• 대한기계학회논문집
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• 제17권12호
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• pp.3007-3019
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• 1993

For the same configuration, the stiffness of 6-node two dimensional isoparametric is stiffer than that of 8-node two dimensional isoparametric element. This phenomenon may be called 'Relative Stiffness Stiffening Phenomenon.' In this paper, the relative stiffness stiffening phenomenon was studied, and could be corrected by modifying the position of Gauss integral points used in the numerical integration of the stiffness matrix. For the same deformation (bending) energy of 6-node and 8-node two dimensional isoparametric elements, Gauss integral points of 6-node element have to move closer, in comparison with those of 8-node element, in the case of numerical integration along the thickness direction.

• Ocean Systems Engineering
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• 제7권4호
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• pp.399-412
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• 2017

The Gauss-Legendre integral method is applied to numerically evaluate the Green function and its derivatives in finite water depth. In this method, the singular point of the function in the traditional integral equation can be avoided. Moreover, based on the improved Gauss-Laguerre integral method proposed in the previous research, a new methodology is developed through the Gauss-Legendre integral. Using this new methodology, the Green function with the field and source points near the water surface can be obtained, which is less mentioned in the previous research. The accuracy and efficiency of this new method is investigated. The numerical results using a Gauss-Legendre integral method show good agreements with other numerical results of direct calculations and series form in the far field. Furthermore, the cases with the field and source points near the water surface are also considered. Considering the computational efficiency, the method using the Gauss-Legendre integral proposed in this paper could obtain the accurate numerical results of the Green function and its derivatives in finite water depth and can be adopted in the near field.

• Advances in concrete construction
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• 제1권4호
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• pp.319-340
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• 2013

This paper presents a comparative study on the double-K fracture parameters of concrete obtained using four existing analytical methods such as Gauss-Chebyshev integral method, simplified Green's function method, weight function method and simplified equivalent cohesive force method. Two specimen geometries: three point bend test and compact tension specimen for sizes 100-500 mm at initial notch length to depth ratios 0.25 and 0.4 are used for the comparative study. The required input parameters for determining the double-K fracture parameters are derived from the developed fictitious crack model. It is found that the cohesive toughness and initial cracking toughness determined using weight function method and simplified equivalent cohesive force method agree well with those obtained using Gauss-Chebyshev integral method whereas these fracture parameters determined using simplified Green's function method deviates more than by 11% and 20% respectively as compared with those obtained using Gauss-Chebyshev integral method. It is also shown that all the fracture parameters related with double-K model are size dependent.

• Nonlinear Functional Analysis and Applications
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• 제26권5호
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• pp.935-947
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• 2021

An efficient adaptive scheme based on a triple mixed quadrature rule of precision nine for approximate evaluation of line integral of analytic functions has been constructed. At first, a mixed quadrature rule SM₁(f) has been formed using Gauss-Legendre three point transformed rule and five point Booles transformed rule. A suitable linear combination of the resulting rule and Clenshaw-Curtis seven point rule gives a new mixed quadrature rule SM₁₀(f). This mixed rule is termed as triple mixed quadrature rule. An adaptive quadrature scheme is designed. Some test integrals having analytic function integrands have been evaluated using the triple mixed rule and its constituent rules in non-adaptive mode. The same set of test integrals have been evaluated using those rules as base rules in the adaptive scheme. The triple mixed rule based adaptive scheme is found to be the most effective.

• 대한조선학회논문집
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• 제32권2호
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• pp.32-42
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• 1995

프로펠러 뒷날과 같이 두께가 아주 얇아지는 경우, 또는 선미에서와 같이 물체 표면의 곡률이 급격하게 변하는 경우 등에서는 기존의 평균평면 패널로 물체의 표면을 대치하며 경계적분 문제를 다루면, leakage 문제를 야기하거나 유동장점이 패널에서 아주 가까이 있을 경우에는 유기속도 포텐셜이 부정확해 지는 등의 문제가 있다. 쌍곡면 패널은 그 위에 분포된 다이폴에 의해 유기되는 포텐셜을 근사화하지 않고 정확하게 계산할 수 있도록 한다. 본 연구는 방곡면에 분포된 균일 밀도의 다이폴에 의해 유기되는 포텐셜을 표현하는 적분식을 수치적으로 계산하기에 유용한 2가지 서로 다른 방법, 즉, Gauss-Bonnet 정리를 이용하여 증명하는 방법과 면적분을 선적분으로 치환하는 방법, 을 유도하고 그 정확성을 소개한다.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제27권3호
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• pp.194-206
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• 2023

