Structural Engineering and Mechanics

  • 제67권4호
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  • Pages.317-326
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  • 2018
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  • 1225-4568(pISSN)
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  • 1598-6217(eISSN)
테크노프레스 (Techno-Press)
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DOI QR코드

DOI QR Code

Iterative coupling of precise integration FEM and TD-BEM for elastodynamic analysis

  • Lei, Weidong (Shenzhen Graduate School, Harbin institute of Technology) ;
  • Liu, Chun (Shenzhen Graduate School, Harbin institute of Technology) ;
  • Qin, Xiaofei (Shenzhen Graduate School, Harbin institute of Technology) ;
  • Chen, Rui (Shenzhen Graduate School, Harbin institute of Technology)
  • 투고 : 2017.04.22
  • 심사 : 2018.05.24
  • 발행 : 2018.08.25
⟨ 이전 논문 다음 논문 ⟩

초록

The iterative decomposition coupling formulation of the precise integration finite element method (FEM) and the time domain boundary element method (TD-BEM) is presented for elstodynamic problems. In the formulation, the FEM node and the BEM node are not required to be coincident on the common interface between FEM and BEM sub-domains, therefore, the FEM and BEM are independently discretized. The force and displacement converting matrices are used to transfer data between FEM and BEM nodes on the common interface between the FEM and BEM sub-domains, to renew the nodal variables in the process of the iterations for the un-coincident FEM node and BEM node. The iterative coupling formulation for elastodynamics in current paper is of high modeling accuracy, due to the semi-analytical solution incorporated in the precise integration finite element method. The decomposition coupling formulation for elastodynamics is verified by examples of a cantilever bar under a Heaviside-type force and a harmonic load.

키워드

과제정보

연구 과제 주관 기관 : National Natural Science Foundation of China, Shenzhen Science and Technology Innovation Commission

