• Ocean and Polar Research
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• 제23권2호
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• pp.161-172
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• 2001

A model-to-model comparison is attempted between Princeton Ocean Model (POM) and Miami Isopycnic Coordinate Ocean Model (MICOM) as a first step to extend our knowledge of models' performances in studying the East Sea circulation. The two models have fundamentally different numerical schemes and boundary conditions imposed on these models are not exactly the same each other. This study indicates that MICOM has a critical weak point in that it does not reproduce the shallow surface currents properly while it handles the thermohaline processes and associated movements of intermediate and deep waters efficiently. It is suggested that the mixed layer scheme needs to be modified so that it can match with inflow boundary conditions in order to reproduce the surface currents properly in MICOM. POM reproduces the surface current pattern better than MICOM, although the surface currents in POM appear to undergo the unrealistic seasonal variation and have exaggeratedly large vertical scale. These defects seem to arise during the process of adapting POM to the East Sea, and removing these defects is left as a future task.

• Structural Engineering and Mechanics
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• 제73권1호
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• pp.97-108
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• 2020

This study presents a 4 node, 11 DOF/node plate element based on higher order shear deformation theory for lamina composite plates. The theory accounts for parabolic distribution of the transverse shear strain through the thickness of the plate. Differential field equations of composite plates are obtained from energy methods using virtual work principle. Differential field equations of composite plates are obtained from energy methods using virtual work principle. These equations were transformed into the operator form and then transformed into functions with geometric and dynamic boundary conditions with the help of the Gâteaux differential method, after determining that they provide the potential condition. Boundary conditions were determined by performing variational operations. By using the mixed finite element method, plate element named HOPLT44 was developed. After coding in FORTRAN computer program, finite element matrices were transformed into system matrices and various analyzes were performed. The current results are verified with those results obtained in the previous work and the new results are presented in tables and graphs.

• 대한수학회논문집
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• 제30권3호
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• pp.297-311
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• 2015

We present a robust and accurate boundary condition for pricing financial options that is a hybrid combination of the payoff-consistent extrapolation and the Dirichlet boundary conditions. The payoff-consistent extrapolation is an extrapolation which is based on the payoff profile. We apply the new hybrid boundary condition to the multi-dimensional Black-Scholes equations with a high correlation. Correlation terms in mixed derivatives make it more difficult to get stable numerical solutions. However, the proposed new boundary treatments guarantee the stability of the numerical solution with high correlation. To verify the excellence of the new boundary condition, we have several numerical tests such as higher dimensional problem and exotic option with nonlinear payoff. The numerical results demonstrate the robustness and accuracy of the proposed numerical scheme.

• 호남수학학술지
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• 제38권3호
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• pp.661-674
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• 2016

In [15] they introduced a new finite element method for accurate numerical solutions of Poisson equations with corner singularities, which is useful for the problem with known stress intensity factor. They consider the Poisson equations with homogeneous Dirichlet boundary condition, compute the finite element solution using standard FEM and use the extraction formula to compute the stress intensity factor, then they pose a PDE with a regular solution by imposing the nonhomogeneous boundary condition using the computed stress intensity factor, which converges with optimal speed. From the solution we could get accurate solution just by adding the singular part. This approach works for the case when we have the accurate stress intensity factor. In this paper we consider Poisson equations with mixed boundary conditions and show the method depends the accrucy of the stress intensity factor by considering two algorithms.

• 대한기계학회논문집A
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• 제30권8호
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• pp.949-956
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• 2006

The method of Greenwood and Williamson is extended to obtain a solution to the coupled non-linear problem of steady-state electrical and thermal conduction across a crack in a conductive layer, for which the electrical resistivity and thermal conductivity are functions of temperature. The problem can be decomposed into the solution of a pair of non-linear algebraic equations involving boundary values and material properties. The new mixed-boundary value problem given from the thermal and electrical boundary conditions for the crack in the conductive layer is reduced in order to solve a singular integral equation of the first kind, the solution of which can be expressed in terms of the product of a series of the Chebyshev polynomials and their weight function. The non-existence of the solution for an infinite conductor in electrical and thermal conduction is shown. Numerical results are given showing the temperature field around the crack.

