Soil-structure interaction and wave propagation problems in 2D by a Duhamel integral based approach and the convolution quadrature method

Moser, Wolfgang; Antes, H.; Beer, Gernot

doi:10.1007/s00466-005-0679-0

Cited by 26 publications

(11 citation statements)

References 18 publications

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“…Various methods have been devised to overcome this difficulty . At present, BEMs can be efficiently applied to solve a lot of practical problems, as in the study of soil‐structure interaction , in acoustic problems and in the analysis of the electromagnetic scattering . The use of advanced numerical techniques, like finite element and finite difference methods to solve differential equations is now well‐established, but it has been realized that for a growing number of problems the solution can be obtained by discretization of the boundary only.…”

Section: Introductionmentioning

confidence: 99%

Energetic boundary element method analysis of wave propagation in 2D multilayered media

Aimi

Gazzola

Guardasoni

2012

Math Methods in App Sciences

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The analysis of scalar wave propagation in 2D zonewise homogeneous media with vanishing initial and mixed boundary conditions is carried out. The problem is formulated in terms of time-dependent boundary integral equations, and then it is set in a weak form, based on a natural energy identity satisfied by the differential problem solution. Several numerical results have been obtained by means of the related energetic Galerkin boundary element method showing accuracy and stability of the method.A. AIMI, S. GAZZOLA AND C. GUARDASONI precise continuity and coerciveness properties [26,27]. Consequently, it can be discretized by unconditionally stable schemes with well-behaved stability constants even for large times.We remark that the idea of introducing a space-time weak formulation for the transient wave problem based on the energy identity is not new. In fact, in [16], it was exploited to get a satisfactory stability result for the acoustic wave equation with the aid of absorbing boundary condition. Unfortunately, the cases of Dirichlet and Neumann boundary conditions on a bounded time interval, as we have always considered, are much more difficult to be theoretically treated, and they have been analyzed in [26,27].The proposed procedure can be generalized to multi-domain wave propagation BIE problems as introduced in [28] within the limit of bi-domain cases. Here, the extension to n-domain case is proposed and further numerical simulations are presented and discussed: through comparisons with available (when possible) literature results [13,29], the stability and accuracy of the energetic approach are shown even in this framework. Plenty of examples, not easily findable in mathematical and even engineering papers on the subject, and numerical results included in this work illustrate the applicability and potentialities of this technique, even if theoretical analysis of stability and convergence for the multi-domain case is still to be done.H 1=2 .S/ :D fu 2 H 1=2 : i .U/ D uj @ i , i D 1, 2^ .U/ D u for some U 2 H 1 . /g, Figure 1. Example of bi-domain.

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Section: Introductionmentioning

confidence: 99%

Energetic boundary element method analysis of wave propagation in 2D multilayered media

Aimi

Gazzola

Guardasoni

2012

Math Methods in App Sciences

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“…The contribution of the initial displacement field u 0 (X) can be computed subtracting from the initial displacement field itself, the response corresponding to a pseudo-force as presented in Eq. (8). In Eq.…”

Section: Boundary Integral Equation With Initial Conditionsmentioning

confidence: 99%

“…Application of the CQM to plane frame dynamic modelling was performed by Antes et al [6]. A method based on Duhamel integrals, in combination with the CQM, for the analysis of one-dimensional wave propagation in a layered medium was presented by Moser et al [7], which was extended to plane strain elastodynamic BEM-FEM (finite element method) coupling later on [8]. Recently, Dobromil and Schanz [9] and Schanz et al [10] applied the CQM to a poroelastic boundary elements approach shown that BEM based on CQM is very robust and suitable for such kinds of problems.…”

Section: Introductionmentioning

confidence: 99%

Time and space derivatives in a BEM formulation based on the CQM with initial conditions contribution

Abreu¹,

Ferro²,

Mansur³

2007

WIT Transactions on Modelling and Simulation, Vol 44

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This work is concerned with the numerical computation of time and space derivatives of the time-domain solution of scalar wave propagation problems using the boundary element method (TD-BEM). In the present formulation, the BEM based on the so-called convolution quadrature method (CQM-BEM) is employed. The CQM-BEM takes into account non-homogeneous initial conditions by means of a general procedure, known as the initial condition pseudo-force procedure (ICPF), which replaces the initial conditions by equivalent pseudo-forces. The boundary integral equation with initial conditions contribution is derived analytically and the quadrature weights of the standard ICPF-CQM-BEM formulation are transformed in order to compute time and space derivatives. Two numerical examples are presented at the end of the work illustrating the efficacy of the implemented formulation.

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“…It has been shown in [108,109] that a direct stiffness formulation can be used, along with a sampling of the stiffness matrix in the upper complex ω plane.…”

Section: Convolution Techniquesmentioning

confidence: 99%

Dynamics of structures coupled with elastic media—A review of numerical models and methods

Clouteau

Cottereau

Lombaert

2013

Journal of Sound and Vibration

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This paper reviews issues and developments in the field of structure-environment interaction problems, in which the environment is an elastic body, possibly unbounded. It covers in particular the fields of soil-structure interaction, ground-borne noise and vibration emitted by transportation systems and wave diffraction by obstacles in an elastic medium. The general setting for a linear bounded structure coupled to an unbounded linear environment through a bounded interface is first recalled, and the domain decomposition technique classically used for its description is put up. Extensions for the cases of non-linear structure and uncertain environment are then discussed. Finally, the ongoing research in the fields of unbounded interface, moving interface, and multiple interfaces are reviewed and summarized.

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Soil-structure interaction and wave propagation problems in 2D by a Duhamel integral based approach and the convolution quadrature method

Cited by 26 publications

References 18 publications

Energetic boundary element method analysis of wave propagation in 2D multilayered media

Energetic boundary element method analysis of wave propagation in 2D multilayered media

Time and space derivatives in a BEM formulation based on the CQM with initial conditions contribution

Dynamics of structures coupled with elastic media—A review of numerical models and methods

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