• Structural Engineering and Mechanics
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• v.55 no.5
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• pp.1055-1086
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• 2015

The dynamic response of two-dimensional unbounded domain on the rigid bedrock in the time domain is numerically obtained. It is realized by the modified scaled boundary finite element method (SBFEM) in which the original scaling center is replaced by a scaling line. The formulation bases on expanding dynamic stiffness by using the continued fraction approach. The solution converges rapidly over the whole time range along with the order of the continued fraction increases. In addition, the method is suitable for large scale systems. The numerical method is employed which is a combination of the time domain SBFEM for far field and the finite element method used for near field. By using the continued fraction solution and introducing auxiliary variables, the equation of motion of unbounded domain is built. Applying the spectral shifting technique, the virtual modes of motion equation are eliminated. Standard procedure in structural dynamic is directly applicable for time domain problem. Since the coefficient matrixes of equation are banded and symmetric, the equation can be solved efficiently by using the direct time domain integration method. Numerical examples demonstrate the increased robustness, accuracy and superiority of the proposed method. The suitability of proposed method for time domain simulations of complex systems is also demonstrated.

• Earthquakes and Structures
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• v.9 no.1
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• pp.173-194
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• 2015

Site response analysis is an important topic in earthquake engineering. A time-domain numerical method called as one-dimensional (1D) finite element artificial boundary method is proposed to simulate the homogeneous plane elastic wave propagation in a layered half space subjected to the obliquely incident plane body wave. In this method, an exact artificial boundary condition combining the absorbing boundary condition with the inputting boundary condition is developed to model the wave absorption and input effects of the truncated half space under layer system. The spatially two-dimensional (2D) problem consisting of the layer system with the artificial boundary condition is transformed equivalently into a 1D one along the vertical direction according to Snell's law. The resulting 1D problem is solved by the finite element method with a new explicit time integration algorithm. The 1D finite element artificial boundary method is verified by analyzing two engineering sites in time domain and by comparing with the frequency-domain transfer matrix method with fast Fourier transform.

• Structural Engineering and Mechanics
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• v.21 no.4
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• pp.437-450
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• 2005

In this study, a complete analysis of soil-structure interaction problems is presented which includes a modelling of the near surrounding of the building (near-field) and a special description of the wave propagation process in larger distances (far-field). In order to reduce the computational effort which can be very high for time domain analysis of wave propagation problems, a special approach based on similarity transformation of the infinite domain on the near-field/far-field interface is applied for the wave radiation of the far-field. The near-field is discretised with standard Finite Elements, which also allows to introduce non-linear material behaviour. In this paper, a new approach to calculate the involved convolution integrals is presented. This approximation in time leads to a dramatically reduced computational effort for long simulation times, while the accuracy of the method is not affected. Finally, some benchmark examples are presented, which are compared to a coupled Finite Element/Boundary Element approach. The results are in excellent agreement with those of the coupled Finite Element/Boundary Element procedure, while the accuracy is not reduced. Furthermore, the presented approach is easy to incorporate in any Finite Element code, so the practical relevance is high.

• Bulletin of the Korean Mathematical Society
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• v.35 no.2
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• pp.345-362
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• 1998

We introduce and anlyze a naturally parallelizable frequency-domain method for parabolic problems with a Neumann boundary condition. After taking the Fourier transformation of given equations in the space-time domain into the space-frequency domain, we solve an indefinite, complex elliptic problem for each frequency. Fourier inversion will then recover the solution of the original problem in the space-time domain. Existence and uniqueness of a solution of the transformed problem corresponding to each frequency is established. Fourier invertibility of the solution in the frequency-domain is also examined. Error estimates for a finite element approximation to solutions fo transformed problems and full error estimates for solving the given problem using a discrete Fourier inverse transform are given.

