• Journal of applied mathematics & informatics
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• 제15권1_2호
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• pp.29-51
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• 2004

In this paper, we propose a new mixed finite element method, called the characteristics-mixed method, for approximating the solution to Burgers' equation. This method is based upon a space-time variational form of Burgers' equation. The hyperbolic part of the equation is approximated along the characteristics in time and the diffusion part is approximated by a mixed finite element method of lowest order. The scheme is locally conservative since fluid is transported along the approximate characteristics on the discrete level and the test function can be piecewise constant. Our analysis show the new method approximate the scalar unknown and the vector flux optimally and simultaneously. We also show this scheme has much smaller time-truncation errors than those of standard methods. Numerical example is presented to show that the new scheme is easily implemented, shocks and boundary layers are handled with almost no oscillations. One of the contributions of the paper is to show how the optimal error estimates in $L^2(\Omega)$ are obtained which are much more difficult than in the standard finite element methods. These results seem to be new in the literature of finite element methods.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제6권1호
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• pp.1-15
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• 2002

Advection-dominated transport problems possess difficulties in the design of numerical methods for solving them. Because of the hyperbolic nature of advective transport, many characteristic numerical methods have been developed such as the classical characteristic method, the Eulerian-Lagrangian method, the transport diffusion method, the modified method of characteristics, the operator splitting method, the Eulerian-Lagrangian localized adjoint method, the characteristic mixed method, and the Eulerian-Lagrangian mixed discontinuous method. In this paper relationships among these characteristic methods are examined. In particular, we show that these sometimes diverse methods can be given a unified formulation. This paper focuses on characteristic finite element methods. Similar examination can be presented for characteristic finite difference methods.

• 한국분무공학회지
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• 제27권1호
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• pp.36-41
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• 2022

In this study, the combustion instability characteristics according to the change in the hydrogen ratio in the fuel in the single nozzle system of the hydrogen-natural gas mixed gas turbine for power generation was analyzed using a three-dimensional finite element analysis-based Helmholtz solver. This combustor shows the instability characteristics in which mode transition occurs from a mode having a low amplitude near 70 Hz to a mode having a high amplitude of 250 Hz or higher as the hydrogen fraction in the fuel increases. The current modeling results are found to reasonably predict the main characteristics of the change in measured instability frequency and growth rate with the change in fuel composition.

• 한국정밀공학회:학술대회논문집
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• 한국정밀공학회 1993년도 추계학술대회 논문집
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• pp.644-649
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• 1993

Practical structures are subject not only to tension but also to shear and torsional loading. In this study, the mode 1 and 2 stress intensity factors of specimens were calculated by using elastic finite element mothod. The stress fields at the crack tip subjected to mixed-mode loading were also studied by usingf eleatic finite element method and were compared with theoretical results. The three-point-bending, four-point-bending, and mixed-mode-loading experiment were carried out. And, crack propagation rate da/dN and crack growth direction were examined. Also, the elastic finite element method was applied to calculate the stress intensity factors of branch crack tip and we relate the stress intenity factor range of branch crack tip(the result of FEM) to crack propagation rate(the experimental result). The .DELTA. -da/dN relation corelated with that of mode 1.

• 한국전산구조공학회논문집
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• 제12권3호
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• pp.363-370
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• 1999

본 연구에서는 철근콘크리트기둥과 철골보로 이루어진 혼합구조 접합부의 해석에 대한 유한 유소법을 이용한 해석 모델 방법을 제시하였다. 혼합구조 접합부에서 콘크리트와 강판이 접하는 접촉면은 두 접촉면 사이를 부착과 마찰의 개념으로 표현할 수 있는 주-종속 접촉 알고리즘(master-slave contact algorithm)을 이용하여 모델링하였다. 그리고, 휨응력의 지배를 받는 강관에는 비적합 모드 요소를 사용하였다. 본 연구에서의 혼합구조 특징은 보에서 기둥으로 힘의 전달을 원활히 하기 위하여 다이아프램이 사용되었고, 이러한 혼합구조 접합부 모델링 방법에 대한 타당성을 알아보기 위하여 3차원 비선형 해석을 행하여 실험결과와 비교한 결과 잘 일치하는 결과를 얻었다.

• Computers and Concrete
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• 제3권5호
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• pp.285-299
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• 2006

The free vibration of stiffened and damaged coupled shear walls is investigated using the mixed finite element method. The anisotropic damage model is adopted to describe the damage extent of the reinforced concrete shear wall element. The internal energy of a locally damaged shear wall element is derived. Polynomial shape functions established by Kwan are used to present the component of displacements vector on each point within the wall element. The principle of virtual work is employed to deduce the stiffness matrix of a damaged shear wall element. The stiffened system is reinforced by an additional stiffening beam at some level of the structure. This induces additional axial forces, and thus reduces the bending moments in the walls and the lateral deflection, and increases the natural frequencies. The effects of the damage extent and the stiffening beam on the free vibration characteristics of the structure are studied. The optimal location of the stiffening beam for increasing as far as possible the first natural frequency of vibration is presented.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제14권3호
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• pp.189-200
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• 2010

A numerical method is proposed and analyzed to approximate a mathematical model of age-dependent population dynamics with spatial diffusion. The model takes a form of nonlinear and nonlocal system of integro-differential equations. A finite difference method along the characteristic age-time direction is considered and primal mixed finite elements are used in the spatial variable. A priori error estimates are derived for the relevant variables.

• 대한기계학회논문집B
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• 제27권9호
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• pp.1327-1334
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• 2003

Flow characteristics of the fluid laden with many particles in the two-dimensional channel are investigated using the Navier-Stokes equations coupled with the equation of motion of particles by direct numerical simulation. A four-step fractional step method with Crank-Nicolson scheme and ALE technique is used for P2P1 mixed finite element method. The motion and distribution of particles in the fluid is virtually described as a result of direct numerical simulation and the increase of viscosity is compared with theoretical equations. The effect of channel height on the relative viscosity and the tubular pinch effect are discussed.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제23권4호
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• pp.367-380
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• 2019

A 1kW-class horizontal axis wind turbine (HAWT) rotor blade is taken into account to investigate elastic characteristics in 2-D. The elastic blade field is composed of symmetric cross-ply laminated composite material. Blade element momentum theory is applied to obtain the boundary conditions pressuring the blade, and the plane stress elasticity problem is formulated in terms of two displacement parameters with mixed boundary conditions. For the elastic characteristics a fair of differential equations are derived based on the elastic theory. The domain is divided by triangular and rectangular elements due to the complexity of the blade configuration, and a finite element method is developed for the governing equations to search approximate solutions. The results describe that the elastic behavior is deeply influenced by the layered angle of the middle laminate and the stability of the blade can be improved by controlling the layered angle of laminates, which can be evaluated by the mathematical approach.

• 대한전기학회:학술대회논문집
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• 대한전기학회 1998년도 하계학술대회 논문집 A
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• pp.70-72
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• 1998

This paper discusses the development of a new optimization algorithm for DC motor design. In principle, the new algorithm utilizes a mixed method that consists of genetic algorithms in conjunction with direct search method. The genetic algorithms are used for locating the global optimum region while the direct search method is used to achieve objective function convergence. In order to validate the effectiveness, the new algorithm has been applied to an actual DC motor. Field and torque characteristics of the DC motor are computed using finite element method and the principle of virtual work, respectively.