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http://dx.doi.org/10.12989/csm.2012.1.1.019

FEM-BEM iterative coupling procedures to analyze interacting wave propagation models: fluid-fluid, solid-solid and fluid-solid analyses  

Soares, Delfim Jr. (Structural Engineering Department, Federal University of Juiz de Fora)
Publication Information
Coupled systems mechanics / v.1, no.1, 2012 , pp. 19-37 More about this Journal
Abstract
In this work, the iterative coupling of finite element and boundary element methods for the investigation of coupled fluid-fluid, solid-solid and fluid-solid wave propagation models is reviewed. In order to perform the coupling of the two numerical methods, a successive renewal of the variables on the common interface between the two sub-domains is performed through an iterative procedure until convergence is achieved. In the case of local nonlinearities within the finite element sub-domain, it is straightforward to perform the iterative coupling together with the iterations needed to solve the nonlinear system. In particular, a more efficient and stable performance of the coupling procedure is achieved by a special formulation that allows to use different time steps in each sub-domain. Optimized relaxation parameters are also considered in the analyses, in order to speed up and/or to ensure the convergence of the iterative process.
Keywords
wave propagation; iterative coupling; finite element method; boundary element method; multi-domain decomposition; different time-steps; nonlinear calculations;
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1 Bathe, K.J. (1996), Finite element procedures, Prentice-Hall.
2 Becker, A.A. (1992), The boundary element method in engineering, McGraw-Hill.
3 Belytschko, T. and Lu, Y.Y. (1994), "A variational coupled FE-BE method for transient problems", Int. J. Num. Meth. Eng., 37(1), 91-105.   DOI   ScienceOn
4 Belytschko, T., Liu, W.K. and Moran, B (2000), Nonlinear finite elements for continua & structures, J. Wiley & Sons.
5 Beskos, D.E. (1987), "Boundary element methods in dynamic analysis", App. Mech. Rev., 40(1), 1-23.   DOI
6 Beskos, D.E. (1996), "Boundary element methods in dynamic analysis: Part II", App. Mech. Rev., 50(3), 149-197.
7 Beskos, D.E. (2003), Dynamic Analysis of Structures and Structural Systems, (Eds. Beskos, D.E. and Maier, G.), Boundary Element Advances in Solid Mechanics, CISM International Centre for Mechanical Sciences, 440, 1- 53.
8 Crisfield, M.A. (1991), Non-linear Finite Element Analysis of Solid Structures, John Wiley & Sons.
9 Czygan, O. and von Estorff, O. (2002), "Fluid-structure interaction by coupling BEM and nonlinear FEM", Eng. Anal. Bound. Elem., 26(9), 773-779.   DOI   ScienceOn
10 Dominguez, J. (1993), Boundary elements in dynamics, Computational Mechanics Publications.
11 Elleithy, W.M., Al-Gahtani, H.J. and El-Gebeily, M. (2001), "Iterative coupling of BE and FE methods in elastostatics", Eng. Anal. Bound. Elem., 25(8), 685-695.   DOI   ScienceOn
12 Elleithy, W. and Grzibovskis, R. (2009), "An adaptive domain decomposition coupled finite element - boundary element method for solving problems in elasto-plasticity", Int. J. Num. Meth. Eng., 79, 1019-1040.   DOI   ScienceOn
13 Elleithy, W.M. and Tanaka, M. (2002), "BEM-BEM coupling and FEM-BEM coupling via interface relaxation", Eng. Anal. Bound. Elem.,19(9), 37-42.
14 Firuziaan, M. and von Estorff, O. (2002), Transient 3D soil/structure interaction analyses including nonlinear effects, (Eds. Grundmann, H. and Schuëller, G.I.), Structural Dynamics, EURODYN2002, Swets &Zeitlinger B.V.
15 Hughes, T.J.R. (1987), The finite element method, Prentice-Hall.
16 Jacob, B.P. and Ebecken, N.F.F. (1994), "An optimized implementation of the Newmark/Newton-Raphson algorithm for the time integration of non-linear problems", Commun. Numer. Meth. En., 10(12), 983-992.   DOI   ScienceOn
17 Lin, C.C. (1996), "An iterative finite element-boundary element algorithm", Comput. Struct., 59(5), 899-909.   DOI   ScienceOn
18 Mansur W.J. (1983), A time-stepping technique to solve wave propagation problems using the boundary element method, Ph.D. Thesis, University of Southampton, England.
19 Newmark, N.M. (1959), "A method of computation for structural dynamics", J. Eng. Mech. - ASCE, 85(7), 67-94.
20 Pavlatos, G.D. and Beskos, D.E. (1994), "Dynamic elastoplastic analysis by BEM/FEM", Eng. Anal. Bound. Elem., 14(1), 51-63.   DOI   ScienceOn
21 Soares, D. (2008a), "A time-domain FEM-BEM iterative coupling algorithm to numerically model the propagation of electromagnetic waves", Comput. Model. Eng.Sci., 32, 57-68.