• Kyungpook Mathematical Journal
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• 제56권1호
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• pp.221-233
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• 2016

The present paper proposes a new monotone iteration method for existence as well as approximation of the coupled solutions for a coupled periodic boundary value problem of first order ordinary nonlinear differential equations. A new hybrid coupled fixed point theorem involving the Dhage iteration principle is proved in a partially ordered normed linear space and applied to the coupled periodic boundary value problems for proving the main existence and approximation results of this paper. An algorithm for the coupled solutions is developed and it is shown that the sequences of successive approximations defined in a certain way converge monotonically to the coupled solutions of the related differential equations under some suitable mixed hybrid conditions. A numerical example is also indicated to illustrate the abstract theory developed in the paper.

• International Journal of Naval Architecture and Ocean Engineering
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• 제13권1호
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• pp.526-544
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• 2021

Based on the potential flow theory, a fully nonlinear numerical procedure is developed with boundary element method to analyze the interaction between a fixed semi-submersible platform and incident waves in open water. The incident wave is separated from the scattered wave under fully nonlinear boundary conditions. The mixed Euler-Lagrangian method is used to capture the position of the disturbed wave surface in local coordinate systems. The wave forces exerted on an inverted conical frustum are used to ensure the accuracy of the present method and good agreements with published results are obtained. The hydrodynamic characteristics of the semi-submersible platform interacting with regular waves are analyzed. Pressure distribution with time and space, tension and compression of the platform under wave action are investigated. 3D behaviors of wave run-ups are predicted. Strong nonlinear phenomena such as wave upwelling and wave interference are observed and analyzed.

• Ocean Systems Engineering
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• 제1권4호
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• pp.355-372
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• 2011

Based on the fully nonlinear velocity potential theory, the liquid sloshing in a three dimensional tank under random excitation is studied. The governing Laplace equation with fully nonlinear boundary conditions on the moving free surface is solved using the indirect desingularized boundary integral equation method (DBIEM). The fourth-order predictor-corrector Adams-Bashforth-Moulton scheme (ABM4) and mixed Eulerian-Lagrangian (MEL) method are used for the time-stepping integration of the free surface boundary conditions. A smoothing scheme, B-spline curve, is applied to both the longitudinal and transverse directions of the tank to eliminate the possible saw-tooth instabilities. When the tank is undergoing one dimensional regular motion of small amplitude, the calculated results are found to be in very good agreement with linear analytical solution. In the simulation, the normal standing waves, travelling waves and bores are observed. The extensive calculation has been made for the tank undergoing specified random oscillation. The nonlinear effect of random sloshing wave is studied and the effect of peak frequency used for the generation of random oscillation is investigated. It is found that, even as the peak value of spectrum for oscillation becomes smaller, the maximum wave elevation on the side wall becomes bigger when the peak frequency is closer to the natural frequency.

• 대한기계학회논문집
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• 제7권2호
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• pp.145-152
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• 1983

An adhesively bonded anisotropic structure containing a part-through crack subjected to in-plane mixed mode deformations is investigated. The problem is reduced to a pair of Fredholm integral equations of the second kind by mathematical analysis. By solving these equations numerically stress intensity factors k$_{1}$ and k$_{2}$ are presented. Two cases are considered with respect to fiber orientations. Case one is to fix the fiber orientations of sound plate bonded to cracked plate with various fiber orientations. The other is to vary fiber orientations for both plates. As boundary conditions, tension and shear loading respectively, are applied to bonded anisotropic plates to observe mixed mode deformations.

• 대한기계학회논문집B
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• 제21권4호
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• pp.551-561
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• 1997

Mixed convection of air in a horizontal concentric cylindrical annulus is investigated numerically. Isothermal boundary conditions are prescribed at the inner and outer cylinders, with the inner cylinder being warmer. The forced flow is induced by the outer cylinder which is rotating slowly with constant angular velocity with its axis at the center of the annulus. The effect of the forced flow on the flow pattern and heat transfer of natural convection is investigated for the annulus of (inner-cylinder radius/gap width) = 1. There appear two eddies, one eddy or no eddy according to the Rayleigh and Reynolds numbers. Map of the three flow regimes is constructed on the Ra-Re plane. (author). 28 refs., 9 figs., 2 tabs.