Skip to main content

Dynamic Analysis of Structures and Structural Systems

  • Chapter
Book cover Boundary Element Advances in Solid Mechanics

Part of the book series: International Centre for Mechanical Sciences ((CISM,volume 440))

Abstract

This chapter deals with the dynamic analysis of various structures and soil-structural systems by the direct conventional boundary element method (BEM) in both the frequency and time domains. When the BEM is used in the frequency or time domain in conjunction with the corresponding elastodynamic fundamental solution, only linear elastodynamic problems are considered. In this case only the surface of the analyzed structure has to be discretized. When the material behavior is inelastic (elastoplastic, viscoplastic or damaged), use is made of the elastostatic fundamental solution and this requires both a surface and an interior discretization to accommodate the inertia and inelastic volume integrals in the time domain formulation. The structures analysed include two — and three — dimensional elastic and inelastic solids and Kirchhoff and Reissner inelastic plates. The soil — structure interacting systems analysed include multiple foundations, underground structures, vibration isolation by trenches or piles and earth and concrete dams. The dynamic input can be either externally applied forces or seismic waves of any direction and time variation. Emphasis is given on recent advanced techniques for accurately and efficiently analyzing three-dimensional structures and structural systems discussed mainly in published works of the author and his co-workers.

The author thanks Mrs E. Kefala for her conscientious typing of the manuscript and Civil Engineer Mr. A. Asimakopoulos for his help in connection with the drawings.

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight 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

  • Abouseeda, H. and Dakoulas, P. (1996), Response of earth dams to P and SV waves using coupled FE-BE formulation, Earth. Engng. Struct. Dyn. 25, 1177–1194.

    Google Scholar 

  • Abouseeda, H. and Dakoulas, P. (1998), Non-linear dynamic earth dam-foundation interaction using a BE-FE method, Earth. Engng. Struct. Dyn. 27, 917–936.

    Google Scholar 

  • Adam, M., Pflanz, G. and Schmid, G. (2000), Two-and three-dimensional modeling of half-space and train-track embankment under dynamic loading, Soil Dyn. Earth. Engng. 19, 559–573.

    Google Scholar 

  • Agnantiaris, J.P., Polyzos, D. and Beskos, D.E. (1996), Some studies on dual reciprocity BEM for elastodynamic analysis, Comput. Mech. 17, 270–277.

    Google Scholar 

  • Agnantiaris, J.P., Polyzos, D. and Beskos, D.E. (1998), Three-dimensional structural vibration analysis by the dual reciprocity BEM, Comput. Mech. 21, 372–381.

    MATH  Google Scholar 

  • Agnantiaris, J.P., Polyzos, D. and Beskos, D.E. (2001), Free vibration analysis of non-axisymmetric and axisymmetric structures by the dual reciprocity BEM, Engng. Anal. Bound. Elem., to appear.

    Google Scholar 

  • Ahmad, S. and Banerjee, P.K. (1986), Free vibration analysis by BEM using particular integrals, J. Engng. Mech. ASCE, 112, 682–695.

    Google Scholar 

  • Ahmad, S. and Banerjee, P.K. (1988), Multi-domain BEM for two-dimensional problems of elastodynamics, Int. J. Num. Meth. Engng. 26, 891–911.

    MATH  Google Scholar 

  • Ahmad, S. and Banerjee, P.K. (1990), Inelastic transient dynamic analysis of three-dimensional problems by BEM, Int. J. Num. Meth. Engng. 29, 371–390.

    MATH  Google Scholar 

  • Ahmad, S., Al-Hussaini, T.M. and Fishman, K.L. (1996), Investigation of active isolation of machine foundations by open trenches, J. Geotech. Engng. ASCE, 122, 454–461.

    Google Scholar 

  • Albuquerque, E.L. and Sollero, P. (1998), The boundary element method applied to transient dynamic anisotropic problems, in Boundary Elements XX, A. Kassab, M. Chopra and C.A. Brebbia (eds), Computational Mechanics Publications, Southampton, 617–624.

