• Journal of the Computational Structural Engineering Institute of Korea
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• v.29 no.3
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• pp.237-244
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• 2016

This paper presents a nonlinear Moving Least Squares(MLS) difference method for material nonlinearity problem. The MLS difference method, which employs strong formulation involving the fast derivative approximation, discretizes governing partial differential equation based on a node model. However, the conventional MLS difference method cannot explicitly handle constitutive equation since it solves solid mechanics problems by using the Navier's equation that unifies unknowns into one variable, displacement. In this study, a double derivative approximation is devised to treat the constitutive equation of inelastic material in the framework of strong formulation; in fact, it manipulates the first order derivative approximation two times. The equilibrium equation described by the divergence of stress tensor is directly discretized and is linearized by the Newton method; as a result, an iterative procedure is developed to find convergent solution. Stresses and internal variables are calculated and updated by the return mapping algorithm. Effectiveness and stability of the iterative procedure is improved by using algorithmic tangent modulus. The consistency of the double derivative approximation was shown by the reproducing property test. Also, accuracy and stability of the procedure were verified by analyzing inelastic beam under incremental tensile loading.

• The Optical Journal
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• v.12 no.5 s.69
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• pp.29-39
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• 2000

지난 호의 '1. 광학계의 형상설계'에 이어서, '2. 광학설계의 최적화 기법'을 게재한다. 이번 호에는 광학설계, 최적화의 수학적 기반인 비선형 연립방정식의 해에 대하여 살펴본 후에 광학설계에서 사용되고 있는 최적화 기법을 소개하고, 아울러 광학설계의 최적화 과정에서 발생하는 여러 문제점에 대해여 살펴본다.

• Transactions of the Korean Society of Mechanical Engineers
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• v.6 no.2
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• pp.176-182
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• 1982

이 논문에서는 평판의 배선형 해석에 대한 Berger의 방정식을 쉘좌표가 직교곡선좌표계로 표시 되는 Shallow 쉘에 대하여 일반화하여 운동방정식을 유도하였다. 해석의 예로서, 이 방정식을 사용하여 고정된 경계를 가진 원판과 Shallow 구쉘에 대한 배선형 진동문제를 해석하였으며, 정력학의 문제로서 원판이 동심원내에 균일하중을 받을때와 중심에 집중하중을 받을 때의 large deflection에 대하여 고찰하였고 나중문제에 대한 수치해를 구하였다.

• Proceedings of the Korean Society of Coastal and Ocean Engineers Conference
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• 2002.08a
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• pp.62-65
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• 2002

파랑은 주로 먼바다에서 바람에 의해 생성되어 육지로 전파해오면서 천수, 굴절, 회절, 반사, 부서 짐 등의 여러 가지 변형의 과정을 거친다. 이러한 파랑의 변형을 예측하는 한 방법은 비압축성 유체와 비회전류의 연속방정식인 Laplace 방정식을 지배 방정식으로 하고 해수면에서의 운동학적 경계조건과 동역학적 경계 조건, 그리고 바닥에서의 운동학적 경계조건을 적용하여 해를 구한다. (중략)

• Journal of the Korean Society of Safety
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• v.19 no.4 s.68
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• pp.155-160
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• 2004

A simply supported rectangular thin plate with temperature distribution varying over the thickness is analyzed. Since the thermal deflections are large compared to the plate thickness during bending and membrane stresses are developed md as such a nonlinear stress analysis is necessary. For the geometrically nonlinear, large deflection behavior of the plate, the classical von Karman equations are used. These equations are solved numerically by using the finite difference method. An iterative technique is employed to solve these quasi-linear algebraic equations. The results obtained from the suggested method are presented and discussed.

