• Journal of Korean Society of Coastal and Ocean Engineers
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• v.10 no.4
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• pp.197-203
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• 1998

An approach of decomposing the reflecting components is proposed by using the mild-slope equation of hyperbolic type which has the similar form to the shallow water equations. The approach is verified on Booij's problem and sinusoidally varying ripples. Inclusion of higher-order bottom effect given by chamberlain and Porter(1995) yields even more satisfactory results than the Berkhoff's mild-slope equation when compared with finite element solution or experiments.

• Journal of Energy Engineering
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• v.8 no.4
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• pp.540-545
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• 1999

The classical Fourier heat conduction equation is invalid at temperatures near absolute zero or at very early times in highly transient heat transfer processes. In such situations, a hyperbolic equation model for heat conduction based on the modified Fourier law is introduced because the wave nature of heat propagation becomes dominant. The Fourier model and the hyperbolic model for heat conduction are analyzed by using the Green's function technique together with the integral transform. Analytical expressions for the heat flux and temperature distributions in a finite slab subjected to a periodic surface heating at one of its surfaces are presented and the results obtained from each model are compared with each other. The thermal wave implied b the hyperbolic model is shown to travel through a medium and to reflect back toward the origin at the other insulated surface. On the other hand, the heat by the Fourier model propagates at an infinite speed instantaneously after a thermal disturbance is felt throughout the medium.

• Journal of Korean Society of Coastal and Ocean Engineers
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• v.10 no.3
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• pp.125-131
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• 1998

The paper deals with the application of Boundary-Fitted Coordinate System (BFCS) to the two wave models of parabolic and hyperbolic types developed on a rectangular grid system. Since the BFCS conforms the boundaries of the region in such wary that boundary conditions or calculation process can be accurately represented, improvement in predicting the wave fields can be achieved. The numerical results show a good agreement with the analytical results for either waves propagating or reflecting along a circular channel of constant depth. Simulation of reflecting waves in a parabolic wave model is accomplished by the backward calculation as if waves approached at the cross wall take a turn in the opposite direction and propagate against a channel.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.43 no.4
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• pp.469-476
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• 2023

Soil plasticity models for cyclic and dynamic loads are essential in non-linear numerical analysis of geotechnical structures. While a single yield surface model shows a linear behavior for cyclic loads, J₂-bounding surface plasticity model with zero elastic region can effectively simulate a nonlinearity of the ground response with the same material properties. The radius of the yield surface inside the boundary surface converged to 0 to make the elastic region disappear, and plastic hardening modulus and dilatancy define plastic strain increment. This paper presents the stress-strain incremental equation of the developed model, and derives plastic hardening modulus for the hyperbolic model. The comparative analyses of the triaxial compression test and the shallow foundation under the cyclic load can show stable numerical convergence, consistency with the theoretical solution, and hysteresis behavior. In addition, plastic hardening modulus for the modified hyperbolic function is presented, and a methodology to estimate model variables conforming 1D equivalent linear model is proposed for numerical modeling of the multi-dimensional behavior of the ground.

• Journal of Korean Society of Coastal and Ocean Engineers
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• v.6 no.3
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• pp.281-289
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• 1994

An equation set of nonlinear model for regular/irregular waves presented in this study can be applied to waves travelling from deep water to shallow water, which is different from the Boussinesq equations. The presented equations completely satisfy the linear dispersion relationship and when expanded, they are proven to be consistent with the Boussinesq equation of several types. In addition, the position of averaged velocity below the still water level is estimated based on the linear wave theory.

• Proceedings of the Korean Society of Coastal and Ocean Engineers Conference
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• 2003.08a
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• pp.63-70
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• 2003

Berkhoff(1972)는 해저 경사가 완만한 지형에서의 파랑 변형을 계산하는 완경사 방정식을 제안하였다. 이 방정식은 수식이 매우 간단하면서도 비교적 정확하게 파랑을 예측할 수 있어 현재까지도 해안공학 전반에 걸쳐 많이 적용되고 있다. 그러나 Berkhoff(1972)의 완경사 방정식은 계산이 비교적 번거로워 현재는 계산하기 편리한 포물형 완경사 방정식(Radder,1979) 또는 쌍곡선형 완경사 방정식(Copeland,1985) 등의 근사 모델을 사용하고 있다. 하지만, 이러한 근사모델은 지배방정식을 유도할 때 생기는 가정들에 의해 실제현장 적용성과 해의 정확성에는 언제나 일정한 한계가 있다. (중략)