    Google Scholar 

  • Al-Hussaini, T.M. and Ahmad, S. (1996), Active isolation of machine foundations by in-filled trench barriers, J. Geotech. Engng. ASCE, 122, 288–294.

    Google Scholar 

  • Aliabadi, M.H. (ed) (1998), Plate Bending Analysis with Boundary Elements, Computational Mechanics Publications, Southampton.

    MATH  Google Scholar 

  • Araujo, F.C., Mansur, W.J. and Nishikava, L.K. (1999), A linear 0 time-marching algorithm in 3D BEM formulation for elastodynamics, Engng. Anal. Bound. Elem. 23, 825–833.

    MATH  Google Scholar 

  • Banerjee, P.K. (1994), Boundary Elements Methods in Engineering, McGraw-Hill, London.

    Google Scholar 

  • Banerjee, P.K. and Mamoon, S.M. (1990), A fundamental solution due to a periodic point force in the interior of an elastic half space, Earth. Engng. Struct. Dyn. 19, 91–105.

    Google Scholar 

  • Beskos, D.E. (1987), Boundary element methods in dynamic analysis, Appl. Mech. Rev. ASME, 40, 123.

    Google Scholar 

  • Beskos, D.E. (ed) (1991), Boundary Element Analysis of Plates and Shells, Springer-Verlag, Berlin.

    Google Scholar 

  • Beskos, D.E. (1995), Dynamic inelastic structural analysis by boundary element methods, Arch. Comput. Meth. Engng. 2, 55–87.

    Google Scholar 

  • Beskos, D.E. (1997), Boundary element methods in dynamic analysis: Part II (1986–1996), Appl. Mech. Rev. ASME, 50, 149–197.

    Google Scholar 

  • Birgisson, B. and Crouch, S.L. (1998), Elastodynamic boundary element method for piecewice homogeneous media, Int. J. Num. Meth. Engng. 42, 1045–1069.

    MathSciNet  MATH  Google Scholar 

  • Birgisson, B. Siebrits, E. and Pierce, A.P. (1999), Elastodynamic direct boundary element methods with enhanced numerical stability properties, Int. J. Num. Meth. Engng. 46, 871–888.

    MATH  Google Scholar 

  • Bonnet, M. and Bui, H.D. (1993), Regularization of the displacement and traction BIE for 3D elastodynamics using indirect methods, in Advances in Boundary Element Techniques, Kane, J.H., et al, (eds), Springer-Varlag, Berlin, 1–29.

    Google Scholar 

  • Bu, S. (1996), Fundamental solutions for dynamic BEM analyses of incompressible problems, Engng. Anal. Bound. Elem. 17, 303–305.

    Google Scholar 

  • Bu, S. (1997), Infinite boundary elements for the dynamic analysis of machine foundations, Int. J. Num. Meth. Engng. 40, 3901–3917.

    MathSciNet  MATH  Google Scholar 

  • Carrer, J.A.M. and Mansur, W.J. (2000), Time discontinuous linear traction approximation in time-domain BEM: 2-D elastodynamics, Int. J. Num. Meth. Engng. 49, 833–848.

    MATH  Google Scholar 

  • Carrer, J.A.M. and Telles, J.F.C. (1992), A boundary element formulation to solve transient dynamic elastoplastic problems, Comput. Struct. 45, 707–713.

    MATH  Google Scholar 

  • Coda, H.B. and Venturini, W.S. (1999), On the coupling of 3D BEM and FEM frame model applied to elastodynamic analysis, Int. J. Solids Struct. 36, 4789–4804.

    MATH  Google Scholar 

  • Coda, H.B., Venturini, W.S. and Aliabadi, M.H. (1999), A general 3D BEM/FEM coupling applied to elastodynamic continua/frame structures interaction analysis, Int. J. Num. Meth. Engng. 46, 695–712.