• Journal of KIISE:Computer Systems and Theory
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• v.32 no.9
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• pp.445-456
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• 2005

We propose a fast and accurate fluid solver of the Wavier-Stokes equations for the physics-based fluid simulations. Our method utilizes the solution of the Stokes equation as an initial guess for the velocity of the nonlinear term in the Wavier-Stokes equations. By guessing the initial velocity close to the exact solution of the given nonlinear differential equations, we can develop remarkably accurate and stable fluid solver. Our solver is based on the implicit scheme of finite difference methods, that makes it work well for large time steps. Since we employ the ADI method, our solver is also fast and has a uniform computation time. The experimental results show that our solver is excellent for fluids with high Reynolds numbers such as smoke and clouds.

• Journal of the Korean Institute of Telematics and Electronics
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• v.10 no.6
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• pp.45-55
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• 1973

This paper discusses the nonlinear time-invarient circuit composed of a tunnel diode. Prior to determine the solution of the nonlinear network which has negative resistance elements, the static characteristics of the nonlinear resistance elements need to be represented by function. Polynomial curve fitting is discussed to represent the static characteristies by least squares approximation. In order to solve the nonlinear network, the state equations for the networks are set up and solved by prediction corrector method. Finally, the limit cycle is plotted to discuss the stability of the nonlinear network and the oscillation condition.

• Proceedings of the KIEE Conference
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• 1999.11c
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• pp.564-566
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• 1999

계측 시스템이나 시스템 식별을 수행할 때 정확히 모델링 되는 플랜트를 가정할 경우, 입출력 신호간 혹은 상태 변수들 사이의 비선형 함수 관계를 유도해 낼 수 있다. 그런데 특히 비선형 함수가 매우 복잡하여 해를 닫힌 형태로 구할 수 없을 경우 고려하는 변수들 양자간의 수학적 모델링을 기반으로 루프내 변수가 방정식의 해로 수렴하는 대수 루프를 구성할 수 있다. 이는 모델을 정확히 아는 시스템에 대하여 출력으로부터 입력을 추정하는 역시스템(inverse system)을 구성하는 것과 유사하다. 이러한 개념을 응용한 간단한 예로 용량형 센서의 입출력 비선형성을 제거해주는 역시스템을 대수 루프를 통하여 구현하였다. 또한 구현한 루프가 항상 유일한 해로 수렴할 수 있도록 하는 조건을 구하였다. 해석된 결과를 바탕으로 구현된 루프가 컴퓨터 시뮬레이션 및 아날로그 회로 실험에서도 잘 동작함을 검증하였다. 시뮬레이션 결과로 보인 잡음에 대한 강인성과 실제 회로 실험 결과는 대수 루프의 구현이 실제 용량형 센서 등에 용이하게 적용될 수 있음을 보여준다.

• The Journal of the Acoustical Society of Korea
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• v.18 no.4
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• pp.71-77
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• 1999

Exact forward modeling of acoustic propagation is crucial in MFP such as inverse problems and various other acoustic applications. As acoustic propagation in shallow water environments become important, range dependent modeling has to be considered of which PE method is considered as one of the most accurate and relatively fast. In this paper higher order numerical rode employing the PE method is developed. To approximate the depth directional operator, Galerkin's method is used with partial collocation to lessen necessary calculations. Linearization of tile depth directional operator is achieved via expansion into a multiplication form of (equation omitted) approximation. To approximate the range directional equation, Crank-Nicolson's method is used. Final1y, numerical self stater is employed. Numerical tests are performed for various occan environment scenarios. The results of these tests are compared to exact solutions, OASES and RAM results.

• Geotechnical Engineering
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• v.13 no.3
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• pp.5-20
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• 1997

A governing equation of uncoupled three dimensional finite strain theory of consolidation is presented. This equation is suitable for relatively thick layers, possessing large strain, non-linear material property, and variable permeability. A special numerical solution procedure has to be adopted for the finite difference scheme because the solution is not stable in using Forward-Time Centered-Space (FTCS) method and the governing equation is highly non-linear. The solution is capable of predicting settlement with respect to time. The results predicted by the developed method of analysis have been compared with those of experimental tests on different types of highly compressible soils with vertical wick drain. The uncoupled three dimensional finite strain theory of consolidation appears to predict settlement behavior well. A detailed comparison shows good agreement in terms of total settlement, and reasonable agreement with respect to time.