• Earthquakes and Structures
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• v.3 no.2
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• pp.97-115
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• 2012

The energy-transmitting boundary, which is used in the well-known finite element method (FEM) program FLUSH, is quite efficient for the earthquake response analysis of buildings considering soil-structure interaction. However, it is applicable only in the frequency domain. The author proposed methods for transforming frequency dependent impedance into the time domain, and studied the time domain transform of the boundary. In this paper, first, the estimation methods for both the halfspace condition under the bottom of the soil model and the pseudo three-dimensional effect were studied with the time domain transmitting boundary. Next, response behavior when using the boundary was studied in detail using a practical soil and building model. The response accuracy was compared with those using viscous boundary, and the boundary that considers the excavation force. Through these studies, the accuracy and efficiency of the proposed time domain transmitting boundary were confirmed.

• Proceedings of the Korea Committee for Ocean Resources and Engineering Conference
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• 2006.11a
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• pp.382-385
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• 2006

A high-order spectral/boundary-element method is newly adapted as an efficient numerical tool. In this method, the velocity potential is expressed as the sum of surface potential and body potential. Then, surface potential is solved fly using the high-order spectral method and body potential is solved fly using the high-order boundary element method. Through the combination of these two methods, the wave-making problems fly a submerged sphere moving with the large amplitude oscillation are solved in time-domain. With the example calculations, nonlinear effects on free-surface profiles and hydrodynamic forces are shown and discussed.

• Journal of Ocean Engineering and Technology
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• v.20 no.6 s.73
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• pp.67-74
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• 2006

A high-order spectral/boundary-element method is newly adapted as an efficient numerical tool. This method is one of the most efficient numerical methods by which the nonlinear gravity waves can be simulated and hydrodynamic forces also can be calculated in time-domain. In this method, the velocity potential is expressed as the sum of surface potential and body potential. Then, surface potential is solved by using the high-order spectral method and body potential is solved by using the high-order boundary element method. By the combination of these two methods, the wave-making problems by a submerged sphere oscillating with large amplitude under the free~surface are solved in time-domain. Through the example calculations, nonlinear effects on free-surface profiles and hydrodynamic forces are shown and discussed.

• Journal of Power System Engineering
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• v.14 no.6
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• pp.75-82
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• 2010

In this study, the topics for free-surface wave simulation, nonlinear hydrodynamic force, and the critical resonance frequency of so-called ${\tau}=U{\omega}/g$=1/4 are discussed. A high-order spectral/boundary element method is newly adapted as an efficient numerical tool. This method is one of the most efficient numerical methods by which the nonlinear gravity waves can be simulated and hydrodynamic forces also can be calculated in time domain. In this method, the velocity potential is expressed as the sum of surface potential and body potential. Then, surface potential is solved by using the high-order spectral method and body potential is solved by using the high-order boundary element method. By the combination of these two methods, the wave-making problems by a submerged sphere oscillating with forward speed under the free-surface are solved in time domain.

• Structural Engineering and Mechanics
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• v.23 no.3
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• pp.263-278
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• 2006

This work presents a time-truncation scheme, based on the Lagrange interpolation polynomial, for the solution of the two-dimensional scalar wave problem by the time-domain boundary element method. The aim is to reduce the number of stored matrices, due to the convolution integral performed from the initial time to the current time, and to keep a compromise between computational economy and efficiency and the numerical accuracy. In order to verify the accuracy of the proposed formulation, three examples are presented and discussed at the end of the article.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.29 no.11 s.242
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• pp.1439-1444
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• 2005

A two-dimensional boundary element method was used for the scattering analysis of side-drilled hole(SDH). The far-field scattering amplitude was calculated for shear vertical(SV) wave, and their frequency and time-domain results were presented. The time-domain scattering amplitude showed the directly reflected wave from the SDH leading edge as well as the creeping wave. In an immersion, pulse-echo testing, two measurement models were introduced to predict the response from SDHs. The 2-D boundary element scattering amplitude was converted to the 3-D amplitude to be used in the measurement model. The receiver voltage was calculated fer SV wave incidence at 45$^{\circ}C$ on the 1 m diameter SDH, and the result was compared with experiment.