    MATH  Google Scholar 

  • Cutillas, A.M. and Alarcon, E. (1997), Dynamic stiffness analysis of bridge abutments, Eur. J. Mech. A/Solids, 16, 645–669.

    MATH  Google Scholar 

  • Dakoulas, P. and Abouseeda, H. (1997), Response of earth dams to Rayleigh waves using coupled FE-BE method, J. Engng. Mech. ASCE, 123, 1311–1320.

    Google Scholar 

  • Davey, K., Alonso Rasgado, M.T. and Rosindale, I. (1999), The 3-D elastodynamic boundary element method: semi-analytical integration for linear isoparametric triangular elements, Int. J. Num. Meth. Engng. 44, 1031–1054.

    MathSciNet  MATH  Google Scholar 

  • Do Rego Silva, J.J. (1994), Acoustic and Elastic Wave Scattering Using Boundary Elements, Computational Mechanics Publications, Southampton.

    MATH  Google Scholar 

  • Dominguez, J. (1993), Boundary Elements in Dynamics, Computational Mechanics Publications, Southampton.

    MATH  Google Scholar 

  • Dominguez, J. (1997), Earth and concrete dams, in Computer Analysis and Design of Earthquake Resistant Structures: A Handbook, D.E. Beskos and S.A. Anagnostopoulos (eds), Computational Mechanics Publications, Southampton, 661–694.

    Google Scholar 

  • Dominguez, J. and Maeso, O. (1993), Earthquake analysis of arch dams II: dam-water-foundation interaction, J. Engngn. Mech. ASCE, 119, 513–530.

    Google Scholar 

  • Dravinski, M. and Mossessian, T.K. (1988), On evaluation of the Green functions for harmonic line loads in a viscoelastic half space, Int. J. Num. Meth. Engng. 26, 823–841.

    Google Scholar 

  • Du, J., Kobayashi, A.S. and Hawkins, N.M. (1989), FEM dynamic fracture analysis of concrete beams, J. Engng. Mech. ASCE, 115, 2136–2149.

    Google Scholar 

  • Frangi, A. (1999), Elastodynamics by BEM: a new direct formulation, Int. J. Num. Meth. Engng. 45, 721–740.

    MathSciNet  MATH  Google Scholar 

  • Frangi, A. (2000), Causal shape functions in the time domain boundary element method, Comput. Mech. 25, 533–541.

    MathSciNet  MATH  Google Scholar 

  • Frangi, A. and Novati, G. (1999), On the numerical stability of time-domain elastodynamic analyses by BEM, Comput. Meth. Appl. Mech. Engng. 173, 403–417.

    MathSciNet  MATH  Google Scholar 

  • Guan, F. and Novak, M. (1994) Transient response of an elastic homogeneous half-space to suddenly applied rectangular loading, J. Appl. Mech. ASME, 61, 256–263.

    MATH  Google Scholar 

  • Guiggiani, M. (1992), Computing principal value integrals in 3D BEM for time-harmonic elastodynamics-a direct approach, Comm. Appl. Num. Meth. 8, 141–149.

    Google Scholar 

  • Guiggiani, M. (1994), Hypersingular formulation for boundary stress evaluation, Engng. Anal. Bound. Elem. 13, 169–179.

    Google Scholar 

  • Guiggiani, M. and Gigante, A. (1990), A general algorithm for multidimensional Cauchy principal value integrals in the boundary element method, J. Appl. Mech. ASME, 57, 906–915.

    MathSciNet  MATH  Google Scholar 

  • Hall, J.F. and Chopra, A.K. (1983), Dynamic analysis of arch dams including hydrodynamic effects, J. Engng. Mech. Div. ASCE, 109, 149–163.

    Google Scholar 

  • Hatzigeorgiou, G.D. and Beskos, D.E. (2000), Dynamic response of 3-D elastoplastic or damaged structures by BEM, in CD-Rom Proceedings of European Congress on Computational Methods in Applied Sciences and Engineering - ECCOMAS 2000, Barcelona, 11–14 September 2000, 9 pages.

