DOI QR코드

DOI QR Code

Partitioned analysis of nonlinear soil-structure interaction using iterative coupling

  • Jahromi, H. Zolghadr (Department of Civil and Environmental Engineering, Imperial College) ;
  • Izzuddin, B.A. (Department of Civil and Environmental Engineering, Imperial College) ;
  • Zdravkovic, L. (Department of Civil and Environmental Engineering, Imperial College)
  • Received : 2007.07.27
  • Accepted : 2007.11.05
  • Published : 2008.03.25

Abstract

This paper investigates the modelling of coupled soil-structure interaction problems by domain decomposition techniques. It is assumed that the soil-structure system is physically partitioned into soil and structure subdomains, which are independently modelled. Coupling of the separately modelled partitioned subdomains is undertaken with various algorithms based on the sequential iterative Dirichlet-Neumann sub-structuring method, which ensures compatibility and equilibrium at the interface boundaries of the subdomains. A number of mathematical and computational characteristics of the coupling algorithms, including the convergence conditions and choice of algorithmic parameters leading to enhanced convergence of the iterative method, are discussed. Based on the presented coupling algorithms a simulation environment, utilizing discipline-oriented solvers for nonlinear structural and geotechnical analysis, is developed which is used here to demonstrate the performance characteristics and benefits of various algorithms. Finally, the developed tool is used in a case study involving nonlinear soil-structure interaction analysis between a plane frame and soil subjected to ground excavation. This study highlights the relative performance of the various considered coupling algorithms in modelling real soil-structure interaction problems, in which nonlinearity arises in both the structure and the soil, and leads to important conclusions regarding their adequacy for such problems as well as the prospects for further enhancements.

References

  1. Elleithy, W.M., Al-Gahtani, H.J., El-Gebeily, M. (2001), "Iterative coupling of BE and FE methods in elastostatics", Engineering Analysis with Boundary Elements, 25, 685-695. https://doi.org/10.1016/S0955-7997(01)00054-6
  2. Elleithy, W.M. and Tanaka, M. (2003), "Interface relaxation algorithms for BEM-BEM coupling and FEM-BEM coupling", Computer Methods in Applied Mechanics and Engineering, 192, 2977-2992. https://doi.org/10.1016/S0045-7825(03)00312-8
  3. El-Gebeily, M., Elleithy, W.M. and Al-Gahtani, H.J. (2002), "Convergence of the domain decomposition finite element-boundary element coupling methods", Computer Methods in Applied Mechanics and Engineering, 191, 4851-4867. https://doi.org/10.1016/S0045-7825(02)00405-X
  4. Estorff, O. and Hagen, C. (2005), "Iterative coupling of FEM and BEM in 3D transient elastodynamics", Engineering Analysis with Boundary Elements, 29, 775-787. https://doi.org/10.1016/j.enganabound.2005.04.004
  5. Farhat, C. and Lesoinne M. (2000), "Two efficient staggered algorithms for serial and parallel solution of threedimensional nonlinear transient aeroelastic problems", Computer Methods in Applied Mechanics and Engineering, 182, 499-515. https://doi.org/10.1016/S0045-7825(99)00206-6
  6. Felippa, C.A., Park K.C. and Farhat C. (2001), "Partitioned analysis of coupled mechanical systems", Computer Methods in Applied Mechanics and Engineering, 190, 3247-3270. https://doi.org/10.1016/S0045-7825(00)00391-1
  7. Fox, L. (1964), An Introduction to Numerical Algebra, Clarendon press, Oxford.
  8. Funaro, D., Quarteroni, A. and Zanolli, P., (1998), "An iterative procedure with interface relaxation for domain decomposition methods", SIAM Journal on Numerical Analysis, 25, 6, 1213-1236.
  9. Hagen, C. and Estorff, O. (2005), "Transient dynamic investigation of 3D dam-reservoir-soil problems using an iterative coupling approach", International Conference on Computational Methods for Coupled Problems in Science and Engineering (Coupled Problems 2005), Barcelona.
  10. Huang, M. and Zienkiewicz, O.C. (1998), "New unconditionally stable staggered solution procedures for coupled soil-pore fluid dynamic problems", International Journal for Numererical Methods in Engineering, 43, 1029-1052. https://doi.org/10.1002/(SICI)1097-0207(19981130)43:6<1029::AID-NME459>3.0.CO;2-H
  11. Izzuddin B.A. (1991), "Nonlinear dynamic analysis of framed structures", PhD Thesis, Dept. of Civil Engineering, Imperial College, University of London.
  12. Izzuddin, B.A. and Elnashai, A.S. (1993), "Adaptive space frame analysis. 2. A distributed plasticity approach", Proceedings of the Institution of Civil Engineers-Structures and Buildings, 99, 317-326. https://doi.org/10.1680/istbu.1993.24353
  13. Jardine, R.J., Potts, D.M., Fourie, A.B. and Burland, J.B. (1986), "Studies of the influence of non-linear stressstrain characteristics in soil-structure interaction", Geotechnique, 36, 3, 377-396. https://doi.org/10.1680/geot.1986.36.3.377
  14. Lai, C.H. (1994), "Diakoptics, domain decomposition and parallel computing", The Computer Journal, 37(10).
  15. Marini, L.D. and Quarteroni A. (1989), "A relaxation procedure for domain decomposition methods using finite elements", Numerische Mathematik, 55, 575-598. https://doi.org/10.1007/BF01398917
  16. Noorzaei, J., Viladkar, N. and Godbole, P.N. (1995), "Elasto-plastic analysis for soil-structure interaction in framed structures", Computers and Structures, 55, 5, 797-807. https://doi.org/10.1016/0045-7949(94)00432-3
  17. O'Brien, J. and Rizos D.C. (2005), "A 3D BEM-FEM methodology for simulation of high speed train induced vibrations", Soil Dynamics and Earthquake Engineering, 25, 289-301. https://doi.org/10.1016/j.soildyn.2005.02.005
  18. Piperno, S. (1997), "Explicit/implicit fluid/structure staggered procedures with a structural predictor and fluid subcycling for 2d inviscid aeroelastic simulations", International Journal for Numerical Methods in Fluids, 25, 1207-1226. https://doi.org/10.1002/(SICI)1097-0363(19971130)25:10<1207::AID-FLD616>3.0.CO;2-R
  19. Potts D.M. and Zdravkovic L. (1999), Finite Element Analysis in Geotechnical Engineering: Theory, Thomas Telford, London.
  20. Quarteroni, A. and Valli A. (1999), Domain Decomposition Methods for Partial Differential Equations, Clarendon press, Oxford.
  21. Rizos, D.C. and Wang, Z. (2002), "Coupled BEM-FEM solutions for direct time domain soil-structure interaction analysis", Engineering Analysis with Boundary Elements, 26, 877-888. https://doi.org/10.1016/S0955-7997(02)00057-7
  22. Wall, W.A., Genkinger, S. and Ramm, E., (2007), "A strong coupling partitioned approach for fluid structure interaction with free surfaces", Computers and Fluids, 36, 169-183. https://doi.org/10.1016/j.compfluid.2005.08.007
  23. Zienkiewicz, O.C. and Taylor, R.L. (1991), Finite Element Method Solid and Fluid Mechanics: Dynamics and Nonlinearity, Vol. 2, McGraw-Hill, New York.

