• 대한기계학회논문집
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• 제11권6호
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• pp.1001-1004
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• 1987

본 연구에서는 우선 선형 탄성문제의 변분해(variational solution)가 Sobol- ev 공간[ $H^{1}$(.OMEGA.)]= $H^{1}$(.OMEGA.)* $H^{1}$(.OMEGA.)* $H^{1}$(.OMEGA.)에서 유일하게 존재함을 재 검토하고 다음으로 경계적분식의 해도 변분해와 같음을 보인다. 이것은 선형 탄 성문제의 경우 고전해(classical solution)가 존재하지 않을 경우에도 BEM을 사용하여 변분해의 수치적 근사치를 구할 수 있다는 수학적 근거가 된다. 이를 위해서 Sobol- ev 공간 내에서의 Green's formula를 적용하는데 점하중해의 특이점(singularity)때문 에 Green's formula를 적용하기가 곤란해진다. 이 문제는 적분영역 .OMEGA.를 .OMEGA.-Ｂ$_{\rho }$로 치환하고 .rho.를 0으로 접근시키는 방법으로 해결한다. 이 때 Ｂ$_{\rho}$는 특이 점에 중심을 두고 매우 작은 변경 .rho.를 갖는 구이다.ho.를 갖는 구이다.

• 대한기계학회논문집B
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• 제23권2호
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• pp.243-253
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• 1999

The dual reciprocity boundary element method (DRBEM) is used to solve the Graetz problem of laminar flow inside circular duct. In this method the domain integral tenn of boundary integral equation resulting from source term of governing equation is transformed into equivalent boundary-only integrals by using the radial basis interpolation function, and therefore complicate domain discretization procedure Is completely removed. Velocity profile is obtained by solving the momentum equation first and then, using this velocities as Input data, energy equation Is solved to get the temperature profile by advancing from duct entrance through the axial direction marching scheme. DRBEM solution is tested for the uniform temperature and heat flux boundary condition cases. Local Nusselt number, mixed mean temperature and temperature profile inside duct at each dimensionless axial location are obtained and compared with exact solutions for the accuracy test Solutions arc in good agreement at the entry region as well as fully developed region of circular duct, and their accuracy are verified from error analysis.

• Structural Engineering and Mechanics
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• 제32권3호
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• pp.407-427
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• 2009

A fundamental solution for the transient, quasi-static, plane problems of linear viscoelasticity is introduced for a specific material. An integral equation has been found for any problem as a result of dynamic reciprocal identity which is written between this fundamental solution and the problem to be solved. The formulation is valid for the first, second and mixed boundary-value problems. This integral equation has been solved by BEM and algorithm of the BEM solution is explained on a sample, mixed boundary-value problem. The forms of time-displacement curves coincide with literature while time-surface traction curves being quite different in the results. The formulation does not have any singularity. Generalized functions and the integrals of them are used in a different form.

• 소음진동
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• 제7권6호
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• pp.975-984
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• 1997

A direct boundary element method (DBEM) is developed for thin bodies whose surfaces are rigid or compliant. The Helmholtz integral equation and its normal derivative integral equation are adoped simultaneously to calculate the pressure on both sides of the thin body, instead of the jump values across it, to account for the different surface conditions of each side. Unlike the usual assumption, the normal velocity is assumed to be discontinuous across the thin body. In this approach, only the neutral surface of the thin body has to be discretized. The method is validated by comparison with analytic and/or numerical results for acoustic scattering and radiation from several surface conditions of the thin body; the surfaces are rigid when stationary or vibrating, and part of the interior surface is lined with a sound-absoring material.

• Kyungpook Mathematical Journal
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• 제47권4호
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• pp.529-548
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• 2007

The purpose of this article is to find a relation between the finite difference method and the boundary element method, and propose a new approach deriving a discrete approximation formula as like that of the finite difference method for harmonic functions. We develop a discrete approximation formula on a uniform grid based on the boundary integral formulations. We consider three different boundary integral formulations and derive one discrete approximation formula on the uniform grid for the harmonic function. We show that the proposed discrete approximation formula has the same computational molecules with that of the finite difference formula for the Laplace operator ${\nabla}^2$.

