DOI QR코드

DOI QR Code

Element free formulation for connecting sub-domains modeled by finite elements

  • Pan, Chan-Ping (Department of Construction Engineering, National Taiwan University of Science and Technology) ;
  • Tsai, Hsing-Chih (Ecological and Hazard Mitigation Engineering Research Center, National Taiwan University of Science and Technology)
  • Received : 2005.08.23
  • Accepted : 2006.09.13
  • Published : 2007.03.10

Abstract

Two methods were developed for analyzing problems with two adjacent sub-domains modeled by different kinds of elements in finite element method. Each sub-domain can be defined independently without the consideration of equivalent division with common nodes used for the interface. These two methods employ an individual interface to accomplish the compatibility. The MLSA method uses the moving least square approximation which is the basic formulation for Element Free Galerkin Method to formulate the interface. The displacement field assumed by this method does not pass through nodes on the common boundary. Therefore, nodes can be chosen freely for this method. The results show that the MLSA method has better approximation than traditional methods.

Keywords

References

  1. Aminpour, M.A, Ransom, J.B. and McCleary, S.L. (1995), 'A coupled analysis method for structures with independently modeled finite element subdomains', Int. J. Numer. Meth. Eng., 38(21), 3695-3718 https://doi.org/10.1002/nme.1620382109
  2. Arora, J.S., Chahande, A.I. and Paeng, J.K. (1991), 'Multiplier methods for engineering optimization', Int. J. Numer. Meth. Eng., 32(7), 1485-1525 https://doi.org/10.1002/nme.1620320706
  3. Belytschko, T., Lu, Y.Y. and Gu, L. (1994), 'Element-free Galerkin methods', Int. J. Numer. Meth. Eng., 37(2), 229-256 https://doi.org/10.1002/nme.1620370205
  4. Carey, G.F., Kabaila, A and Utku, M. (1982), 'On penalty methods for interelement constrains', Comput. Meth. Appl. Mech. Eng., 30(2), 151-171 https://doi.org/10.1016/0045-7825(82)90002-0
  5. Chang, T.Y, Saleeb, A.F. and Shyu, S.C. (1987), 'Finite element solutions of two-dimensional contact problems based on a consistent mixed formulation', Comput. Struct., 27(4), 455-466 https://doi.org/10.1016/0045-7949(87)90276-8
  6. Dohrmann, C.R. and Key, S.W. (1999), 'A transition element for uniform strain hexahedral and tetrahedral finite elements', Int. J. Numer. Meth. Eng., 44(12), 1933-1950 https://doi.org/10.1002/(SICI)1097-0207(19990430)44:12<1933::AID-NME574>3.0.CO;2-0
  7. Dohrmann, C.R., Key, S.W. and Heinstein, M.W. (2000), 'A method for connecting dissimilar finite element meshes in two dimensions', Int. J. Numer. Meth. Eng., 48(5), 655-678 https://doi.org/10.1002/(SICI)1097-0207(20000620)48:5<655::AID-NME893>3.0.CO;2-D
  8. Dohrmann, C.R., Key, S.W. and Heinstein, M.W. (2000), 'Methods for connecting dissimilar three-dimensional finite element meshes', Int. J. Numer. Meth. Eng., 47(5), 1057-1080 https://doi.org/10.1002/(SICI)1097-0207(20000220)47:5<1057::AID-NME821>3.0.CO;2-G
  9. Farhat, C. and Geradin, M. (1992), 'Using a reduced number of Lagrange multipliers for assembling parallel incomplete field finite element approximations', Comput. Meth. Appl. Mech. Eng., 97(3), 333-354 https://doi.org/10.1016/0045-7825(92)90050-T
  10. Ginman, K.M.S. (1997), Topology Optimization for 2-D Continuum Using Element Free Galerkin Method, The University of Texas at Arlington
  11. Gordon, W.J. and Wixson, J.A. (1978), 'Shapard's method of metric interpolation to bivariate and multivariate data', Mathematics of Computation, 32(141), 253-264 https://doi.org/10.2307/2006273
  12. Houlsby, G.T., Liu, G. and Augarde, C.E. (2000), 'A tying scheme for imposing displacement constraints in finite element analysis', Communications in Numerical Methods in Engineering, 16(10), 721-732 https://doi.org/10.1002/1099-0887(200010)16:10<721::AID-CNM371>3.0.CO;2-A
  13. Lancaster, P. and Salkauskas, K. (1981), 'Surfaces generated by moving least square method', Mathematics of Computation, 37(155), 141-158 https://doi.org/10.2307/2007507
  14. Liao, C.L., Reddy, J.N. and Engelstad, S.P. (1998), 'A solid-sell transition element for geometrically non-linear analysis of laminated composite structures', Int. J. Numer. Meth. Eng., 26(8), 1843-1854 https://doi.org/10.1002/nme.1620260811
  15. McCune, R.W., Armstrong, C.G. and Robison, D.J. (2000), 'Mixed-dimensional coupling in finite element models', Int. J. Numer. Meth. Eng., 49(6), 725-750 https://doi.org/10.1002/1097-0207(20001030)49:6<725::AID-NME967>3.0.CO;2-W
  16. Nayroles, B., Touzot, G. and Villon, P. (1992), 'Generalizing the finite element method diffuse approximation and diffuse element', Computational Mechanics, 10(5), 307-318 https://doi.org/10.1007/BF00364252
  17. Quiroz, L. and Beckers, P. (1995), 'Non-conforming mesh gluing in the finite elements method', Int. J. Numer. Meth. Eng., 38(13), 2165-2184 https://doi.org/10.1002/nme.1620381303
  18. Rixen, D., Farhat, C. and Geradin, M. (1998), 'Two-step, two-field hybrid method for the static and dynamic analysis of substructure problems with conforming and non-conforming interface', Comput. Meth. Appl. Mech. Eng., 154(3-4), 229-264 https://doi.org/10.1016/S0045-7825(97)00128-X
  19. Shim, K.W., Monaghan, D.J. and Armstrong, C.G. (2002), 'Mixed dimensional coupling in finite element stress analysis', Engineering with Computers, 18(3), 241-252 https://doi.org/10.1007/s003660200021
  20. Tsai, H.C. and Pan, C.P, (2004), 'Element free formulation used for connecting domain boundaries', J. Chinese Ins. Eng., 27(4), 585-596 https://doi.org/10.1080/02533839.2004.9670906