• 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.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제30권4호
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• pp.347-355
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• 2023

For numerical evaluation of Cauchy principal value integrals, we present a simple rational function with a parameter satisfying some reasonable conditions. The proposed rational function is employed in coordinate transformation for accelerating the accuracy of the Gauss quadrature rule. The efficiency of the proposed rational transformation method is demonstrated by the numerical result of a selected test example.

• 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.

• 대한수학회지
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• 제41권6호
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• pp.957-976
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• 2004

It is well known that the application of the nonlinear coordinate transformations is useful for efficient numerical evaluation of weakly singular integrals. In this paper, we consider the trapezoidal rule combined with a nonlinear transformation $\Omega$$_{m}$(b;$\chi$), containing a parameter b, proposed first by Yun [14]. It is shown that the trapezoidal rule with the transformation $\Omega$$_{m}$(b;$\chi$), like the case of the Gauss-Legendre quadrature rule, can improve the asymptotic truncation error by using a moderately large b. By several examples, we compare the numerical results of the present method with those of some existing methods. This shows the superiority of the transformation $\Omega$$_{m}$(b;$\chi$).TEX>).

• 한국전산구조공학회:학술대회논문집
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• 한국전산구조공학회 2002년도 봄 학술발표회 논문집
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• pp.319-326
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• 2002

A p-version finite element model based on degenerate shell element is proposed for the analysis of orthotropic laminated plates. In the nonlinear formulation of the model, the total Lagrangian formulation is adopted with large deflection and moderate rotation being accounted for in the sense of von Karman hypothesis. The material model Is based on the Huber-Mises yield criterion and Prandtl-Reuss flow rule in accordance with the theory of strain hardening yield function, which is generalized for anisotropic materials by introducing the parameters of anisotropy. The model is also based on extension of equivalent-single layer laminate theory(ESL theory) with shear deformation, leading to continuous shear strain at the interface of two layers. The Integrals of Legendre Polynomials we used for shape functions with p-level varying from 1 to 10. Gauss-Lobatto numerical quadrature is used to calculate the stresses at the nodal points instead of Gauss points. The validity of the proposed p-version finite element model is demonstrated through several comparative points of view in terms of ultimate load, convergence characteristics, nonlinear effect, and shape of plastic zone

• 한국전산구조공학회논문집
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• 제15권3호
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• pp.491-499
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• 2002

직교이방성 적층평판해석을 위해 퇴화 쉘요소에 기초를 둔 p-version 유한요소법이 제안되었다. 이 모델의 비선형 정식화과정에서 기하비선형의 경우 von Karman의 대변형-소변형률 가정을 설명하기 위해 Total Lagrangian 방법이 채택되었으며, 재료비선형의 경우 Huber-Mises의 항복기준과 변형률경화 항복함수에 근거를 둔 Prandtl-Reuss 유동법칙이 사용되었다. 재료모델은 이방성을 표현하는 매개변수에 의해 이방겅재료를 고려할 수 있도록 하였다. 적층평판이론으로는 전단변형 효과를 고려할 수 있는 등가단출이론(ESL Theory)에 기초를 두었기 때문에 두 적층간 계면에서의 전단변형률은 연속이라는 조건을 갖게된다 적분형 르장드르 다항식이 형상함수로 사용되었으며 형상함수의 차수는 1차에서 10차까지 변화시킬 수 있다. 또한, Causs-Lobatto 수치적될법을 사용하기 때문에 기존의 가우스 적분점에서 계산되던 응력값은 이 적분법의 적분점이 절점에 위치하므로 절점에서 바로 응력값이 산출되도록 하였다 극한하중 수렴성, 비선형 효과, 소성역의 형상 등의 비교관점을 통해 p-version 유한요소 모델의 적정성을 보이고자 하였다.

• Journal of Radiation Protection and Research
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• 제17권1호
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• pp.43-56
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• 1992

입자 수송방정식에서 각변수(angular variable)를 각분할근사법으로 해석할 때 나타나는 이상 현상인 ray effect를 치유할 수 있는 방법의 하나로써, 유한 분할각(discrete angle quadrature)을 입자속의 공간적 분포로써 조종하는 방법인 각분할요소법 (discrete elements method)을 근거로 하여 2차원 직각좌표계에서의 입자 수송 해석 프로그램(TWODET)을 개발하였다. 평판형 등방적 고정선원이 존재하는 균질 사각형 흡수체에 대해 TWODET로 해석한 결과, 각 요소가 K-2, L인 경우에도 DOT 4.3(S-10)에서보다 ray effect 치유에 더 효과가 있음을 확인하였다. 그러나, 계산시간은 기존의 각분할법에서보다 약 4배 더 소비되었다. 선원에서 바로 진공(vacuum boundary)으로 떨어지는 구조의 경우, TWODET의 결과에서도 심한 왜곡을 보이고 있는데 선원과 바로 이웃한 진공간의 급격한 불연속성으로 인함으로 추측된다 고정선원이 있는 매질에 강한 흡수체가 추가된 구조의 경우에서도 TWODET(K-3, L-4)로 DOT 4.3(S-10)보다 좋은 결과를 보였다.