Cited by

  1. A Dual Super-Element Domain Decomposition Approach for Parallel Nonlinear Finite Element Analysis vol.16, pp.3, 2015, https://doi.org/10.1080/15502287.2015.1043163
  2. Finite Element Analysis of Dam-Foundation Coupled System Considering Cone-Type Local Non-Reflecting Boundary Condition vol.20, pp.3, 2016, https://doi.org/10.1080/13632469.2015.1085464
  3. A general approach for studying the motion of a cantilever beam interacting with a 2D fluid flow vol.1, pp.4, 2008, https://doi.org/10.12989/imm.2008.1.4.449
  4. Mitigating Error and Uncertainty in Partitioned Analysis: A Review of Verification, Calibration and Validation Methods for Coupled Simulations vol.24, pp.3, 2017, https://doi.org/10.1007/s11831-016-9177-0
  5. LONG-TERM INFLUENCE OF CONCRETE DEGRADATION ON DAM–FOUNDATION INTERACTION vol.08, pp.03, 2011, https://doi.org/10.1142/S0219876211002472
  6. Performance of partitioned procedures in fluid–structure interaction vol.88, pp.7-8, 2010, https://doi.org/10.1016/j.compstruc.2009.12.006
  7. Coupled gravity dam–foundation analysis using a simplified direct method of soil–structure interaction vol.34, pp.1, 2012, https://doi.org/10.1016/j.soildyn.2011.10.008
  8. Parallelisation of nonlinear structural analysis using dual partition super elements vol.60-61, 2013, https://doi.org/10.1016/j.advengsoft.2012.10.004
  9. A domain decomposition approach for coupled modelling of nonlinear soil–structure interaction vol.198, pp.33-36, 2009, https://doi.org/10.1016/j.cma.2009.03.018