.R., Gu, Y.T., Dai, K.Y. (2004) Assessment and applications of point interpolation methods for computational mechanics. International Journal for Numerical Methods in Engineering, 59, pp. 1373-1397 https://doi.org/10.1002/nme.925
  20. Liu, W.K., Jun, S., Z, Y.F.(1995) Reproducing kernel particle methods. International Journal of Numerical Methods in Fluids, 20, pp. 1081-1106 https://doi.org/10.1002/fld.1650200824
  21. Mote, C.D. (1970) Global-local finite element method. International Journal for Numerical Methods in Engineering, 3, pp. 565-574 https://doi.org/10.1002/nme.1620030410
  22. Nemat-Nasser, S., Hori, M.(1993) Micromechanics, North Holland Publication, Amsterdam
  23. Park, K.C., Felippa, C.A., Rebel, G.(2002) A simple algorithm for localized construction of non-matching structural interfaces. International Journal for Numerical Methods in Engineering, 53, pp. 2117-2142 https://doi.org/10.1002/nme.374
  24. Quiroz, L., Beckers, P.(1995) Non-conforming mesh gluing in the finite elements methods. International Journal for Numerical Methods in Engineering, 38, pp. 2165-2184 https://doi.org/10.1002/nme.1620381303
  25. Timkshenko, S.P., Goodier, J.N.(1970) Theory of Elasticity (3rd edn), McGraw-Hill, New York