• 한국진공학회지
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• 제12권S1호
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• pp.33-35
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• 2003

The electrooptic properties of the reflected light in a reflective mode, $45^{\circ}C$twisted nematic liquid crystal (TNLC) cell were investigated in the voltage regions near and away from the Freedericksz transition threshold. The measured reflectivity away from the threshold voltage ($V_th$) could not be described by the model which assurnes a constant tilt angle as well as a linearized distribution of twist angle across the cell, although the data are well fitted near $V_th$. We found that in the voltage region away from $V_th$, the model considering the distributions of the tilt angle and the twist angle should be applied for the calculation of the reflectivity. The director-axis distributions were obtained from the numerical integration of the Euler-Lagrange equation.

• 대한수학회보
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• 제47권1호
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• pp.29-37
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• 2010

We establish the existence of weak solutions in an infinite subsonic channel in the self-similar plane to the two-dimensional Burgers system. We consider a boundary value problem in a fixed domain such that a part of the domain is degenerate, and the system becomes a second order elliptic equation in the channel. The problem is motivated by the study of the weak shock reflection problem and 2-D Riemann problems. The two-dimensional Burgers system is obtained through an asymptotic reduction of the 2-D full Euler equations to study weak shock reflection by a ramp.

• 한국전산유체공학회:학술대회논문집
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• 한국전산유체공학회 1997년도 추계 학술대회논문집
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• pp.29-37
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• 1997

An implicit viscous turbulent flow solver is developed for two-dimensional geometries on unstructured triangular meshes. The flux terms are discretized based on a cell-centered finite-volume formulation with the Roe's flux-difference splitting. The solution is advanced in time using an implicit backward-Euler time-stepping scheme. At each time step, the linear system of equations is approximately solved with the Gauss-Seidel relaxation scheme. The effect of turbulence effects is approximated with a standard $k-{\varepsilon}$ two-equation model which is solved separately from the mean flow equations using the same backward-Euler time integration scheme. The triangular meshes are generated using an advancing-front/layer technique. Validations are made for flows over the NACA0012 airfoil and the Douglas 3-element airfoil. Good agreements are obtained between the numerical results and the experiment.

• 에너지공학
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• 제6권1호
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• pp.52-57
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• 1997

유동방향으로 초원형 형상을 갖는 잘록한 관내의 압축성 유동에 관한 동특성을 수치적으로 연구하였다. MacCormack의 양해법, 즉 예측자/보정자 단계를 거친 시간 진행법을 이용하여 Euler 방정식의 해를 구하였는데, 관내 유동은 이차원, 비점성, 압축성 유동이라 가정하였다. 관의 직경비와 형상비가 압력분포에 미치는 영향을 광범위하게 고찰하였으며, 본 연구에서 개발한 전산프로그램을 이용한 수치 결과는 상용코드인 FLUENT를 이용한 결과와 비교하여 일치된 결과를 얻을 수 있었다.

• 한국소음진동공학회:학술대회논문집
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• 한국소음진동공학회 2013년도 춘계학술대회 논문집
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• pp.188-193
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• 2013

The large mass method for dynamic analysis of statically determinate beams subjected to in-phase support motions is justified by showing that the equation of motion of the beams under consideration is equivalent to that of large mass model of the beam when an appropriate large mass ratio is employed. The accuracy of the stress responses based on the beam large mass method is investigated through careful numerical tests. The numerical results are compared to analytic solutions and the comparison shows that the large mass method yields not only the time history of motion but also the distributions of bending moment and shear force accurately.

• 한국전산구조공학회:학술대회논문집
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• 한국전산구조공학회 2000년도 가을 학술발표회논문집
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• pp.201-208
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• 2000

This paper explores the non-linear behavior of tapered beam subjected to a floating concentrated load. For applying the Bernoulli-Euler beam theory to this beam, the bending moment at any point of elastica is obtained from the final equilibrium state. By using the bending moment equation and the Bernoulli-Euler beam theory, the differential equations governing the elastica of clamped-roller beam are derived, and solved numerically. Three kinds of tapered beam types are considered. The numerical results of the non-linear behavior obtained in this study are agreed quite well to the results obtained from the laboratory-scale experiments.

