Skip to main content
SpringerLink
Log in

Time Domain B-Spline BEM Methods for Wave Propagation in 3-D Solids and Fluids Including Dynamic Interaction Effects of Coupled Media

  • Chapter
Recent Advances in Boundary Element Methods

  • 1349 Accesses

Abstract

This chapter summarizes the theoretical developments of the author’s research team during the last 15 years in the area of a new family of direct time domain Boundary Element Methods that are based on the B-Spline fundamental solutions for wave propagation in solid and fluid media, and the resulting methodologies for solving problems involving dynamic interaction of coupled media. Special element types have been developed to accommodate rigid assemblages and fluid-solid interfaces and are summarized herein. Coupling procedures of the proposed BEM methods with the FEM are also outlined. A number of examples reported in the literature by the author and his coworkers are included at the end of the chapter.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 129.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 169.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  • Banerjee PK, Ahmad S, and Manolis GD (1986) Transient elastodynamic analysis of 3-D problems by Boundary Element Method.. Earthquake Engineering and Structural Dynamics, 14:933–949.

    Article  Google Scholar 

  • Banerjee PK, Ahmad S, and Manolis GD (1987) Advanced elastodynamic analysis. In: DE Beskos (ed): Boundary Element Methods in Mechanics pp. 258–284, Elsevier, Amsterdam.

    Google Scholar 

  • Beskos DE, (1997) Boundary element methods in dynamic analysis: Part II 1986–1996. ASME Applied Mechanics Reviews, 50(3):149–197.

    Article  Google Scholar 

  • Bielak J, MacCamy RC, and McGhee DS (1984) On the coupling of finite element and boundary integral methods. In: SK Datta (ed.): Earthquake Source Modeling, Ground Motion, and Structural Response, AMD-60, 115-132, ASME, New York.

    Google Scholar 

  • Bonnet M, (1995) Boundary Integral Equation Methods for Solids and Fluids, John Wiley & Sons, New York.

    Google Scholar 

  • Brebbia CA and Georgiou P (1979) Combination of boundary and finite elements for elastostatics. Applied Mathematical Modeling, 3:212–220.

    Article  MATH  Google Scholar 

  • Chow YK and Smith IM (1982) Infinite elements for dynamic foundation analysis. Numerical Methods in Geomechanics., 1:15–22.

    Google Scholar 

  • Chuhan Z, Feng J, and Guanglun W (1993) A method of FE-BE-IBE coupling for seismic interaction of arch dam-canyons. In M Tanaka et al. (Eds.): Boundary Element Methods. Elsevier, Amsterdam.

    Google Scholar 

  • Czygan O and Estorff O von (2002) Fluid-structure interaction by coupling BEM and nonlinear FEM. Engineering Analysis with Boundary Elements, 26(9):773–779

    Article  MATH  Google Scholar 

  • Erringen AC and Suhubi ES (1975) Elastodynamics – Vol. II, Linear Theory, Academic Press, New York.

    Google Scholar 

  • Estorff O (1990) Soil-structure interaction analysis by a combination of boundary and finite elments. In: SA Savidis (Ed.): Earthquake Resistant Constructions and Design. Balkem, Rotterdam.

    Google Scholar 

  • Estorff O and Firuziaan (2000) Coupled BEM/FEM approach for nonlinear soil/structure interaction, Engineering Analysis with Boundary Elements, 24:715–725.

    Article  MATH  Google Scholar 

  • Estorff von O and Hagen C (2005) Iterative coupling of FEM and BEM in 3D transient elastodynamics. Engineering Analysis with Boundary Elements, 29(8):775–787

    Article  Google Scholar 

  • Estorff O and Kausel E (1989) Coupling of boundary and finite elements for soil-structure interaction problems. Earthquake Engineering and Structural Dynamics, 18:1065–1075.

    Article  Google Scholar 

  • Fukui T (1987) Time marching BE-FE method in 2-D elastodynamic problem. International Conference BEM IX Stuttgart.

    Google Scholar 

  • Karabalis DL and Beskos DE (1984) Dynamic response of rigid surface foundations by time domain boundary element method. Earthquake Engineering and Structural Dynamics, 12:73–93.

    Article  Google Scholar 

  • Karabalis DL and Beskos DE (1985) Dynamic response of 3-D flexible surface foundations by time domain finite and boundary element methods. International Journal of Soil Dynamics and Earthquake Engineering, 4:91–101.

    Article  Google Scholar 

  • Karabalis DL and Beskos DE (1986) Dynamic analysis of 3-D embedded foundations by time domain boundary element method. Computer Methods in Applied Mechanics and Engineering, 56:91–119.