    Google Scholar 

  • Hatzigeorgiou, G.D. and Beskos, D.E. (2001a), Inelastic response of 3-D underground structures in rock under seismic loading, in Earthquake Resistant Engineering Structures III, C.A. Brebbia and A. Corz (eds), WIT Press, Southampton, 599–608.

    Google Scholar 

  • Hatzigeorgiou, G.D. and Beskos, D.E. (2001b), Seismic analysis of inelastic gravity dams under plane strain conditions by a BEM/FEM scheme, unpublished results.

    Google Scholar 

  • Hatzigeorgiou, G.D. and Beskos, D.E. (2002a), Dynamic response of 3-D damaged solids and structures by BEM, Comput. Model. Engng. Sci., to appear.

    Google Scholar 

  • Hatzigeorgiou, G.D. and Beskos, D.E. (2002b), Dynamic elastoplastic analysis of 3-D structures by the D/BEM, Comput. Struct., 80, 339–347.

    Google Scholar 

  • Hinton, E., Owen, D.R.J. and Shantaram, D. (1977), Dynamic transient linear and nonlinear behaviour of thick and thin plates, in The Mathematics of Finite Elements and Applications II, J.R. Whiteman (ed.), Academic Press, London, 423–438.

    Google Scholar 

  • Huber, O., Lang, A. and Kuhn, G. (1993), Evaluation of the stress tensor in 3D elastostatics by direct solving of hypersingular integrals, Comput. Mech. 12, 39–50.

    MathSciNet  MATH  Google Scholar 

  • Karabalis, D.L. and Beskos, D.E. (1997), Numerical methods in earthquake engineering, in Computer Analysis and Design of Earthquake Resistant Structures: A Handbook, D.E. Beskos and S.A. Anagnostopoulos (eds), Computational Mechanics Publications, Southampton, 1–102.

    Google Scholar 

  • Karabalis, D.L. and Mohammadi, M. (1998), 3-D dynamic foundation — soil — foundation interaction on layered soil, Soil Dyn. Earth. Engng. 17, 139–152.

    Google Scholar 

  • Kattis, S.E., Polyzos, D. and Beskos, D.E. (1999a), Vibration isolation by a row of piles using a 3-D frequency domain BEM, Int. J. Num. Meth. Engng. 46, 713–728.

    MATH  Google Scholar 

  • Kattis, S.E., Polyzos, D. and Beskos, D.E. (1999b), Modeling of pile wave barriers by effective trenches and their screening effectiveness, Soil Dyn. Earth. Engng. 18, 1–10.

    Google Scholar 

  • Klein, R., Antes, H. and Le Houedec, D. (1997), Efficient 3D modeling of vibration isolation by open trenches, Comput. Struct. 64, 809–817.

    MATH  Google Scholar 

  • Kogl, M. and Gaul, L. (2000), A 3-D boundary element method for dynamic analysis of anisotropic elastic solids, Comput. Model. Engng. Sci. 1 (4), 27–43.

    Google Scholar 

  • Kontoni, D.P.N. and Beskos, D.E. (1993), Transient dynamic elastoplastic analysis by the dual reciprocity BEM, Engng. Anal. Bound. Elem. 12, 1–16.

    Google Scholar 

  • Krishnasamy, G., Rizzo, F.J. and Rudolphi, T.J. (1992), Hypersingular boundary integral equations: their occurence, interpretation, regularization and computation, in Advanced Dynamic Analysis by Boundary Element Methods, Developments in Boundary Element Methods-7, Banerjee, P.K. and Kobayashi, S. (eds), Elsevier Applied Science, London, 207–252.

    Google Scholar 

  • Leissa, A.W. and Zhang, Z. (1983), Three dimensional vibrations of the cantilever rectangular parallelepiped, J. Acoust. So. Amer. 73, 2013–2021.