• Structural Engineering and Mechanics
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• 제41권5호
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• pp.591-604
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• 2012

This paper provides an iteration approach for the solution of multiple notch problem, which is based on the complex variable boundary integral equation (CVBIE). The contours of notches are applied by some loadings. The source points are assumed on the boundary of individual notch and the displacements along the boundaries become unknowns to be investigated. After discretization of the BIE, many influence matrices are obtained. One does not need to assemble many influence matrices into a larger matrix. This will considerably reduce the work in the program. The displacements along the many boundaries can be obtained from an iteration. There is no limitation for the configuration of notches. Several numerical examples are provided to prove the efficiency of the suggested approach.

• 대한수학회보
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• 제51권4호
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• pp.1195-1204
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• 2014

We newly define the volume integral means of harmonic functions to characterize the weighted harmonic Bergman spaces. It is based on Xiao and Zhu's results on holomorphic Bergman spaces [5].

• 대한토목학회논문집
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• 제11권1호
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• pp.45-53
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• 1991

지하구조물은 물체력과 초기응력이 지배적인 하중조건이 되며, 무한 또는 반무한영역을 경계로 한다. 또한 굴착면 주위에는 응력집중에 의해 비선형 거동이 발생한다. 본 논문에서는 경계요소법으로 물체력과 초기응력을 해석하기 위하여 영역적분은 경계 적분화하였다. 물체력에 대한 영역적분은 Galerkin텐서와 발산정리를 사용한 방법과 극좌표를 이용한 직접적분 방법으로 경계적분화하였고, 초기응력에 대한 영역적분은 극좌표를 이용한 직접적분 방법을 응용하여 경계적분화하였다. 경계요소해석 결과는 유한요소해석 결과와 비교하여 검증하였고 검증된 경계요소 프로그램을 비선형 유한요소 프로그램과 조합하여 굴착면 주위에 발생하는 비선형 거동을 합리적으로 해석하도록 하였다. 경계요소법에서 고려하기 어려운 물체력과 초기응력에 대한 영역적분을 경계적분화하여 효율적으로 해석할 수 있었으며, 조합해석 방법으로 비선형 거동을 합리적으로 해석할 수 있었다. 본 연구의 결과는 지하구조물의 해석에 유용하게 사용될 수 있을 것으로 기대된다.

• 전산구조공학
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• 제9권4호
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• pp.127-134
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• 1996

본 논문은 경계요소법에 의한 콘크리트의 진행성 파괴해석에 관한 연구이다. 콘크리트의 파괴진행해석을 위하여 경계요소법에 의한 변위 및 표면력 경계 적분방정식으로부터 균열을 포함한 연속체의 균열 경계적분 방정식을 정식화하였다. 콘크리트의 균열진행을 해석하기 위하여 균열 선단에서의 파괴진행영역을 Dugdale-Barenblatt형 모델을 사용하여 모델링하였고 균열진행영역의 인장연화상태를 선형으로 가정하여 모델링하였다. 정식화된 경계적분방정식에 의한 콘크리트 보와 여러가지 하중상태에 있는 인장시편에 대한 진행성 파괴해석을 실시하였으며 해석치와 실험치의 비교로부터 경계요소법에 의한 진행성 파괴해석방법은 최대하중 및 최대하중 이후의 거동을 포함한 콘크리트 구조물의 비선형 거동을 잘 예측함을 보여주고 있다 .

• 한국해양공학회지
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• 제14권1호
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• pp.1-5
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• 2000

A numerical analysis for wave motion in the shallow water is presented. The method is based on potential theory. The fully nonlinear free surface boundary condition is assumed in an inner domain and this solution is matched along an assumed common boundary to a linear solution in outer domain. In two-dimensional problem Cauchy's integral theorem is applied to calculate the complex potential and its time derivative along boundary.