    Article  MATH  Google Scholar 

  • Karabalis DL and Beskos DE, (1987) Dynamic soil – structure interaction, Chapter 11. In: DE Beskos (Ed.): Boundary Element Methods in Mechanics, North Holland, Amsterdam.

    Google Scholar 

  • Karabalis DL, Cokkinides GJ, Rizos DC, and Tassoulas JL (1996) Finite Element Transient Analysis (FETA) V1.00, Theoretical and User’s Manual, (Prepared for Westinghouse Savannah River Company), Department of Civil Engineering, University of South Carolina.

    Google Scholar 

  • Karabalis DL, Karavasilis TL, Dimas AA and Rizos DC (2003) Dynamic fluid-structure-soil interaction: application to spherical tanks. INDEPTH Document IDP-TR-UP-2-01, Version 1.0, European Commission.

    Google Scholar 

  • Karabalis DL and Rizos DC (1993), Dynamic analysis of 3-D foundations. Chapter 6, pp. 177–208. In: GD Manolis and TG Davis (Eds): Boundary Element Techniques in Geomechanics, Computational Mechanics Publications, Southampton.

    Google Scholar 

  • Karabalis DL and Rizos DC (1995) On the efficiency and accuracy of a new advanced time domain BEM for 3-D elastodynamics. In: D Hui and S Michaelidis (Eds) Society of Engineering Science 32nd Annual Technical Meeting, (Univ. of New Orleans and Tulane Univ., New Orleans).

    Google Scholar 

  • Kausel E and Tassoulas JL, (1981): Transmitting boundaries: a close form comparison. Bulletin Seismic. Society of America, 71:143–159.

    MathSciNet  Google Scholar 

  • Lysmer J, Seed HB, Udaka T, Huang RN, and Tsai CF (1975) Efficient finite element analysis of seismic soil structure interaction.Earthquake Engineering Research Center, Report No. EERC 75-34, University of California, Berkeley.

    Google Scholar 

  • Mackerle J (1996) FEM and BEM in geomechanics: foundations and soil-structure interaction – a b(1992–1994). Finite Elements in Analysis and Design, 22(3):249–263.

    Article  MATH  Google Scholar 

  • Mackerle J (1998) Finite element and boundary element analysis of bridges, roads and pavements – A bibliography (1994–1997). Finite Elements in Analysis and Design, 29(1):65–83.

    Article  MATH  Google Scholar 

  • Mackerle J (1999) Earthquake analysis of structures: FEM and BEM approaches A bibliography (19951998). Finite Elements in Analysis and Design, 32:113–124.

    Article  MATH  Google Scholar 

  • O’Brien J (2004) Train induced vibrations in a ground-track system. MSc Thesis, Dept. of Civil and Environmental Engineering, University of South Carolina, Columbia, SC, USA.

    Google Scholar 

  • O’Brien J and Rizos DC (2005) A Staggered BEM-FEM methodology for simulation of high speed train induced ibrations. Soil Dynamics and Earthquake Engineering, 25:289–301.

    Google Scholar 

  • Rizos DC (1993) Advanced time domain boundary element method for general 3d elastodynamic problems. PhD thesis, Dep. of Civil and Environmental Engineering, University of South Carolina, Columbia, South Carolina, USA.

    Google Scholar 

  • Rizos DC (2000) A rigid surface boundary element for 3-D soil structure interaction analysis in the direct time domain. Computational Mechanics, 26(6):582–591.

    Article  MATH  Google Scholar 

  • Rizos DC and Karabalis DL (1994) An advanced direct time domain BEM formulation for 3-D elastodynamic problems. Computational Mechanics, 15(3):249–269.

    Article  MATH  MathSciNet  Google Scholar 

  • Rizos DC and Karabalis DL (1995) Applications of an advanced time domain BEM to 3-D Problems in geomechanics. In: S.N. Atluri, G. Yagawa and T.A. Cruse (eEds) Computational Mechanics ‘95 Theory and Applications, pp. 3080—3085, Springer-Verlag, Berlin.

    Google Scholar 

  • Rizos DC and Karabalis DL (1997) A time domain BEM for 3-D elastodynamic analysis using the B-Spline fundamental solutions,. Iin: F.G. Benitez (eEd.), Fundamental Solutions in Boundary Elements: Formulation and Integration, SAND (Camas).

    Google Scholar 

  • Rizos DC and Karabalis DL (1998) A time domain BEM for 3-D elastodynamic analysis using the B-Spline fundamental solutions. Computational Mechanics, 22:108–115.

    Article  MATH  MathSciNet  Google Scholar 

  • Rizos DC and Karabalis DL (1999) Soil-fluid-structure interaction. Invited chapter in: E Kausel and GD Manolis (Eds): Wave Motion Problems in Earthquake Engineering, Computational Mechanics Publications, Southampton.