    MATH  Google Scholar 

  • Liu, S.W., Datta S.K. and Khair, K.R. (1991), Three dimensional dynamics of pipelines buried in back- filled trenches due to oblique incidence of body waves, Soil Dun. Earth. Engng. 10, 182–191.

    Google Scholar 

  • Liu, Y. and Rizzo, F.J. (1993), Hypersingular boundary integral equations for radiation and scattering of elastic waves in three dimensions, Comput. Meth. Appl. Mech. Engng. 100. 131–144.

    MathSciNet  Google Scholar 

  • Luco, J.E. and de Barros, F.C.P. (1993), On the three-dimensional seismic response of a class of cylindrical inclusions embedded in layered media, in Soil Dynamics and Earthquake Engineering VI, A.S. Cakmak and C.A. Brebbia (eds), CMP, Southampton, 565–580.

    Google Scholar 

  • Lysmer, J., Udaka, T., Tsai, C.F. and Seed, H.B. (1975), FLUSH-A Computer Program for Approximate 3-D Analysis of Soil Structure Interaction Problems, Report No EERC 75–30, Earthquake Engineering Research Center, University of California, Berkeley.

    Google Scholar 

  • Maeso, O. and Dominguez, J. (1993), Earthquake analysis of arch dams I: dam-foundation interaction, J. Engng. Mech. ASCE, 119, 496–512.

    Google Scholar 

  • Manolis, G.D. (1989), Computer programs, in Boundary Element Methods in Structural Analysis, D.E. Beskos (ed), ASCE, New York, 309–335.

    Google Scholar 

  • Manolis, D.E. and Beskos, D.E. (1988), Boundary Element Methods in Elastodynamics, Unwin Hyman, London.

    Google Scholar 

  • Manolis, G.D. and Beskos, D.E. (1997), Underground and lifeline structures, in Computer Analysis and Design of Earthquake Resistant Structures: A Handbook, D.E. Beskos and S.A. Anagnostopoulos (eds), Computational Mechanics Publications, Southampton, 775–837.

    Google Scholar 

  • Manolis, G.D., Pitilakis, K., Tetepoulidis, P. and Mavridis, G. (1995), A hierarchy of numerical models for SSI analysis of buried pipelines, in Soil Dynamics and Earthquake Engineering VII, A.S. Cakmak and C.A. Brebbia (eds), Computational Mechanics Publications, Southampton, 643–650.

    Google Scholar 

  • Manolis, G.D., Tetepoulidis, P.I., Talaslidis, D.G. and Apostolidis, G. (1995), Seismic analysis of buried pipeline in a 3D soil continuum, Engng. Anal. Bound. Elern. 15, 371–394.

    Google Scholar 

  • MSC/NASTRAN (1992), Basic Dynamic Analysis, The MacNeal-Schwendler Corporation, Los Angeles.

    Google Scholar 

  • Nardini, D. and Brebbia, C.A. (1982), A new approach to free vibration analysis using boundary elements, in Boundary Element Methods in Engineering, C.A. Brebbia (ed.), Springer-Verlag, Berlin, 313–326.

    Google Scholar 

  • Nishimura, N. and Kobayashi, S. (1988), An improved boundary integral equation method for crack problems, in Advanced Boundary Element Methods, Cruse, T.A. (ed), Springer-Verlag, Berlin, 279–286.

    Google Scholar 

  • Niwa, Y. and Hirose, S. (1986), Application of the BEM to elastodynamics in a three dimensional half space, in Recent Applications in Computational Mechanics, Karabalis, D.L. (ed), ASCE, New York, 1–15.

    Google Scholar 

  • Ozkan, G. and Mengi, Y. (1997), On the use of FFT algorithm for the circumferential co-ordinate in boundary element formulation of axisymmetric problems, Int. J. Num. Meth. Engng. 40, 2385–2412.