22 Soares, D. (2008b), "An optimised FEM-BEM time-domain iterative coupling algorithm for dynamic analyses", Comput. Struct., 86(19-20), 1839-1844.   DOI   ScienceOn
23 Soares, D. (2008c), "Numerical modelling of acoustic-elastodynamic coupled problems by stabilized boundary element techniques", Comput. Mech., 42(6), 787-802.   DOI   ScienceOn
24 Soares, D. (2009a), "Acoustic modelling by BEM-FEM coupling procedures taking into account explicit and implicit multi-domain decomposition techniques", Int. J. Numer. Meth. Eng., 78(9), 1076-1093.   DOI   ScienceOn
25 Soares, D. (2009b), "An iterative time-domain algorithm for acoustic-elastodynamic coupled analysis considering meshless local Petrov-Galerkin formulations", Comput. Model. Eng.Sci., 54, 201-221.
26 Soares, D. (2009c), "Fluid-structure interaction analysis by optimised boundary element - finite element coupling procedures", J. Sound Vib., 322(1-2), 184-195.   DOI
27 Soares, D. (2011), Coupled numerical methods to analyze interacting acoustic-dynamic models by multidomain decomposition techniques, Mathematical Problems in Engineering, 2011, 1-28.
28 Soares, D., Carrer, J.A.M. and Mansur, W.J. (2005a), "Nonlinear elastodynamic analysis by the BEM: an approach based on the iterative coupling of the D-BEM and TD-BEM formulations" Eng. Anal. Bound. Elem., 29, 761-774.   DOI   ScienceOn
29 Soares, D., Godinho, L., Pereira, A. and Dors, C. (2012), "Frequency domain analysis of acoustic wave propagation in heterogeneous media considering iterative coupling procedures between the method of fundamental solutions and Kansa's method", Int. J. Numer. Meth. Eng., 89, 914-938.   DOI   ScienceOn
30 Soares, D., Mansur, W.J. (2006), "Dynamic analysis of fluid-soil-structure interaction problems by the boundary element method", J. Comput. Phys., 219(2), 498-512.   DOI   ScienceOn
31 Soares, D., von Estorff, O. and Mansur, W.J. (2004), "Iterative coupling of BEM and FEM for nonlinear dynamic analyses", Comput. Mech., 34(1), 67-73.
32 Soares, D., von Estorff, O. and Mansur, W.J. (2005b), "Efficient nonlinear solid-fluid interaction analysis by an iterative BEM/FEM coupling", Int. J. Numer. Meth. Eng., 64(11), 1416-1431.   DOI   ScienceOn
33 von Estorff O (Ed.) (2000), Boundary Elements in Acoustics - Advances and Applications, WIT Press, Southampton.
34 von Estorff, O. and Prabucki, M.J. (1990), "Dynamic response in the time domain by coupled boundary and finite elements", Comput. Mech., 6(1), 35-46.   DOI   ScienceOn
35 von Estorff, O. and Antes, H. (1991) "On FEM-BEM coupling for fluid-structure interaction analysis in the time domain", Int. J. Numer. Meth. Eng., 31(6), 1151-1168.   DOI
36 von Estorff, O. and Firuziaan, M. (2000), "Coupled BEM/FEM approach for nonlinear soil/structure interaction", Eng. Anal. Bound. Elem., 24(10), 715-725.   DOI   ScienceOn
37 von Estorff, O. and Hagen, C. (2005), "Iterative coupling of FEM and BEM in 3D transient elastodynamics", Eng. Anal. Bound. Elem., 29(8), 775-787.   DOI   ScienceOn
38 Warszawski, A., Soares, D. and Mansur, W.J. (2008), "A FEM-BEM coupling procedure to model the propagation of interacting acoustic-acoustic / acoustic-elastic waves through axisymmetric media", Comput. Method. Appl. M., 197(45-48), 3828-3835.   DOI   ScienceOn
39 Yan B., Du, J. and Hu, N. (2006), "A domain decomposition algorithm with finite element-boundary element coupling", Appl. Math. Mech - ENGL., 27(4), 519-525.   DOI   ScienceOn
40 Yazdchi, M., Khalili, N. and Valliappan, S. (1999), "Non-linear seismic behavior of concrete gravity dams using coupled finite element-boundary element technique", Int. J. Numer. Meth. Eng., 44(1), 101-130.   DOI   ScienceOn
41 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.   DOI   ScienceOn
42 Zienkiewicz, O.C., Kelly D.M. and Bettes, P. (1977), "The coupling of the finite element method and boundary solution procedures", Int. J. Numer. Meth. Eng., 11(2), 355-376.   DOI   ScienceOn
43 Zienkiewicz, O.C., Kelly, D.M. and Bettes, P. (1979), Marriage a la mode - the best of both worlds (Finite elements and boundary integrals), (Eds. Glowinski, R., Rodin, E.Y. and Zienkiewicz, O.C.), Energy Methods in Finite Element Analysis, J. Wiley & Sons.
44 Zienkiewicz, O.C., and Taylor, R.L. (2002), The finite element method, Butterworth-Heinemann, Oxford.