    Google Scholar 

  • Rizos DC and Loya K. (2002) Dynamic and seismic analysis of foundations based on free field B-Spline characteristic response histories. Journal of Engineering Mechanics ASCE, 128(4):438–448.

    Article  Google Scholar 

  • Rizos DC and Wang J (2002) Coupled BEM-FEM solutions for direct time domain soilstructure interaction analysis. Engineering Analysis with Boundary Elements, 26(10):877–888.

    Article  MATH  Google Scholar 

  • Rizos DC and Wang ZY (1999) Applications of Staggered BEM-FEM solutions to soil structure interaction. In: N Jones and R Ghanem (Eds): Proceedings of the 13th Engineering Mechanics Division Specialty Conference, Johns Hopkins University, Baltimore (CD-ROM).

    Google Scholar 

  • Rizos DC and Zhou S (2005) An Advanced BEM for 3D scalar wave propagation and fluid-structure interaction analysis. BEM/MRM 27, Orlando Florida.

    Google Scholar 

  • Rizos DC and Zhou S (2006a) An advanced direct time domain BEM for 3-D wave propagation in acoustic media”, Journal of Sound and Vibration, 293(1–2):196–212.

    Article  MathSciNet  Google Scholar 

  • Rizos DC and Zhou S (2006b) Efficiency and stability studies of a time domain boundary element methodology for fluid-structure interaction analysis”, 15th U.S. National Congress on Theoretical and Applied Mechanics (USNCTAM06) Boulder Colorado.

    Google Scholar 

  • Rizos DC and Zhou S (2008) A B-spline BEM for fluid-structure-interaction analysis of rigid structures. Engineering Analysis with Boundary Elements (under review).

    Google Scholar 

  • Soares Jr. D, Mansur WJ, and Estorff O. von (2007) An efficient time-domain FEM/BEM coupling approach based on FEM implicit Green’s functions and truncation of BEM time convolution process. Computer Methods in Applied Mechanics and Engineering, 196(9–12):1816–1826.

    Article  Google Scholar 

  • Spyrakos CC and Beskos DE (1986) Dynamic response of flexible strip foundations by boundary and finite elements. Soil Dynamics and Earthquake Engineering, 5:84–96.

    Article  Google Scholar 

  • Stehmeyer E and Rizos DC (2006) A simplified B-Spline impulse response function (BIRF) model for the transient SSI analysis of rigid foundations. Soil Dynamics and Earthquake Engineering, 26(5):421–434.

    Article  Google Scholar 

  • Stehmeyer E and Rizos DC (2007) Considering dynamic soil structure interaction (SSI) effects on seismic isolation retrofit efficiency and the importance of natural frequency ratio. Soil Dynamics and Earthquake Engineering, In Press, Corrected Proof Available online 12 September 2007.

    Google Scholar 

  • Tzong TJ, Gupta S, and Penzien J, (1981) Two-dimensional hybrid modeling of soil-structure interaction, Report No. EERC 81/11, University of California, Berkeley.

    Google Scholar 

  • Zhou S (2005) An advanced boundary element method for ship/water dynamic interaction analysis. PhD Dissertation, Dept. of Civil and Environmental Engineering University of South Carolina, Columbia, SC, USA.

    Google Scholar 

  • Zienkiewicz OC, Kelly DW, and Bettess P (1977) The coupling of the finite element method and boundary solution procedures. International Journal for Numerical methods in Engineering, 11:355–375.

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Civil and Environmental Engineering, University of South Carolina, Columbia, SC 29208, USA

    Dimitris C. Rizos

Authors
  1. Dimitris C. Rizos
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Dimitris C. Rizos .

Editor information

Editors and Affiliations

  1. Department of Civil Engineering, Aristotle University, 54124 Thessaloniki, Greece

    George D. Manolis (Professor) (Professor)

  2. Department of Mechanical Engineering and Institute of Chemical Engineering&High Temperature Processes, University of Patras, 265 00 Patras, Greece

    D. Polyzos

Rights and permissions

Reprints and permissions

Copyright information

© 2009 Springer Science+Business Media B.V.

About this chapter

Cite this chapter

Rizos, D.C. (2009). Time Domain B-Spline BEM Methods for Wave Propagation in 3-D Solids and Fluids Including Dynamic Interaction Effects of Coupled Media. In: Manolis, G.D., Polyzos, D. (eds) Recent Advances in Boundary Element Methods. Springer, Dordrecht. https://doi.org/10.1007/978-1-4020-9710-2_25

Download citation

  • DOI: https://doi.org/10.1007/978-1-4020-9710-2_25

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-1-4020-9709-6

  • Online ISBN: 978-1-4020-9710-2

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics

Search

Navigation