• 대한기계학회논문집A
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• 제31권2호
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• pp.231-236
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• 2007

This paper presents the effect of the center of the series on convergence in solving vibration problems by Differential Transformation Method(DTM) to the transverse vibration of the Euler-Bernoulli beam under varying axial force. The governing differential equation of the transverse vibration of the Euler-Bernoulli beam under varying axial force is derived. The concepts of DTM were briefly introduced. Numerical calculations are carried out and compared with previously published results. The effect of the center of the series on convergence in solving the problem by DTM is discussed.

• Steel and Composite Structures
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• 제32권5호
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• pp.643-655
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• 2019

Perforation and cutouts of structures are compulsory in some modern applications such as in heat exchangers, nuclear power plants, filtration and microeletromicanical system (MEMS). This perforation complicates dynamic analyses of these structures. Thus, this work tends to introduce semi-analytical model capable of investigating the dynamic performance of perforated beam structure under free and forced conditions, for the first time. Closed forms for the equivalent geometrical and material characteristics of the regular square perforated beam regular square, are presented. The governing dynamical equation of motion is derived based on Euler-Bernoulli kinematic displacement. Closed forms for resonant frequencies, corresponding Eigen-mode functions and forced vibration time responses are derived. The proposed analytical procedure is proved and compared with both analytical and numerical analyses and good agreement is noticed. Parametric studies are conducted to illustrate effects of filling ratio and the number of holes on the free vibration characteristic, and forced vibration response of perforated beams. The obtained results are supportive in mechanical design of large devices and small systems (MEMS) based on perforated structure.

• Journal of applied mathematics & informatics
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• 제39권5_6호
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• pp.655-676
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• 2021

A parameter uniform numerical scheme is proposed for solving singularly perturbed parabolic partial differential-difference convection-diffusion equations with a small delay and advance parameters in reaction terms and spatial variable. Taylor's series expansion is applied to approximate problems with the delay and advance terms. The resulting singularly perturbed parabolic convection-diffusion equation is solved by utilizing the implicit Euler method for the temporal discretization and finite difference method for the spatial discretization on a uniform mesh. The proposed numerical scheme is shown to be an ε-uniformly convergent accurate of the first order in time and second-order in space directions. The efficiency of the scheme is proved by some numerical experiments and by comparing the results with other results. It has been found that the proposed numerical scheme gives a more accurate approximate solution than some available numerical methods in the literature.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제19권2호
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• pp.197-215
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• 2015

Modeling water flow in variably saturated, porous media is important in many branches of science and engineering. Highly nonlinear relationships between water content and hydraulic conductivity and soil-water pressure result in very steep wetting fronts causing numerical problems. These include poor efficiency when modeling water infiltration into very dry porous media, and numerical oscillation near a steep wetting front. A one-dimensional finite element formulation is developed for the numerical simulation of variably saturated flow systems. First order backward Euler implicit and second order Crank-Nicolson time discretization schemes are adopted as a solution strategy in this formulation based on Picard and Newton iterative techniques. Five examples are used to investigate the numerical performance of two approaches and the different factors are highlighted that can affect their convergence and efficiency. The first test case deals with sharp moisture front that infiltrates into the soil column. It shows the capability of providing a mass-conservative behavior. Saturated conditions are not developed in the second test case. Involving of dry initial condition and steep wetting front are the main numerical complexity of the third test example. Fourth test case is a rapid infiltration of water from the surface, followed by a period of redistribution of the water due to the dynamic boundary condition. The last one-dimensional test case involves flow into a layered soil with variable initial conditions. The numerical results indicate that the Crank-Nicolson scheme is inefficient compared to fully implicit backward Euler scheme for the layered soil problem but offers same accuracy for the other homogeneous soil cases.