• Journal of the Computational Structural Engineering Institute of Korea
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• v.13 no.1
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• pp.51-61
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• 2000

This paper discusses the homogenization method to determine effective average elastic constants of a linear structure by considering its microstructure. A detailed description on the homogenization method is given for the linear elastic material and then the finite element approximation is performed for an investigation of elastic properties. An asymptotic expansion is carried out in the cross-section area, or in the unit cell. Two and three lay-up structures made up of individual isotropic constituents are chosen for numerical examples to check discrepancies between results generated by this theoretical development and the conventional approach. Asymptotic characteristics of the process in extracting the stiffness of structure locally formed by spatial repetitions yield underestimated values of stiffness. These discrepancies are detected by the asymptotic corrective term which is ascribed to considerations of microscopic perturbations and proved in the finite element formulation. The asymptotic analysis is the more reasonable in analysing the composite material, rather than the conventional approach to calculate the macroscopic average for elastic properties.

• Journal of the Korean Mathematical Society
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• v.48 no.6
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• pp.1143-1152
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• 2011

The existence of periodic solutions for the planar Hamiltonian systems with positively homogeneous Hamiltonian is discussed. The asymptotic expansion of the Poincar$\acute{e}$ map is calculated up to higher order and some sufficient conditions for the existence of periodic solutions are given in the case when the first order term of the Poincar$\acute{e}$ map is identically zero.

• Coupled systems mechanics
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• v.7 no.1
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• pp.61-77
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• 2018

This paper establish a high concentration ratio approximation of linear elastic properties of materials with periodic microstructure with cubic inclusions. The approximation is derived using first few terms of power series expansion of the solution of the equivalent eigenstrain problem with a homogeneous eigenstrain approximation. Viability of the approximation at high concentration ratios is proved by comparison with a numerical solution of the homogenization problem. To this end some theoretical result of symmetry properties of the homogenization problem are given. Using these results efficient numerical computation on a reduced computational domain is presented.

• 제어로봇시스템학회:학술대회논문집
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• 1995.10a
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• pp.259-262
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• 1995

In this paper, a model of an asymptotically reliable serial production line with quailty control devices is introduced and analyzed. By an asymptotic technique and Taylor series expansion, its average production rate is approximated in a closed form. The results are applied to a case study of a surface mount system.

• The Transactions of the Korean Institute of Electrical Engineers
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• v.32 no.5
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• pp.183-188
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• 1983

This paper deals with short-term load forecasting. The load model is represented by the state variable form to exploit the Kalman filter technique. The load model is derived from Taylor series expansion and remainder term is considered as noise term. In order to solve recursive filter form, among various algorithm of solving Kalman filter, this paper uses exponential data weighting technique. This paper also deals with the asymptotic stability of filter. Case studies are carried out for the hourly power demand forecasting of the Korea electrical system.

• Journal of the Korean Statistical Society
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• v.25 no.2
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• pp.161-173
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• 1996

When we deal with a Hilbert space-valued Stochastic Differential Equation (SDE) (or Stochastic Partial Differential Equation (SPDE)), depending on some unknown parameters, the solution usually has a Fourier series expansion. In this situation we consider the maximum likelihood method for the statistical estimation problem and derive the asymptotic properties (consistency and normality) of the Maximum Likelihood Estimator (MLE).

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2001.11b
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• pp.565-575
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• 2001

나는 대학원생인 여명환군과의 공동연구를 통해 결함 없는(perfect) 원판의 비선형 비대칭진동에 관한 Sridhar, Mook, Nayfeh에 의한 기존연구[1]에서 구한 가해조건(solvability conditions： 해를 asymptotic expansion으로 근사하는 과정에서 해가 유한하기 위해 응답특성이 만족해야 하는 조건)에 오류가 있음을 발견하고 수정하게 되었다. (중략)

• Transactions of the Korean Society of Mechanical Engineers
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• v.18 no.5
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• pp.1245-1252
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• 1994

A solution of heat transfer problems of composite materials has been tried using homogenization technique. Homogenization technique, which was derived by applying asymptotic expansion to the standard finite element method, helped compute the equivalent thermal conductivity matrices of base cells which constituted the composite material with repeated patterns. The homogenization technique made it possible to compute the solution of the heat transfer problem of composite materials with lower degrees of freedom compared to those of other numerical methods. The equivalent thermal conductivities computed by computed by homogenization technique are also applicable to other numerical methods such as finite difference method.

• Journal of the Korean Society of Fisheries and Ocean Technology
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• v.32 no.3
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• pp.286-293
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• 1996

This paper established the analytical model of sea surface oscilation of simple type fishing port with vertical wave absorbor. This model is composed by MAEM(Matched Asymptotic Expansion Method) for wave amplification in fishing port and EEM(Eigen - function Expansion Method) for wave absorbing characteristics against vertical perforated plates. Dimensionless porosity by adopting Darcy's law was introduced to evaluate wave absorbing characteristics of the perforated structure. Using the model, the efficiency of the vertical perforated plates was studied for fishing port tranqulity with number of plates, array method and plate intervals. Optimal design and arrangement of perforated plates can be applied to develop multipurpose fishing ports and villages.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2001.04a
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• pp.301-308
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• 2001

The problem of predicting crack propagation in anisotropic solids which is a subject of considerable practical importance is examined. The effect of the second term in the asymptotic expansion of the crack tip stress field on the direction of initial crack extension is made explicitly. We employ the normal stress ratio theory to determine values for the direction of initial crack extension. The theoretical analysis is performed for the wide range of the anisotropic material properties. It is shown that the use of second order term in the series expansion is essential for the accurate determination of crack growth direction in anisotropic solids.