×

Efficient nonlinear solid-fluid interaction analysis by an iterative BEM/FEM coupling. (English) Zbl 1122.74382

Summary: An iterative coupling of finite element and boundary element methods for the time domain modelling of coupled fluid-solid systems is presented. While finite elements are used to model the solid, the adjacent fluid is represented by boundary elements. In order to perform the coupling of the two numerical methods, a successive renewal of the variables on the interface between the two subdomains is performed through an iterative procedure until the final convergence is achieved. In the case of local non-linearities within the finite element subdomain, it is straightforward to perform the iterative coupling together with the iterations needed to solve the non-linear system. In particular a more efficient and a more stable performance of the new coupling procedure is achieved by a special formulation that allows to use different time steps in each subdomain.

MSC:

74F10 Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.)
74S05 Finite element methods applied to problems in solid mechanics
76M15 Boundary element methods applied to problems in fluid mechanics
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] The Finite Element Method. Dover: New York, 1987.
[2] Finite Element Procedures. Prentice-Hall: Englewood Cliffs, NJ, 1996.
[3] The Boundary Element Method in Engineering. McGraw-Hill: Berkshire, 1992.
[4] Boundary Elements in Dynamics. Computational Mechanics Publications: Southampton, Boston, 1993.
[5] (ed.). Boundary Elements in Acoustics–Advances and Applications. WIT Press: Southampton, 2000. · Zbl 0987.76515
[6] Zienkiewicz, International Journal for Numerical Methods in Engineering 11 pp 355– (1977)
[7] , . Marriage a la mode–the best of both worlds (Finite elements and boundary integrals). In Energy Methods in Finite Element Analysis, Chapter 5, , (eds). Wiley: London, 1979; 81-106.
[8] Time marching BE-FE method in 2-D elastodynamic problems. In Boundary Elements IX, , (eds), Computational Mechanics Publications. Springer: Berlin, Heidelberg, 1987; 291-304.
[9] von Estorff, Computational Mechanics 6 pp 35– (1990)
[10] von Estorff, International Journal for Numerical Methods in Engineering 31 pp 1151– (1991)
[11] Belytschko, International Journal for Numerical Methods in Engineering 37 pp 91– (1994)
[12] Yu, Computers and Structures 79 pp 811– (2001)
[13] Rizos, Engineering Analysis with Boundary Elements 26 pp 877– (2002)
[14] Beskos, Applied Mechanics Reviews 40 pp 1– (1987)
[15] Beskos, Applied Mechanics Reviews 50 pp 149– (1997)
[16] Dynamic analysis of structures and structural systems. In Boundary Element Advances in Solid Mechanics, (eds), CISM International Centre for Mechanical Sciences, vol. 440. Springer: Wien, New York, 2003; 1-54.
[17] Godinho, Journal of Wave Motion 38 pp 131– (2003)
[18] Tadeu, Engineering Analysis with Boundary Elements 27 pp 215– (2003)
[19] Pavlatos, Engineering Analysis with Boundary Elements 14 pp 51– (1994)
[20] Yazdchi, International Journal for Numerical Methods in Engineering 44 pp 101– (1999)
[21] Nonlinear seismic analysis of irregular sites and underground structures by coupling BEM to FEM. Ph.D. Thesis, Okayama University, Japan, 1997.
[22] von Estorff, Engineering Analysis with Boundary Elements 24 pp 715– (2000) · Zbl 0987.76515
[23] . Transient 3D soil/structure interaction analyses including nonlinear effects. In Structural Dynamics, EURODYN2002, (eds). Swets & Zeitlinger B.V.: Lisse, 2002; 1291-1302.
[24] Czygan, Engineering Analysis with Boundary Elements 26 pp 773– (2002)
[25] Elleithy, Engineering Analysis with Boundary Elements 25 pp 685– (2001)
[26] Soares, Computational Mechanics 34 pp 67– (2004)
[27] Non-linear Finite Element Analysis of Solid Structures–Vols 1 and 2. Wiley: Chichester, 1991.
[28] , . Nonlinear Finite Elements for Continua and Structures. Wiley: New York, 2000. · Zbl 0959.74001
[29] A time-stepping technique to solve wave propagation problems using the boundary element method. Ph.D. Thesis, University of Southampton, England, 1983.
[30] Soares, Computational Mechanics 30 pp 38– (2002)
[31] Carrer, Engineering Analysis with Boundary Elements 12 pp 283– (1993)
[32] Lectures on Cauchy’s Problem in Linear Partial Differential Equations. Dover: New York, 1952. · Zbl 0049.34805
[33] . FEM/BEM coupling for fluid-structure interaction including nonlinear effects. Proceedings of the BEM 22 Conference, Cambridge, 2000.
[34] Fluid/structure coupling of 2D and axisymmetric systems taking into account a nonlinear structural behavior (in German). Ph.D. Thesis, TU Hamburg-Harburg, Germany, 2002.
[35] . Combination of FEM and BEM by an iterative coupling procedure. Proceedings of the ECCOMAS 2004 Congress, Jyväskylä, Finland, 2004.
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.