Consistent transmitting boundary with continued-fraction absorbing boundary conditions for analysis of soil–structure interaction in a layered half-space

Lee, Jin Ho; Tassoulas, John L.

doi:10.1016/j.cma.2011.01.004

Cited by 34 publications

(9 citation statements)

References 20 publications

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“…Therefore, the approach in this study must be extended to problems in half‐spaces. In order to consider energy radiation into infinity for a half‐space, the paraxial boundary condition and the continued‐fraction absorbing boundary condition (or perfectly matched discrete layer) have been combined with consistent transmitting boundaries 27–29 . The PML can also be utilized to represent a half‐space in the framework of the thin‐layer method 30 .…”

Section: Discussionmentioning

confidence: 99%

“…In order to consider energy radiation into infinity for a half-space, the paraxial boundary condition and the continued-fraction absorbing boundary condition (or perfectly matched discrete layer) have been combined with consistent transmitting boundaries. [27][28][29] The PML can also be utilized to represent a half-space in the framework of the thin-layer method. 30 The approach in this study can be combined with the consistent transmitting boundary method to consider half-space conditions.…”

Section: Discussionmentioning

confidence: 99%

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Consistent transmitting boundaries for time‐domain analyses of wave propagation in layered anisotropic waveguides

Lee

2022

Numerical Meth Engineering

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Consistent transmitting boundaries for time-domain analyses of scalar-and elastic-wave propagation in horizontally layered anisotropic or transversely isotropic waveguides are developed. Governing equations and corresponding consistent nodal forces are derived for scalar and elastic waves in layered waveguides for which finite-element discretization is considered in the vertical layering direction. Auxiliary variables for the horizontal derivatives and integrals of displacements are introduced to modify the governing equations and the nodal forces. The desired consistent transmitting boundaries applicable to time-domain analyses of scalar-and elastic-wave propagation in isotropic and anisotropic waveguides are then derived. The transmitting boundary for a scalar wave satisfies the criteria for an accurate and well-posed boundary condition and shows convergent, accurate, and stable behaviors for a variety of scalar-wave propagation problems in waveguides. Although the boundary for an elastic wave is demonstrated as convergent and stable for elastic-wave propagation problems in waveguides, limited accuracy is observed in the numerical examples. Nevertheless, the newly proposed approach is expected to provide another way to solve elastic-wave propagation problems.

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Section: Discussionmentioning

confidence: 99%

Section: Discussionmentioning

confidence: 99%

Consistent transmitting boundaries for time‐domain analyses of wave propagation in layered anisotropic waveguides

Lee

2022

Numerical Meth Engineering

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“…However, these e®ects may be overcome by employing in¯nite elements 7,8 or energy transmitting boundaries. 9 Lysmer 10 and Liang 11 employed the 2D plane-strain models to study the cross-interaction of two or more foundations or structures subjected to vertically propagating harmonic SVwaves. Castaneda 12 and Solari et al 13 applied FEM with the consistent boundaries to study the three dimensional problem of two rigid square foundations under vertically propagating S-waves.…”

Section: Introductionmentioning

confidence: 99%

Dynamic Interaction Between Rigid Surface Foundations on Multi-Layered Half Space

Lin

2016

Int. J. Str. Stab. Dyn.

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A numerical approach is presented to calculate the dynamic response of a group of rigid surface foundations. The formulation is unconditionally stable and has the computational simplicity with only the algebraic calculations involved. It imposes no limit to the foundation shape, foundation separations, thickness of the layered medium and magnitude of frequency. In the analysis, the foundation-ground interface is discretized into a number of sub square-regions. The Green's function, which is obtained by the Fourier-Bessel transform and precise integration method, is employed to calculate the dynamic response of each sub-region. Finally, a system of linear algebraic equation in terms of the contact forces within each sub-region is observed, which leads to the desired dynamic impedance functions of the foundations. Comparison is carried out between the proposed method and the solutions available in the literature. Parametric studies on the dynamic interaction between adjacent foundations are also described. Addressed in this study are the e®ects of the distance and direction of foundation alignment. Several conclusions are drawn the signi¯cance of each factor. Illustrative results for a case of several closely-spaced foundations are also presented. Although the dynamic interaction analysis of foundations is concerned here, further applications of this approach can be extended to the interaction analysis of structures.

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“…Lee and Tassoulas 67 combined consistent boundary with continued-fraction ABC. To the best of the authors' knowledge, the method is the first work to construct an accurate ABC for wave propagation in layered half-space.…”

Section: Introductionmentioning

confidence: 99%

Accurate H‐shaped absorbing boundary condition in frequency domain for scalar wave propagation in layered half‐space

Zhao

2020

Numerical Meth Engineering

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An accurate absorbing boundary condition (ABC) is developed in frequency domain for finite element analysis of scalar wave propagation in unbounded layered half‐space. The proposed ABC is H‐shaped line that consists of two parts: a new ABC at horizontal bottom boundary of finite domain to replace semiinfinite strip below horizontal boundary and between two vertical boundaries, and a general consistent ABC at vertical lateral boundary to replace semiinfinite layered half‐space outside vertical boundary. The key point for constructing the ABC is that a new continued fraction (CF) is presented to expand dynamic stiffness of underlying half‐space, and the CF‐based stress‐displacement relationship is then transformed into an auxiliary variable system with square of horizontal wavenumber. The ABC has only one undetermined real parameter that is the CF‐order independent of frequency and incidence angle of propagating outgoing waves. The parameter can be chosen relatively small value to achieve an accurate ABC. Moreover, the ABC can couple seamlessly with finite element method of finite domain. The finite domain can be chosen very small size due to high accuracy of the ABC. Numerical examples are finally given to demonstrate the effectiveness of the ABC.

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Consistent transmitting boundary with continued-fraction absorbing boundary conditions for analysis of soil–structure interaction in a layered half-space

Cited by 34 publications

References 20 publications

Consistent transmitting boundaries for time‐domain analyses of wave propagation in layered anisotropic waveguides

Consistent transmitting boundaries for time‐domain analyses of wave propagation in layered anisotropic waveguides

Dynamic Interaction Between Rigid Surface Foundations on Multi-Layered Half Space

Accurate H‐shaped absorbing boundary condition in frequency domain for scalar wave propagation in layered half‐space

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