    MathSciNet  MATH  Google Scholar 

  • Pan, G. and Atluri, S.N. (1995), Dynamic response of finite sized elastic runways subjected to moving loads: a coupled BEM/FEM approach, Int. J. Num. Meth. Engng. 38, 3143–3166.

    MATH  Google Scholar 

  • Pan, G., Okada, H. and Atluri, S.N. (1994), Nonlinear transient dynamic analysis of soil-pavement interaction under moving load: a coupled BEM-FEM approach, Engng. Anal. Bound. Elem. 14, 99–112.

    Google Scholar 

  • Pavlatos, G.D. and Beskos, D.E. (1994), Dynamic elastoplastic analysis by BEM/FEM, Engng. Anal. Bound. Elem. 14, 51–63.

    Google Scholar 

  • Pavlatos, G.D. and Beskos, D.E. (1999), Dynamic inelastic soil-structure interaction using a hybrid BEM/FEM scheme, in Discretization Methods in Structural Mechanics, H.A.Mang and F.G. Rammerstorfer (eds), Kluwer Academic Publishers, Dordrecht, 233–240.

    Google Scholar 

  • Polyzos, D., Dassios, G. and Beskos, D.E. (1994), On the equivalence of dual reciprocity and particular integral approaches in the BEM, Bound. Elem. Comm 5, 285–288.

    Google Scholar 

  • Polyzos, D., Tsinopoulos, S.V. and Beskos, D.E. (1998), Static and dynamic boundary element analysis in incompressible linear elasticity, Eur. J. Meh., A/Solids, 17, 515–536.

    MATH  Google Scholar 

  • Providakis, C.P. (1996), A general and advanced boundary element transient analysis of elastoplastic plates, Engng. Anal. Bound. Elem. 17, 133–143.

    Google Scholar 

  • Providakis, C.P. (1997), Transient boundary element analysis of elastoplastic plates on elastic foundation, Soil. Dyn. Earth. Engng. 16, 21–27.

    Google Scholar 

  • Providakis, C.P. (1998), Comparison of boundary element and finite element methods for dynamic analysis of elastoplastic plates, Adv. Engng. Software 30, 353–360.

    Google Scholar 

  • Providakis, C.P. and Beskos, D.E. (1989a), Free and forced vibrations of plates by boundary elements, Comput. Meth. Appl. Mech. Engng. 74, 231–250.

    MathSciNet  MATH  Google Scholar 

  • Providakis, C.P. and Beskos, D.E. (1989b), Free and forced vibrations of plates by boundary and interior elements, Int. J. Num. Meth. Engng. 28, 1977–1994.

    MATH  Google Scholar 

  • Providakis, C.P. and Beskos, D.E. (1994), Dynamic analysis of elasto-plastic flexural plates by the D/BEM, Engng. Anal. Bound. Elem. 14, 75–80.

    Google Scholar 

  • Providakis, C.P. and Beskos, D.E. (1999), Dynamic analysis of plates by boundary elements, Appl. Mech. Rev. ASME, 52, 213–236.

    Google Scholar 

  • Providakis, C.P. and Beskos, D.E. (2000), Inelastic transient dynamic analysis of Reissner-Mindlin plates, Int. J. Num. Meth. Engng. 49, 383–397.

    MATH  Google Scholar 

  • Providakis, C.P., Beskos, D.E. and Sotiropoulos, D.A. (1994), Dynamic analysis of inelastic plates by the D/BEM, Comp. Mech. 13, 276–284.

    MATH  Google Scholar 

  • Qian, J. and Beskos, D.E. (1995), Dynamic interaction between 3-D rigid surface foundations and comparison with the ATC-3 provisions, Earth. Engng. Struct. Dyn. 24, 419–437.

    Google Scholar 

  • Qian, J. and Beskos, D.E. (1996), Harmonic wave response of two 3-D rigid surface foundations, Soil. Dyn. Earth. Engng. 15, 95–110.