참고문헌

  1. Brebbia, C.A. (1980), Boundary Element Techniques in Engineering, Pentech Press, London, U.K.
  2. Cai, J.G. (2001), Effects of Parallel Fractures on Wave Attenuation in Rock, Ph.D. Dissertation, Nanyang Technological University, Singapore.
  3. Carrer, J.A.M. and Telles, J.C.F. (1992), "A boundary element formulation to solve transient dynamic elastoplastic problems", Comput. Struct., 45(4), 707-713. https://doi.org/10.1016/0045-7949(92)90489-M
  4. Carrer, J.A.M. and Mansur, W.J. (1999), "Stress and velocity in 2D transient elastodynamic analysis by the boundary element method", Eng. Anal. Bound. Elem., 23(3), 233-245. https://doi.org/10.1016/S0955-7997(98)00080-0
  5. Carrer, J.A.M., Pereira, W.L.A. and Mansur, W.J. (2012), "Two-dimensional elastodynamics by the time-domain boundary element method: Lagrange interpolation strategy in time integration", Eng. Analy. Bound. Elem., 36(7), 1164-1172. https://doi.org/10.1016/j.enganabound.2012.01.004
  6. Carrer, J.A.M. and Mansur, W.J. (2015), "Time-domain BEM analysis for the 2d scalar wave equation: Initial conditions contributions to space and time derivatives", Int. J. Numer. Meth. Eng., 39(13), 2169-2188. https://doi.org/10.1002/(SICI)1097-0207(19960715)39:13<2169::AID-NME949>3.0.CO;2-1
  7. Cifuentes, C., Kim, S., Kim, M.H. and Park, W.S. (2015), "Numerical simulation of the coupled dynamic response of a submerged floating tunnel with mooring lines in regular waves", Struct. Eng. Mech., 5(2), 109-123.
  8. Elleithy, W.M. and Al-Gahtani, H.J. (2000), "An overlapping domain decomposition approach for coupling the finite and boundary element methods", Eng. Analy. Bound. Elem., 24(5), 391-398. https://doi.org/10.1016/S0955-7997(00)00014-X
  9. Elleithy, W.M., Al-Gahtani, H.J. and El-Gebeily, M. (2001), "Iterative coupling of BE and FE methods in elastostatics", Eng. Analy. Bound. Elem., 25(8), 685-695. https://doi.org/10.1016/S0955-7997(01)00054-6
  10. Elleithy, W.M. and Tanaka, M. (2003), "Interface relaxation algorithms for BEM-BEM coupling and FEM-BEM coupling", Comput. Meth. Appl. Mech. Eng., 192(26-27), 2977-2992. https://doi.org/10.1016/S0045-7825(03)00312-8
  11. Elleithy, W.M. and Tanaka, M. (2004), "A Guzik interface relaxation FEM-BEM coupling method for elasto-plasticanalysis", Eng. Analy. Bound. Elem., 28(7), 849-857. https://doi.org/10.1016/j.enganabound.2003.12.002
  12. Eringen, A.C and Suhubi E.S. (1975), Elastodynamics, Linear Theory, Vol. 2, Academic Press, New York, U.S.A.
  13. Estorff, O.V and Prabucki, M.J. (1990), "Dynamic response in the time domain by coupled boundary and finite elements", Comput. Mech., 6(1), 35-46. https://doi.org/10.1007/BF00373797
  14. Israil, A.S.M. and Banerjee, P.K. (1990), "Advanced development of time-domain BEM for two-dimensional scalar wave propagation", Int. J. Numer. Meth. Eng., 29(5), 1003-1020. https://doi.org/10.1002/nme.1620290507
  15. Kuhlmeyer, R.L. and Lysmer, J. (1973), "Finite element method accuracy for wave propagation problems", J. Soil Mech. Found. Div., 99, 421-427.
  16. Lei, W.D., Ji, D.F., Li, H.J. and Li, Q.X. (2015), "On an analytical method to solve singular integrals both in space and time for 2-D elastodynamics by TD-BEM", Appl. Math. Model., 39(20) 6307-6318 . https://doi.org/10.1016/j.apm.2015.01.045
  17. Lei, W.D., Li, H.J., Qin, X.F., Chen, R. and Ji, D.F. (2018), "Dynamics-based analytical solutions to singular integrals for elastodynamics by time domain boundary element method", Appl. Math. Model., 56, 612-625. https://doi.org/10.1016/j.apm.2017.12.019
  18. Leung, K.L., Zavareh, P.B. and Beskos, D.E. (1995), "2D elastostatic analysis by a symmetric BEM/FEM scheme", Eng. Analy. Bound. Elem., 15(1), 67-78. https://doi.org/10.1016/0955-7997(95)00020-O
  19. Li, H.B., Han, G.M., Mang, H.A. and Torzicky, P. (1986), "A new method for the coupling of the finite element and boundary element discretized subdomains of elastic bodies", Comput. Meth. Appl. Mech. Eng., 54(2), 161-185. https://doi.org/10.1016/0045-7825(86)90124-6
  20. Lin, C.C. and Lawton, E.C. (1996), "An iterative finite element-boundary element algorithm", Comput. Struct., 59(5), 899-909. https://doi.org/10.1016/0045-7949(95)00285-5
  21. Lu, S., Liu, J., Lin, G. and Wang, W.Y. (2015), "Time-domain analyses of the layered soil by the modified scaled boundary finite element method", Struct. Eng. Mech., 55(5), 1055-1086. https://doi.org/10.12989/sem.2015.55.5.1055
  22. Mansur, W.J., Carrer, J.A.M. and Siqueira, E.F.N. (1998), "Time discontinuous linear traction approximation in time-domain BEM scalar wave propagation analysis", Int. J. Numer. Meth. Eng., 42(4), 667-683. https://doi.org/10.1002/(SICI)1097-0207(19980630)42:4<667::AID-NME380>3.0.CO;2-8
  23. Prasad, N.N.V. (1992), Integrated Techniques for Coupled Elastostatic BEM and FEM Analysis, M.Sc. Dissertation, The University of New Mexico, Albuquerque, U.S.A.
  24. Soares, D. (2008), "An optimised FEM-BEM time-domain iterative coupling algorithm for dynamic analyses", Comput. Struct., 86(19-20), 1839-1844. https://doi.org/10.1016/j.compstruc.2008.04.001
  25. Soares, D. (2012), "FEM-BEM iterative coupling procedures to analyze interacting wave propagation models: Fluid-fluid, solid-solid and fluid-solid analyses", Coupled Syst. Mech., 1(1), 19-37. https://doi.org/10.12989/csm.2012.1.1.019
  26. Soares, D., Estorff, O.V. and Mamsur, W.J. (2004), "Iterative coupling of BEM and FEM for nonlinear dynamic analyses", Comput. Mech., 34(1), 67-73. https://doi.org/10.1007/s00466-004-0554-4
  27. Soares, D., Goncalves, K.A. and Telles, J.C.D.F. (2015), "Elastodynamic analysis by a frequency-domain FEM-BEM iterative coupling procedure", Coupled Syst. Mech., 4(3), 263-277. https://doi.org/10.12989/csm.2015.4.3.263
  28. Song, L.F. and Nie, G.H. (2009), "Treatment of corners using discontinuous boundary elelment", Chin. Q. Mech., 30(3), 371-377.
  29. Wang, M.F. and Zhou, X.Y. (2005), "Modified precise time step integration method of structural dynamic analysis", Earthq. Eng. Eng. Vibr., 4(2), 287-293. https://doi.org/10.1007/s11803-005-0011-1
  30. Yan, B., Du, J., Hu, N. and Sekine, H. (2006), "A domain decomposition algorithm with finite element boundary element coupling", Appl. Math. Mech., 27(4), 519-525. https://doi.org/10.1007/s10483-006-0412-y
  31. Yu, G., Mansur, W.J., Carrer, J.A.M. and Lie, S.T. (2001), "A more stable scheme for BEM/FEM coupling applied to two-dimensional elastodynamics", Comput. Struct., 79(8), 811-823. https://doi.org/10.1016/S0045-7949(00)00188-7
  32. Zhong, W.X. and Williams, F.W. (1994), "A precise time step integration method", J. Mech. Eng. Sci., 208(63), 427-430. https://doi.org/10.1243/PIME_PROC_1994_208_148_02
  33. Zienkiewicz, O.C. and Kelly, D.W. (1977), "The coupling of the finite element method and boundary solution procedures", Int. J. Numer. Meth. Eng., 11(2), 355-375. https://doi.org/10.1002/nme.1620110210