On a hybrid Laplace-time domain approach to dynamic interaction problems
DOI:
https://doi.org/10.13052/17797179.2012.731254Keywords:
impedance matrix, convolution quadrature method, dynamic soil–structure interactionAbstract
Dynamic interaction problems between two subdomains lead in time to convolution integrals on the interface when one (linear) subdomain is modelled by an impedance operator and the other exhibits non-linear behaviour. In the present work, a convolution quadrature method is used to address a Laplace transform-based approach to evaluate these convolution products. Its properties are discussed on some numerical soil–structure interaction applications: one that is fully linear and the other showing material non-linearities.
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Cottereau, R., Clouteau, D., Soize, C., & Cambier, S. (2006). Probabilistic nonparametric models of
impedance matrices. Application to the seismic design of a structure. European Journal of Computational
Mechanics, 15(1–3), 131–142.
Darbre, G., & Wolf, J. (1988). Criterion of stability and implementation issues of hybrid frequency time
domain procedure for non-linear dynamic analysis. Earthquake Engineering and Structural
Dynamics, 16(4), 569–581.
François, S., & Degrande G. (2005). A time domain coupled boundary element-finite element method for
the dynamic response of structures. In J.L. Bento Coelho (Ed.), Proceedings of the 12th International
Congress on Sound and Vibration, July 2005, Lisbon, Portugal.
Gaul, L., & Schanz, M. (1999). A comparative study of three boundary element approaches to calculate
the transient response of viscoelastic solids with unbounded domains. Computer Methods in Applied
Mechanics and Engineering, 179, 111–123.
Karpel, M. (1982). Design for active flutter suppression and gust alleviating using state-space unsteady
aeroelastic modelling. Journal of Aircraft, 19(3), 221–227.
Lubich, C. (1988a). Convolution quadrature and discretized operational calculus I. Numerische Mathematik,
, 129–145.
Lubich, C. (1988b). Convolution quadrature and discretized operational calculus II. Numerische Mathematik,
, 413–425.
Lubich, C. (1994). On the multistep time discretization of linear initial-boundary value problems and
their boundary integral equations. Numerische Mathematik, 67, 365–389.
Moser, W., Antes, H., & Beer, G. (2005a). A Duhamel integral based approach to one-dimensional wave
propagation analysis in layered media. Computational Mechanics, 35, 115–126.
Moser, W., Antes, H., & Beer, G. (2005b). Soil–structure interaction and wave propagation problems in
D by a Duhamel integral based approach and the convolution quadrature method. Computational
Mechanics, 36, 431–443.
Nieto Ferro, A., Clouteau, D., Greffet, N., & Devésa, G. (2011). Hybrid Laplace-time domain approach
for nonlinear dynamic soil–structure interaction problems. In M. Papadrakakis, M. Fragiadakis, & V.
Plevris (Eds.), Proceedings of the 3rd ECCOMAS thematic conference on computational methods in
structural dynamics and earthquake engineering, May 2011, Corfu, Greece.
Pereira, A., & Beer, G. (2009). Interface dynamic stiffness matrix approach for three-dimensional
transient multi-region boundary element analysis. International Journal for Numerical Methods in
Engineering, 80, 1463–1495.
Schanz, M., & Antes, H. (2006). Application of ‘Operational Quadrature Methods’ in time domain
boundary element methods. Meccanica, 32, 179–186.
Wolf, J. (1995). Unit-impulse response matrix of unbounded medium by infinitesimal finite-element cell
method. Computer Methods in Applied Mechanics and Engineering, 122, 251–272.
Wolf, J. (1988). Soil–structure interaction analysis in the time domain. Englewood Cliffs, NJ: Prentice-
Hall.
European Journal of Computational Mechanics.