    Google Scholar 

  • Qian, J., Tham, L.G. and Cheung, Y.K. (1996), Dynamic cross-interaction between flexible surface footings by combined BEM and FEM, Earth. Engng. Struct. Dyn. 25, 509–526.

    Google Scholar 

  • Rizos, D.C. (2000), A rigid surface boundary element for soil — structure interaction analysis in the direct time domain, Comput. Mech. 26, 582–591.

    MATH  Google Scholar 

  • Rizos, D.C. and Karabalis, D.L. (1994), An advanced direct time domain BEM formulation for general 3-D elastodynamic problems, Comput. Mech. 15, 249–269.

    MathSciNet  MATH  Google Scholar 

  • Rizos, D.C., Wang, J. and Karabalis, D.L. (2001), A direct time domain BEM-FEM scheme for soil-structure interaction problems, in Boundary Elements XXIII, D.E. Beskos et al (eds), WIT Press, Southampton, 103–115.

    Google Scholar 

  • Saez, A. and Dominguez, J. (1999), BEM analysis of wave scattering in transversely isotropic solids, Int. J. Num. Meth. Engng. 44, 1283–1300.

    MATH  Google Scholar 

  • Siebrits, E. and Peirce, A.P. (1997), Implementation and application of elastodynamic boundary element discretizations with improved stability properties, Engng. Comput. 14, 669–691.

    MATH  Google Scholar 

  • Stamos, A.A. and Beskos, D.E. (1994), Dynamic analysis of large 3-D underground structures by the BEM, Earth. Engng. Struct. Dyn. 24, 917–934.

    Google Scholar 

  • Stamos, A.A. and Beskos, D.E. (1996), 3-D seismic response analysis of long lined tunnels in half-space, Soil Dyn. Earth. Engng. 15, 111–118.

    Google Scholar 

  • Stamos, A.A., Von Estorff, O., Antes, H. and Beskos, D.E. (1994), Vibration isolation in road-tunnel traffic systems, Int. J. Engng. Anal. Des. 1, 109–121.

    Google Scholar 

  • Tadeu, A.J.B., Kausel, E. and Vrettos, C. (1996), Scattering of waves by subterranean structures via the boundary element method, Soil Dyn. Earth. Engng. 15, 387–397.

    Google Scholar 

  • Tadeu, A.J.B., Santos, P.F.A. and Kausel, E. (1999), Closed-form integration of singular terms for constant, linear and quadratic boundary elements, Part 1: SH wave propagation & Part 2: SV-P wave propagation, Engng. Anal. Bound. Elem. 23, 671–681 & 757–768.

    Google Scholar 

  • Takemiya, H. and Guan, F. (1993), Transeint Lamb’s solution for surface strip impulses, J. Engng. Mech. ASCE, 119, 2385–2403.

    Google Scholar 

  • Tan, H. and Chopra, A.K. (1995), Dam-foundation rock interaction effects in frequency-response functions of arch dams, Earth. Engng. Struct. Dyn. 24, 1475–1489.

    Google Scholar 

  • Tanaka, M., Sladek, V. and Sladek, J. (1994), Regularization techniques applied to boundary element methods, Appl. Mech. Rev. ASME 47, 457–499.

    Google Scholar 

  • Telles, J.F.C. and Carrer, J.A.M. (1994), Static and transient dynamic nonlinear stress analysis by the boundary element method with implicit techniques, Engng. Anal. Bound. Elem. 14, 65–74.

    Google Scholar 

  • Telles, J.F.C., Carrer, J.A.M. and Mansur, W.J. (1999), Transient dynamic elastoplastic analysis by the time-domain BEM formulation, Engng. Anal. Bound. Elem. 23, 479–486.

    MATH  Google Scholar 

  • Tham, L.G., Qian, J. and Cheung, Y.K. (1998), Dynamic response of a group of flexible foundations to incident seismic waves, Soil. Dyn. Earth. Engng. 17, 127–137.

