3D viscous-spring artificial boundary in time domain

Liu, Jingbo; Du, Ying; Du, Xiuli; Wang, Zhengyu; Wu, Jun

doi:10.1007/s11803-006-0585-2

Cited by 289 publications

(90 citation statements)

References 12 publications

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“…The artificial boundary condition is always used to absorb the energy of the scattering waves propagating from the generalized structure into the infinite or semi-infinite medium. Because the viscous spring artificial boundary can efficiently simulate radiation damping and elasticity recovery of the infinite and semi-infinite media with good stability and high accuracy (Liu et al, 2006;Du et al, 2006), the 3D viscous spring artificial boundary was adopted to achieve the halfspace simulation outside the basin in this model. This artificial boundary can be achieved by establishing a series of distributed springs and dampers on the truncated boundary of the finite element model, as shown in Figure 3.…”

Section: B Finite-element Model Discretization and Boundary Conditionsmentioning

confidence: 99%

Three-Dimensional Numerical Modeling of Seismic Wave Propagation in Wudu Basin

Zhang¹,

Zhou

et al. 2017

Proceedings of the 2017 2nd International Conference on Modelling, Simulation and Applied Mathematics (MSAM2017)

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Abstract-The Mw 7.9 earthquake occurred in Wenchuan, Sichuan, China, on 12 May 2008, and it caused huge casualties, economic loss, and serious damage to engineering structures and infrastructures in the area near the fault rupture. In particular, the Wudu township far away from the fault rupture (>100km), which is located in a sedimentary basin, also suffered serious damage, and was in the area with seismic intensity VIII-IX in the Isoseismal Map of Wenchuan Earthquake. In this study, full elastic wave field simulations in the Wudu Basin were conducted by using a three-dimensional (3D) finite element method based on the parallel computing cluster platform of the ABAQUS software. The 3D Wudu Basin model is constructed based on the the digital terrain data borehole spatial distribution data in regional geological survey. The basin model consists of Four major subsurfaces and the basin basement, All calculations were executed in the time domain, and the soil and rock were assumed to be linearly elastic. The viscous spring artificial boundary was adopted as the artificial condition, and the oblique incidenct wave was transformed into the equivalent nodal forces acting on the viscous spring artificial boundary of the finite model. In the simulation, an impulse with a duration of 0.25 s was taken as the input SV wave. The simulating results of seismic response characteristics varying greatly from different points in the Wudu Basin revealed the basin edge effect, and the basin-focusing effect. The surface wave generated after the primary S wave is trapped at the shallow part of the basin, and most of the energy is reflected from the interfaces of soil strata and focused back into the basin when the wave propagates through the deepest part of the basin. Moreover, a part of the seismic wave front turns and follows the shallow basin edge, resulting in further amplification. The phenomenon, the incident angle of the seismic waves can produce unusually strong shaking distribution, was demonstrated. It indicates that the complex Wudu Basin geometry, the fairly low velocity of the surface soil layer, and the incident angle of seismic waves dominate the amplification and wave propagation behavior, which results in extraordinary strong shaking patterns in the Wudu basin area.

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Section: B Finite-element Model Discretization and Boundary Conditionsmentioning

confidence: 99%

Three-Dimensional Numerical Modeling of Seismic Wave Propagation in Wudu Basin

Zhang¹,

Zhou

et al. 2017

Proceedings of the 2017 2nd International Conference on Modelling, Simulation and Applied Mathematics (MSAM2017)

View full text Add to dashboard Cite

show abstract

“…The artificial boundary condition is always used to absorb the energy of the scattering waves propagating from the generalized structure into the infinite or semi-infinite medium. Because the viscous spring artificial boundary can efficiently simulate radiation damping and elasticity recovery of the infinite and semi-infinite media with good stability and high accuracy (Liu et al, 2006;Du et al, 2006), the 3D viscous spring artificial boundary was adopted to achieve the half-space simulation outside the basin in this model. This artificial boundary can be achieved by establishing a series of distributed springs and dampers on the truncated boundary of the finite element model, as shown in Figure 3.…”

Section: Finite-element Model Discretization and Boundary Conditionsmentioning

confidence: 99%

Three-Dimensional Numerical Modeling of Seismic Wave Propagation in Wudu Basin, China

Zhang¹,

Li²,

Zhou³

et al. 2017

Proceedings of the 6th International Conference on Computational Methods in Structural Dynamics and Earthquake Engineering (COM

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“…Clearly, it is a challenge for the most ABCs to represent this modal dynamic-stiffness coefficient with high accuracy. Transforming Equation (14) back into time domain leads to a temporal convolution…”

Section: Dynamic-stiffness Abcmentioning

confidence: 99%

Explicit finite element artificial boundary scheme for transient scalar waves in two‐dimensional unbounded waveguide

Zhao

Liu

et al. 2011

Numerical Meth Engineering

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SUMMARYTo simulate the transient scalar wave propagation in a two-dimensional unbounded waveguide, an explicit finite element artificial boundary scheme is proposed, which couples the standard dynamic finite element method for complex near field and a high-order accurate artificial boundary condition (ABC) for simple far field. An exact dynamic-stiffness ABC that is global in space and time is constructed. A temporal localization method is developed, which consists of the rational function approximation in the frequency domain and the auxiliary variable realization into time domain. This method is applied to the dynamicstiffness ABC to result in a high-order accurate ABC that is local in time but global in space. By discretizing the high-order accurate ABC along artificial boundary and coupling the result with the standard lumped-mass finite element equation of near field, a coupled dynamic equation is obtained, which is a symmetric system of purely second-order ordinary differential equations in time with the diagonal mass and non-diagonal damping matrices. A new explicit time integration algorithm in structural dynamics is used to solve this equation. Numerical examples are given to demonstrate the effectiveness of the proposed scheme.

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3D viscous-spring artificial boundary in time domain

Cited by 289 publications

References 12 publications

Three-Dimensional Numerical Modeling of Seismic Wave Propagation in Wudu Basin

Three-Dimensional Numerical Modeling of Seismic Wave Propagation in Wudu Basin

Three-Dimensional Numerical Modeling of Seismic Wave Propagation in Wudu Basin, China

Explicit finite element artificial boundary scheme for transient scalar waves in two‐dimensional unbounded waveguide

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