• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2007.05a
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• pp.859-865
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• 2007

This paper presents a method to analyze the unbalance response of a high speed polygon mirror scanner motor supported by sintered bearing and flexible supporting structures by using the finite element method and the mode superposition method. The appropriate finite element equations for polygon mirror are described by rotating annular sector element using Kirchhoff plate theory and von Karman non-linear strain, and its rigid body motion is also considered. The rotating components except for the polygon mirror are modeled by Timoshenko beam element including the gyroscopic effect. The flexible supporting structures are modeled by using a 4-node tetrahedron element and 4-node shell element with rotational degrees of freedom. Finite element equations of each component of the polygon mirror scanner motor and the flexible supporting structures are consistently derived by satisfying the geometric compatibility in the internal boundary between each component. The rigid link constraints are also imposed at the interface area between sleeve and sintered bearing to describe the physical motion at this interface. A global matrix equation obtained by assembling the finite element equations of each substructure is transformed to a state-space matrix-vector equation, and both damped natural frequencies and modal damping ratios are calculated by solving the associated eigenvalue problem by using the restarted Arnoldi iteration method. Unbalance responses in time and frequency domain are performed by superposing the eigenvalues and eigenvectors from the free vibration analysis. The validity of the proposed method is verified by comparing the simulated unbalance response with the experimental results. This research also shows that the flexibility of supporting structures plays an important role in determining the unbalance response of the polygon mirror scanner motor.

• East Asian mathematical journal
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• v.38 no.5
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• pp.603-610
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• 2022

In [6, 7] they introduced a new finite element method for accurate numerical solutions of Poisson equations with corner singularities. They consider the Poisson equations with homogeneous boundary conditions, compute the finite element solutions using standard FEM and use the extraction formula to compute the stress intensity factor(s), then they posed new PDE with a regular solution by imposing the nonhomogeneous boundary condition using the computed stress intensity factor(s), which converges with optimal speed. From the solution they could get an accurate solution just by adding the singular part. They considered a partial differential equation with the input function f ∈ L²(Ω). In this paper we consider a PDE with the input function f ∈ H¹(Ω) and find the corresponding singular and dual singular functions. We also induce the corresponding extraction formula which are the basic element for the approach.

• Transactions of the Korean Society of Mechanical Engineers
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• v.17 no.11
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• pp.2773-2781
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• 1993

Laplace's equation is, perhaps, the most important equation, which governs various kinds of physical phenomena. Due to its importance, there have been several numerical techniques such as the finite element method, the finite difference method, and the boundary element method. However, these techniques do not appear very effective as they require a substantial amount of numerical calculation. In this paper, we develop a new most efficient technique based on analytic solutions for Laplace's equation in some convex polygons. Although a similar approach was used for the same problem, the present technique is unique as it solves directly Laplace's equation with the utilization of analytical solutions.

• Journal of the Korean Society of Safety
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• v.14 no.1
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• pp.10-18
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• 1999

An integral equation representation of cracks was presented, which differs from well-known "dislocation layer" representation. In this new representation, the integral equation representation of cracks was developed and coupled to the direct boundary-element method for treatment of cracks in finite plane bodies. The method was developed for in-plane(mode I and II) loadings only. In this paper, the method is formulated and applied to various crack problems involving multiple and branch cracks in finite region. The results are compared to exact solutions where available and the method is shown to be very accurate despite of its simplicity.implicity.

• Communications of the Korean Mathematical Society
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• v.22 no.4
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• pp.623-640
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• 2007

The Lotka-McKendrick model which describes the evolution of a single population is developed from the well known Malthus model. In this paper, we introduce the Lotka-McKendrick model. We approximate the solution to the model using hp-discontinuous Galerkin finite element method. The numerical results show that the presented hp-discontinuous Galerkin method is very efficient in case that the solution has a sharp decay.

• Kyungpook Mathematical Journal
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• v.50 no.3
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• pp.419-431
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• 2010

A low-order finite element preconditioner is analyzed for a cubic spline collocation method which is used for discretizations of coupled elliptic problems derived from an optimal control problrm subject to an elliptic equation. Some numerical evidences are also provided.

• Transactions of Materials Processing
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• v.13 no.2
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• pp.180-187
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• 2004

A computer code was developed to simulate the filling stage of the injection/compression molding process by a finite element method. The constitutive equation used here was the compressible Leonov model. The PVT relationship was assumed to follow the Tait equation. The flow-induced birefringence was related to the calculated flow stresses through the linear stress-optical law. Simulations of a disk part under different process conditions including the variation of compression stroke and compression speed were carried out to understand their effects on birefringence variation. The simulated results were also compared with those by conventional injection molding.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.7 no.2
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• pp.13-22
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• 2003

Simulations on the nonlinear partial differential equation derived from Black-Scholes equation with transaction costs are performed. These numerical experiments using finite element methods are applied to KOSPI200 in 2002 and the option prices obtained with transaction costs are closer to the real prices in market than the prices used in Korea Stock Exchange.

• Structural Monitoring and Maintenance
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• v.9 no.1
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• pp.81-105
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• 2022

The use of concrete filled steel tube (CFST) column is widely accepted due to its property of high axial load carrying capacity, more ductility and more resistant to earthquake specially using in bridges and high-rise buildings. The initial imperfection (δ) that produces during casting or fixing causes the reduction in load carrying capacity, this is the reason, experimental capacity is always less then theoretical one. In this research, the effect of δ on load carrying capacity and behavior of concrete filled steel tube (CFST) column have been investigated by numerically simulation of large number of models with different δ and other geometric parameters that include length (L), width (B), steel tube thickness (t), f'_c and f_y. Finite element analysis software ANSYS v18 is used to develop model of SCFST column to evaluate strength capacity, buckling and failure pattern of member which is applied during experimental study under cyclic axial loading. After validation of results, 42 models with different parameters are evaluated to develop empirical equation predicting axial load carrying capacity for different value of δ. Results indicate that empirical equation shows the 0 to 9% error for finite element analysis Forty-two models in comparison with ANSYS results, respectively. Empirical equation can be used for predicting the axial capacity of early estimating the axial capacity of SCFT column including 𝛿.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.28 no.8 s.227
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• pp.1140-1151
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• 2004

This paper reports on the finite elements analysis for die compaction process of cemented carbide tool parts. Experimental data were obtained under die compaction and triaxial compression with various loading conditions. The elastoplastic constitutive equations based on the yield function of Shima and Oyane were implemented into an explicit finite element program (ABAQUS/Explicit) and implicit finite element program (PMsolver/Compaction-3D) to simulate compaction response of cemented carbide powder during die compaction. For simulation of die compaction, the material parameters for Shima and Oyane model were obtained by uniaxial die compaction test. Explicit finite element results were compared with implicit results for cemented carbide powder.