    Google Scholar 

  • Triantafyllidis, T. (1991), 3-D time domain BEM using half-space Green’s functions, Engng. Anal. Bound. Elem. 8, 115–124.

    Google Scholar 

  • Triantafyllidis, T. and Neidhart, T. (1989), Diffraction effects between foundations due to incident Rayleigh waves, Earth. Engng. Struct. Dyn. 18, 815–835.

    Google Scholar 

  • Tsinopoulos, S.V., Kattis, S.E., Polyzos, D. and Beskos, D.E. (1999), An advanced boundary element method for axisymmetric elastodynamic analysis, Comput. Meth. Appl. Mech. Engrg. 175, 53–70.

    MATH  Google Scholar 

  • Wang, C.C., Wang, H.C. and Liou, G.S. (1997), Quadratic time domain BEM formulation for 2D elastodynamic transient analysis, Int. J. Solids Struct. 34, 129–151.

    MATH  Google Scholar 

  • Wang, H.C. and Banerjee, P.K. (1990a) Generalized axisymmetric elastodynamic analysis by boundary element method, Int. J. Num. Meth. Engng. 30, 115–131.

    MATH  Google Scholar 

  • Wang, H.C. and Banerjee, P.K. (1990b), Axisymmetric transient elastodynamic analysis by boundary element method, Int. J. Solids Struct. 26, 401–415.

    MATH  Google Scholar 

  • Wang, Y., Rajapakse R.K.N.D. and Shah, H.A. (1991), Dynamic interaction between flexible strip foundations, Earth. Engng. Struct. Dyn. 20, 441–454.

    Google Scholar 

  • Westergaard, H.M. (1933), Water pressures on dams during earthquakes, Trans. ASCE 98, 418–433.

    Google Scholar 

  • Yazdchi, M., Khalili, N. and Valliappan, S. (1999a), Nonlinear seismic behaviour of concrete gravity dams using coupled finite element — boundary element technique, Int. J. Num. Meth. Engng. 44, 101–130.

    MATH  Google Scholar 

  • Yazdchi, M., Khalili, N. and Valliappan, S. (1999b), Dynamic soil — structure interaction analysis via coupled finite element-boundary element method, Soil Dyn. Earth. Engng. 18, 499–517.

    Google Scholar 

  • Yu, G., Mansur, W.J. and Carrer, J. A.M. (1999), The linear 0 method for 2-D elastodynamic BE analysis, Comput. Mech. 24, 82–89.

    MATH  Google Scholar 

  • Zhang, C., Song, C. and Pekau, O.A. (1991), Infinite boundary elements for dynamic problems of 3-D half-space, Int. J. Num. Meth. Engng. 31, 447–462.

    MATH  Google Scholar 

  • Zhang, L.P. and Chopra, A.K. (1991), Impedance functions for three-dimensional foundations supported on an infinitely long canyon of uniform cross-section in a homogeneous half-space, Earth. Engng. Struct. Dyn., 20, 1011–1028 (1991).

    Google Scholar 

  • Zienkiewicz, O.C. and Taylor, R.L. (1991), The Finite Element Method; Vol. 2: Soil and Fluid Mechanics, Dynamics and Non-Linearity, McGraw-Hill Book Co, London.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2003 Springer-Verlag Wien

About this chapter

Cite this chapter

Beskos, D.E. (2003). Dynamic Analysis of Structures and Structural Systems. In: Beskos, D., Maier, G. (eds) Boundary Element Advances in Solid Mechanics. International Centre for Mechanical Sciences, vol 440. Springer, Vienna. https://doi.org/10.1007/978-3-7091-2790-2_1

Download citation

  • DOI: https://doi.org/10.1007/978-3-7091-2790-2_1

  • Publisher Name: Springer, Vienna

  • Print ISBN: 978-3-211-00378-7

  • Online ISBN: 978-3-7091-2790-2

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics