• 한국정밀공학회지
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• 제23권11호
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• pp.93-102
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• 2006

In this study an advanced domain decomposition method is suggested in order to construct surface models from very large amount of points. In this method the spatial domain of interest that is occupied by the input set of points is divided in repetitive manner. First, the space is divided into smaller domains where the problem can be solved independently. Then each subdomain is again divided into much smaller domains where the problem can be solved locally. These local solutions of subdivided domains are blended together to obtain a solution of each subdomain using partition of unity function. Then the solutions of subdomains are merged together in order to construct whole surface model. The suggested methods are conceptually very simple and easy to implement. Since RDDM(Repetitive Domain Decomposition Method) is effective in the computation time and memory consumption, the present study is capable of providing a fast and accurate reconstructions of complex shapes from large amount of point data containing millions of points. The effectiveness and validity of the suggested methods are demonstrated by performing numerical experiments for the various types of point data.

• 한국항공우주학회지
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• 제31권5호
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• pp.55-62
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• 2003

복합재료 구조물의 동적 접촉 문제를 효율적으로 해석하기 위하여 부영역과 공유면에 기반을 둔 변분 정식화 과정을 제안하였다. 벌칙 함수법을 이용하여 접촉면에서의 부등식 구속 조건은 물론, 유한요소 부영역과 공유면의 연결을 위한 등식 적합 조건까지 만족하게 하였다. 이에 따라 구조 형상이 복잡한 경우라도 공유면에서의 절점 연속성을 별도로 고려하지 않고 전체 영역긍 분할한 후, 분할된 부영역별로 독립적인 유한요소로 모델링하여 필요한 수치 연산을 수행할 수 있다. 개발된 컴퓨터 코드를 이용한 수치 해석을 통하여 제안된 정식화에 대한 여러 특성을 고찰하였다.

• Journal of Electrical Engineering and Technology
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• 제10권4호
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• pp.1674-1681
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• 2015

This paper presented an improved analytical method for calculating armature-reaction field in the surface-mounted permanent magnet machines accounting for opening slots. The analytical model is divided into two types of subdomains. The current of the armature is centralized in the center of the slots. The field solution of each subdomain is obtained by applying the interface and boundary conditions of the model. Two 30-pole/36-slot prototype machines with different slot-opening width are used for validation. The FE (finite element) results confirm the validity of the analytical results with the proposed model. The investigation shows that the wider the slot-opening width is, the smaller the peak value of radial and circumferential components of flux density, and the analytical armature-reaction field produced by centralized current in the slots is similar with the armature-reaction field produced by distributed current in the slots in the FE.

• 대한조선학회논문집
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• 제30권3호
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• pp.29-40
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• 1993

본 연구는 정수면으로 부터 얕게 잠겨 항주하는 3차원 수중익에 의한 비선형 조파현상의 특성규명을 위한 기초연구로서 수중익이 예인수조안에서 일정속도로 항주할 때 자유표면에 발생하는 비선형 파형의 특성과 수중익에 작용하는 유체력을 계산하기 위한 수치해법의 개발을 목적으로 하였다. 수치해법으로는 변분원리에 기초한 유한요소법올 사용하였으며 수중익 근처에서는 비선형 자유표면조건을 엄밀하게 만족시켰고 수중익으로 부터 충분히 떨어진 영역에서는 종래의 선형화된 자유표면 경계조건을 만족시켰다. 수치해법의 계산효율을 높이기 위하여 비선형영역과 선형영역 사이에 인위적인 비선형-선형 완충영역을 도입하여 계산영역을 크게 줄였다. 수중익을 간단한 직사각형 보오텍스계로 표현하여 유속과 몰수길이, 보오텍스의 세기 및 분포의 변화에 따른 비선형 파형의 특성을 조사하였으며 특히 자유 보오텍스선이 비선형 파형에 미치는 영향을 파악하였다. 파동에 의하며 수중익에 유기되는 속도성분들의 크기 및 분포, 양력 및 유기항력에 대한 계산을 수행하여 자유표면의 비선형성에 의한 영향을 규명하였다.

• Korean Journal of Mathematics
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• 제31권4호
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• pp.419-431
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• 2023

In this paper, we propose an iterative method for a symmetric interior penalty Galerkin method for heterogeneous elliptic problems. The iterative method consists mainly of two parts based on a non-overlapping domain decomposition approach. One is an intermediate preconditioner constructed by understanding the properties of the discontinuous finite element functions and the other is a preconditioning related to the dual-primal finite element tearing and interconnecting (FETI-DP) methodology. Numerical results for the proposed method are presented, which demonstrate the performance of the iterative method in terms of various parameters associated with the elliptic model problem, the finite element discretization, and non-overlapping subdomain decomposition.

• 대한조선학회논문집
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• 제43권6호
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• pp.683-692
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• 2006

The BEM, known as solving boundary value problems, could have some advantages In solving domain problems which are mostly solved by FEM and FDM. Lately, in the elastic-plastic nonlinear problems, BEM could provide the subdomain approach for the region where the plastic deformation could occur and the unknown nodal displacement of this region are added as the unknown of the boundary integral equation for this approach. In this paper, initial stress method was used to establish the formulation of such BEM approach. And a simple rectangular plate having a circular hole was analyzed to verify the suggested method and the result is compared with that from FEM. It is shown that the result of two methods are showing similar stress-strain curves at the root of perforated plate and furthermore the plastic deformation obtained by BEM shows more reasonable behavior than that of FEM.

• International Journal of CAD/CAM
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• 제11권1호
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• pp.11-17
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• 2011

A new method has been developed in this paper for automatic quadrilateral mesh generation for a two-dimensional domain. The method is named 'centering method' because it centers a point at the domain and then divides it into sub-domains using cutting lines from the center point. Each of the cutting lines is selected based on the criterion using the angles between the boundary of the domain and the cutting line. The decomposition of the domain into sub-domains is repeated until every subdomain has four or six nodes. Pre-defined splitters are used to divide six-node domains into quadrilateral elements depending on their configuration and presence on the boundary of the initial domain. Arbitrary domains are meshed as examples to verify the robustness of the new method.

• 대한조선학회지
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• 제19권4호
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• pp.19-29
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• 1982

Galerkin's finite element method is applied to a two-dimensional heat convection-diffusion problem arising in the hydrodynamic lubrication of thrust bearings used in naval vessels. A parabolized thermal energy equation for the lubricant, and thermal diffusion equations for both bearing pad and the collar are treated together, with proper juncture conditions on the interface boundaries. it has been known that a numerical instability arises when the classical Galerkin's method, which is equivalent to a centered difference approximation, is applied to a parabolic-type partial differential equation. Probably the simplest remedy for this instability is to use a one-sided finite difference formula for the first derivative term in the finite difference method. However, in the present coupled heat convection-diffusion problem in which the governing equation is parabolized in a subdomain(Lubricant), uniformly stable numerical solutions for a wide range of the Peclet number are obtained in the numerical test based on Galerkin's classical finite element method. In the present numerical convergence errors in several error norms are presented in the first model problem. Additional numerical results for a more realistic bearing lubrication problem are presented for a second numerical model.

• Structural Engineering and Mechanics
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• 제81권5호
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• pp.607-616
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• 2022

In this work, the free vibration problem of a rotating Rayleigh beam is solved using the meshless Petrov-Galerkin method which is a truly meshless method. The Rayleigh beam includes rotatory inertia in addition to Euler-Bernoulli beam theory. The radial basis functions, which satisfy the Kronecker delta property, are used for the interpolation. The essential boundary conditions can be easily applied with radial basis functions. The results are obtained using six nodes within a subdomain. The results accurately match with the published literature. Also, the results with Euler-Bernoulli are obtained to compare the change in higher natural frequencies with change in the slenderness ratio (${\sqrt{A_0R^2/I_0}}$). The mass and stiffness matrices are derived where we get two stiffness matrices for the node and boundary respectively. The non-dimensional form is discussed as well.

• 한국소성가공학회:학술대회논문집
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• 한국소성가공학회 1999년도 압출 및 인발 심포지엄
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• pp.5-8
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• 1999

The present work is concerned with three-dimensional finite element analysis of the hollow section extrusion process using a porthole die. For economic computation, mismatching refinement, an efficient domain decomposition method with different mesh density for each subdomain, is implemented. The proposed method improves the computational efficiency significantly, especially fur the three-dimensional analysis of extrusion problems. As a numerical example, extrusion of the underframe part of a railroad vehicle are analyzed. For three-dimensional mesh generation of a complicated shape with hexahedral elements, a modified grid-based approach with the surface element layer is utilized. The analysis results are then successfully reflected on the industrial porthole die design.