• Bulletin of the Korean Mathematical Society
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• v.36 no.4
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• pp.637-647
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• 1999

In this paper, we consider a free boundary problem with Pushchino dynamics satisfying the Dirichlet boundary condition. We shall the stationary solutions ($v^{*}(x),s^{*}$) exist and the Hopf bifurcation occurs at a critical point when s $\in$ (1/3,1).

• Communications of the Korean Mathematical Society
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• v.14 no.2
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• pp.441-447
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• 1999

A free boundary problem is derived from a singular limit system of a reaction diffusion equation whose reaction terms are bistable type. In this paper, we shall consider a free boundary problem with two layers satisfying the zero flux boundary condition and shall show that the Hopf bifurcation can not occur as a parameter varies.

• Korean Journal of Mathematics
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• v.6 no.2
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• pp.173-181
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• 1998

The local behaviors of the Hopf bifurcation in the free boundary problem satisfying the zero flux boundary condition was examined in [3]. In this paper, we shall examine the global behaviors for this problem and shall apply the center-index theory to show the globality.

• Structural Engineering and Mechanics
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• v.78 no.4
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• pp.497-518
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• 2021

In this study, a new method for treating the wall boundary in smoothed particle hydrodynamics (SPH) is proposed to simulate free surface flows effectively. Unlike conventional methods of wall boundary treatment through boundary particles, in the proposed method, the wall boundary condition is directly imposed by adding boundary truncation terms to the mass and momentum conservation equations. Thus, boundary particles are not used in boundary modeling. Doing so, the wall boundary condition is accurately imposed, boundary modeling is simplified, and computation is made efficient without losing stability in SPH. Performance of the proposed method is demonstrated through several numerical examples: dam break, dam break with a wedge, sloshing, inclined bed, cross-lever rotation, pulsating tank and sloshing with a flexible baffle. These results are compared with available experimental results, analytical solutions, and results obtained using the boundary particle method.

• Selected Papers of The Society of Naval Architects of Korea
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• v.2 no.1
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• pp.63-78
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• 1994

This paper deals with the treatment of the open boundary in two-dimensional free-surface wave problems. Two numerical schemes are investigated for the implementation of the open boundary condition. One is to add the artificial damping term to the dynamic free-surface boundary condition, in which the determination of suitable damping coefficient and the damping zone is the most important. The other is a modified Orlanski's method, which is known to be very useful for the uni-directional waves. Using these two schemes, numerical tests have been conducted for a few typical free-surface wave problems. To obtain the numerical solution of the free-surface boundary value problem, the fundamental source-distribution method is used and the fully nonlinear free-surface boundary conditions are applied. The computed results are presented in comparison with those of others for the proof of practicality of these two schemes.

• Journal of applied mathematics & informatics
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• v.22 no.1_2
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• pp.223-235
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• 2006

By applying the Landau-type transformation, we transform a Stefan problem with nonlinear free boundary condition into a system consisting of a parabolic equation and the ordinary differential equations. Fully discrete finite element method is developed to approximate the solution of a system of a parabolic equation and the ordinary differential equations. We derive optimal orders of convergence of fully discrete approximations in $L_2,\;H^1$ and $H^2$ normed spaces.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.17 no.3 s.120
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• pp.220-225
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• 2007

Free vibration analysis using the method of NDIF (non-dimensional dynamic influence function), which was developed by the author, is extended to arbitrarily shaped polygonal plates with free edges. Local Cartesian coordinate systems are employed to apply the free boundary condition to nodes distributed along the edges of the plate of interest. Furthermore, a new way for applying the free boundary condition to nodes located at corners of the plate is for the first time introduced by considering the phenomenon of stress concentration at the corners. Two case studies show that the proposed method is valid and accurate when the eigenvalues by the proposed method are compared to those by FEM(ANSYS).

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2003.05a
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• pp.870-875
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• 2003

This paper deals with the free vibrations of horizontally curved beams with the general boundary condition, which consists of translational and rotational springs. The equations of general boundary condition of such beams are derived, while the ordinary differential equations governing free vibrations are adopted from the literature. The parabola as the curved beam's curvilinear shape is considered in numerical examples. For calculating the natural frequencies, the governing equations are solved by numerical methods. The Runge-Kutta and Determinant Search Methods are used for integrating the differential equations and for calculating the natural frequencies, respectively. for validation purpose, the numerical results obtained herein are compared to those obtained from the SAP 2000. With regard to numerical results, the relationships between frequency parameters and various beam parameters are presented in the forms of Table and figures.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.28 no.6B
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• pp.691-696
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• 2008

In this paper, a three-dimensional non-hydrostatic pressure model for free surface flows using a normalized vertical coordinate system is presented. To strongly couple the free surface and non-hydrostatic pressure in the momentum equations, a double predictor-corrector method is employed. This research is especially focused on implementing the dynamic boundary condition (a zero pressure condition) at the free surface. This boundary condition can be specified accurately with a small modification to existing models. Numerical results with and without this modification clearly show that a precise implementation of the dynamic boundary condition is paramountly important.

• Proceedings of the Korean Geotechical Society Conference
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• 2000.03b
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• pp.159-166
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• 2000

Non-destructive out-hole tests, impact-echo and impact-response are widely applied to evaluate integrity of drilled shafts. In these tests, vibratory motions of drilled shafts are interpreted, which induced by impacts on the shaft head. In applying the tests to evaluating integrity of shaft, it has been attended whether the tests have resolutions enough to distinguish existence of slime at between the shaft end and a bearing soil deposit. To distinguish existence of slime by tests, modes of shaft vibrations need to be reasonably interpreted, which generally vary according to a shaft boundary condition such as, a free-free or a free-fixed condition. The boundary condition of a shaft is, however, found to be significantly affected by stiffness of soil deposits around shaft as well as penetration depths of shaft into a bearing soil deposit. Thus, these effects on the boundary condition of a shaft should be considered reasonably in interpreting test results to decide the existence of slime. To investigate the effects, in this study, vibratory motions of shafts constructed in various soil conditions and end penetration depths are examined analytically. Based on the studies, variations of boundary condition are characterized in terms of soil stiffness contrast between a shaft perimeter and a shaft end, and also the ratio of a penetration depth to a shaft length. The results can be applied to verify the applicability of tests to identify the slime.