• Computational Structural Engineering
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• v.8 no.3
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• pp.91-102
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• 1995

For the wave propagation problems, the influence of time-dependent dynamic behavior must be accounted in the analysis. In this study, the dynamic analysis method which combines finite elements and boundary elements is developed for the wave propagation problem modelling the infinity of medium through 3-D boundary elements and underground structure through degenerated finite shell elements. Performing dynamic analysis of underground tunnels by the proposed coupling method of boundary and finite elements, it is found that the change of the stiffness of structures has a good effect on the response. It is also found that the consideration of the repeating effect due to moving traffic loads which is difficult with existing 2-D dynamic analysis can be possible with the 3-D analysis in time domain.

• KIEE International Transaction on Electrical Machinery and Energy Conversion Systems
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• v.4B no.4
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• pp.180-183
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• 2004

This paper presents a description of the point collocation method and its application to the electromagnetic field computation. The interpolation scheme is based on the fast moving least square reproducing kernel approximation. In the method, the integration cell is not required and the essential boundary conditions can be enforced directly. Numerical simulations on 1-D and 2-D problems are carried out to validate the method. It is found that computational efficiency is higher than the general mesh-free methods.

• 한국전산유체공학회:학술대회논문집
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• 1995.04a
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• pp.5-29
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• 1995

A three-dimensional flow field induced by two trains passing by each other inside a tunnel is studied based on the numerical simulation of the three-dimensional compressible Euler/Navier-Stokes equations formulated in the finite difference approximation. Domain decomposition method with the FSA(fortified solution algorithm) interface scheme is used to treat this moving-body problem. The computed resluts show basic characteristic of the flow field created when two trains passing by each other. History of the pressure distributions and the aerodynamic forces acting on the trains are mailnly discussed. The results indicate that the phenomenon is complicated due to the interaction of the flow induced by two trains. Strong side force occurs between the two trains when the front portion of the opposite train passes by. It fluctuates rapidly and maximum suction force occurs when two trains are aligned side by side. The results also indicate the effectiveness of the present numerical method for moving boundary problems.

• The Pure and Applied Mathematics
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• v.6 no.2
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• pp.113-120
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• 1999

This paper studies the problem of an infinite confined aquifer which at time t ＜ 0 is assumed motionless. At time t = 0 crude oil seeps into the aquifer, thereby contaminating the valuable drinking water. Since the crude oil and water are im-miscible, the problem is posed as a one-dimensional two-phase unsteady moving boundary problem. A similarity solution is developed in which the moving front parameter is obtained by Newton-Ralphson iteration. A numerical scheme, involving the front tracking method, is devised employing the fourth order Runge-Kutta method. Comparison of the exact and numerical schemes shows an error of only 3%. Thus the developed numerical scheme is quite accurate in tackling more realistic problems where exact solutions are not possible.

• Structural Engineering and Mechanics
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• v.25 no.4
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• pp.467-480
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• 2007

Two methods were developed for analyzing problems with two adjacent sub-domains modeled by different kinds of elements in finite element method. Each sub-domain can be defined independently without the consideration of equivalent division with common nodes used for the interface. These two methods employ an individual interface to accomplish the compatibility. The MLSA method uses the moving least square approximation which is the basic formulation for Element Free Galerkin Method to formulate the interface. The displacement field assumed by this method does not pass through nodes on the common boundary. Therefore, nodes can be chosen freely for this method. The results show that the MLSA method has better approximation than traditional methods.

• Structural Engineering and Mechanics
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• v.35 no.4
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• pp.511-533
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• 2010

As a truly meshfree method, meshless equilibrium on line method (MELM), for 2D elasticity problems is presented. In MELM, the problem domain is represented by a set of distributed nodes, and equilibrium is satisfied on lines for any node within this domain. In contrary to conventional meshfree methods, test domains are lines in this method, and all integrals can be easily evaluated over straight lines along x and y directions. Proposed weak formulation has the same concept as the equilibrium on line method which was previously used by the authors for enforcement of the Neumann boundary conditions in the strong-form meshless methods. In this paper, the idea of the equilibrium on line method is developed to use as the weak forms of the governing equations at inner nodes of the problem domain. The moving least squares (MLS) approximation is used to interpolate solution variables in this paper. Numerical studies have shown that this method is simple to implement, while leading to accurate results.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.20 no.4
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• pp.493-499
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• 2007

The Taylor expansion expresses a differentiable function and its coefficients provide good approximations for the given function and its derivatives. In this study, m-th order Taylor Polynomial is constructed and the coefficients are computed by the Moving Least Squares method. The coefficients are applied to the governing partial differential equation for solid problems including crack problems. The discrete system of difference equations are set up based on the concept of point collocation. The developed method effectively overcomes the shortcomings of the finite difference method which is dependent of the grid structure and has no approximation function, and the Galerkin-based meshfree method which involves time-consuming integration of weak form and differentiation of the shape function and cumbersome treatment of essential boundary.

• Journal of KSNVE
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• v.8 no.1
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• pp.122-131
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• 1998

Internal and external acoustic fields of the engine inlet are calculated by using a finite element method. The far fields non reflecting boundary condition is enforced by using a wave envelope element, which is a kind of infinite element. The geometry is assumed an axisymetric duct. Sources of the fan are modeled by the Tyler and Sofrin's theory. Effects of uniformly moving medium are considered. A pulsating sphere and an oscillating piston problem are calculated to verify the external problems, and compared with exact solutions. When the wave envelope element is applied at the far boundary, the calculated finite element solutions show good agreements with the exact solutions. The engine inlet is solved with the combined internal and external grid. The cut-off phenomena on engine inlet duct are observed.

• Journal of Mechanical Science and Technology
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• v.18 no.3
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• pp.460-470
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• 2004

A computational analysis of engineering problems with moving domain or/and boundary according to either Lagrangian or Eulerian approach may encounter inherent numerical difficulties, the extreme mesh distortion in the former and the material boundary indistinctness in the latter. In order to overcome such defects in classical numerical approaches, the ALE(arbitrary Lagrangian Eulerian) method is widely being adopted in which the finite element mesh moves with arbitrary velocity. This paper is concerned with the ALE finite element formulation, aiming at the dynamic response analysis of baffled fuel-storage container in yawing motion, for which the coupled time integration scheme, the remeshing and smoothing algorithm and the mesh velocity determination are addressed. Numerical simulation illustrating theoretical works is also presented.

• Journal of the Korean Society of Safety
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• v.23 no.3
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• pp.87-92
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• 2008

A finite element method which is discontinuous in time is developed for the solution of the classical parabolic model of heat conduction problems. The approximations are continuous with respect to the space variables for each fixed time, but they admit discontinuities with respect to the time variable at each time step. The method is superior to other well-known approaches to these problems in that it allows a wider range of moving boundary value problems to be dealt with, such as are encountered in complex engineering operations like ground freezing. The method is applied to one-dimensional and two-dimensional heat conduction problems in this paper, although it could be extended to more higher dimensional problems. Several example problems are discussed and illustrated, and comparisons are made with analytical approaches where these can also be used.