We present families of nonlinear transformations useful for numerical evaluation of weakly singular integrals. First, for end-point singular integrals, we define a prototype function with some appropriate features and then suggest a family of transformations. In addition, for interior-point singular integrals, we develop a family of nonlinear transformations based on the aforementioned prototype function. We take some examples to explore the efficiency of the proposed nonlinear transformations in using the Gauss-Legendre quadrature rule. From the numerical results, we can find the superiority of the proposed transformations compared to some existing transformations, especially for the integrals with high singularity strength.

• 대한기계학회논문집
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• 제16권8호
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• pp.1429-1437
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• 1992

본 연구에서는 이완형 물성방정식을 바탕으로 하며 프와송 비가 일정하다는 가정을 하지 않는다. 또한 점탄성 지배방정식에 변분원리를 적용하고 유도되어진 식 에 유한요소해법을 사용하여 시스템 기본해석을 위한 연립방정식을 유도한다. 이와 함께 점탄성 물성함수의 유도 및 응력계산을 위한 공식화 과정도 설명한다. 제시된 방법론의 타당성 및 정확성을 보이기 위해서 평면응력 및 평면변형 문제의 변위 및 응력을 수치해석하여 이론해와 비교 검토하며, 아울러 시간증분의 변화와 Gauss poi- nts수가 수치정확도에 끼치는 영향을 조사한다.

• Structural Engineering and Mechanics
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• 제18권6호
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• pp.731-744
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• 2004

Modified virtual crack closure integral (MVCCI) technique has become very popular for computation of strain energy release rate (SERR) and stress intensity factor (SIF) for 2-D crack problems. The objective of this paper is to propose a numerical integration procedure for MVCCI so as to generalize the technique and make its application much wider. This new procedure called as numerically integrated MVCCI (NI-MVCCI) will remove the dependence of MVCCI equations on the type of finite element employed in the basic stress analysis. Numerical studies on fracture analysis of 2-D crack (mode I and II) problems have been conducted by employing 4-noded, 8-noded (regular & quarter-point), 9-noded and 12-noded finite elements. For non-singular (regular) elements at crack tip, NI-MVCCI technique generates the same results as MVCCI, but the advantage for higher order regular and singular elements is that complex equations for MVCCI need not be derived. Gauss numerical integration rule to be employed for 8-noded singular (quarter-point) element for accurate computation of SERR and SIF has been recommended based on the numerical studies.

• 지구물리와물리탐사
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• 제21권1호
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• pp.1-7
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• 2018

전기탐사 2차원 모델링에서는 다수의 파수영역 전위를 계산하고 이를 푸리에 역변환하여 공간영역 전위를 계산한다. 푸리에 역변환은 여러 개의 서로 다른 파수에서의 파수영역 전위를 사용하여 수치적으로 얻어진다. 적분의 정확도를 향상시키기 위하여 파수의 크기에 따라 적분 구간을 지수 근사와 대수 근사 구간으로 분할하는 방법이 널리 사용되고 있다. 푸리에 역변환에는 크게 구간 적분법과 가우스 적분법이 사용되고 있다. 그러나 이들 방법은 송수신 간격을 고려하지 못하므로 송수신 간격에 따른 오차를 피할 수 없다. 특히 송수신 간격이 매우 작거나 클 경우 오차가 급격하게 증가하는 문제점을 가지고 있다. 이 연구에서는 송수신 간격을 고려하여 가우스 좌표값 및 가중값을 적용하는 새로운 수치 적분법을 개발하였다. 반무한 공간에 대한 수치 실험 결과, 개발된 수치 적분법은 송수신 간격에 관계없이 0.4% 이하의 정밀도를 나타내었다.

• 대한기계학회논문집
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• 제19권4호
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• pp.990-1004
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• 1995

A modified 16-node element for composite plate has been proposed and compared with the 20-node element to check the validity of it. The fields of numerical inspection include mode analysis and specific damping analysis. By symetrizing the conventional unsymmetric damping matrix in the analysis of specific damping capacity, we could compute the specific damping capacity and make a program, effectively. In addition, we could predict the errors caused by reduction of integration order in thickness direction depending upon the number of layers.