• Journal of the Korea Academia-Industrial cooperation Society
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• v.1 no.1
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• pp.15-22
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• 2000

There are lots of industrial machines of which functions are achieved by operation of multi-phase fluids. Some of them take advantage of the characteristics of counter-current two-phase flow The maximum flow rates of gas and liquid phases which flow in opposite-directions (counter-current flow) are limited by a phenomenon known as a Counter-Current Flow Limitation (CCFL or Flooding) The mass and momentum conservation equations for each Phase were established to build a first-order hyperbolic partial derivative equations system. A new CCFL model is developed based on the characteristic equation of the hyperbolic PDE system. The present model has its applicationto the case in which a non-uniform flow is developed around a square or sharp-edged entrance of liquid phase. The model is able to he used to Predict the operating-limit of components in which mass and heat transfer are taking place between liquid and gas phases.

• Journal of the Korean GEO-environmental Society
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• v.3 no.3
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• pp.53-63
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• 2002

Until recently the other attempts except linear elastic analysis using assumed elastic modulus had not been made in order to evaluate the settlement of the rock fill materials in Korea. Especially, it was almost impossible to predict the precise settlement of the breakwater structure made with dumped rubble stone. In this study, 3 sets of large scaled triaxial compression tests for porous basaltic quarry rocks were carried out and numerical simulation of those triaxial compression tests were performed applying non linear elastic model. Two stress-strain behaviors were compared to study the adaptability of hyperbolic constitutive model for the rubble stone. The results showed quite good agreements between the two stress-strain behaviors. Thus, the hyperbolic constitutive model is thought to be alternative approach evaluate the settlements of the loose rock-fill material.

• Journal of Power System Engineering
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• v.4 no.4
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• pp.16-24
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• 2000

고체내의 열에너지의 전달을 분석하기 위하여 고전적인 Fourier 열전도 법칙과 에너지 보존식에서 유도되는 열전도 방정식을 사용해 왔다. 이러한 열전도 방정식은 열전도가 무한한 속도로 진행된다는 것을 의미하고 있다. 그러나 극저온상태에서나 매우 급속한 열전도과정 중 매우 짧은 시간의 상태에서 non-Fourier 모델에 기초를 둔 쌍곡선형 열전도 방정식이 도입되었다. 최근의 이에 관한 연구에서 열전도가 파장의 형태로 유한한 전파속도를 갖는다는 것이 실험적으로 증명되었고 이로부터 여러 가지 실험적인 해석과 이론 해석이 전개되었다. 본 논문에서는 열전파 속도의 유한한 성질을 나타내는 수정된 열전도 법칙을 이용하여 1차원 평판에 대하여 공간에 대한 finite Fourier 변환 방법과 Green 함수 방법으로 해석하여 열전도파의 파동 성질, 공진 현상 및 위상차를 고찰하고자 한다. 열전도파가 갖는 모달 주파수에 대해 임계값을 갖으며 이 임계값을 초과할 때 공진 현상과 위상차를 고찰할 수 있었다.

• Journal of the Korean GEO-environmental Society
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• v.19 no.12
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• pp.47-58
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• 2018

Duncan & Chang(1970) proposed the Duncan-Chang model that a linear relation of transformed stress-strain plots was reconstituted from a nonlinear relation of stress-strain curve of triaxial compression test using hyperbolic theory so as to estimate an initial tangent modulus and ultimate deviator stress for the soil specimen. Although the transformed stress-strain plots show a linear relationship theoretically, they actually show a nonlinearity at both low and high values of strain of the test. This phenomenon indicates that the stress-strain curve is not a complete form of a hyperbola. So, if linear regression analyses for the transformed stress-strain plot are performed over a full range of strain of a test, error in the estimation of their linear equations is unavoidable depending on ranges of strain with non-linearity. In order to reduce such an error, a modified regression analysis method is proposed in this study, in which linear regression analyses for transformed stress-strain plots are performed over the entire range of strain except the range the non-linearity is shown around starting and ending of the test, and then the initial tangent modulus and ultimate deviator stresses are calculated. Isotropically consolidated-drained triaxial compression tests were performed on compacted weathered soil with a modified Proctor density to obtain their model parameters. The modified regression analyses for transformed stress-strain plots were performed and analyzed results are compared with results estimated by 2 points method (Duncan et al., 1980). As a result of analyses, initial tangent moduli are about 4.0% higher and ultimate deviator stresses are about 2.9% lower than those values estimated by Duncan's 2 points method.