• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제22권3호
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• pp.201-215
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• 2018

In this paper we consider a class of singularly perturbed system of delay differential equations of convection diffusion type with integral boundary conditions. A finite difference scheme on an appropriate piecewise Shishkin type mesh is suggested to solve the problem. We prove that the method is of almost first order convergent. An error estimate is derived in the discrete maximum norm. Numerical experiments support our theoretical results.

• 충청수학회지
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• 제27권4호
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• pp.651-659
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• 2014

In this paper we present some Gronwall-tpye inequalities with a non-separable kernel and obtain the explicit estimate for solutions of impulsive differential equations. Furthermore, we give an example to illustrate our results.

• 대한수학회논문집
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• 제13권4호
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• pp.875-888
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• 1998

The use of the zeros of Chebyshev polynomial of the first kind $T_{4n＋4(x}$ ) and second kind $U_{2n＋1}$ (x) for Gauss-Chebyshev quad-rature and collocation of singular integral equations of Cauchy type yields computationally accurate solutions over other combinations of $T_{n}$ /(x) and $U_{m}$(x) as in [8]. We show that the coefficient matrix of the overdetermined system has the generalized inverse. We estimate the residual error using the norm of the generalized inverse.e.

• 대한수학회지
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• 제6권2호
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• pp.55-73
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• 1969

• 대한수학회지
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• 제7권1호
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• pp.1-5
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• 1970

• 대한기계학회논문집A
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• 제37권5호
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• pp.631-640
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• 2013

본 논문에서는 R6 코드와 RCC-MR A16 코드에서 원주방향 균열 배관에 대해 제시하는 1,2 차 복합 하중하에서 J-적분 계산법에 대한 정량적인 비교를 하였다. 균열의 형상, 균열의 깊이, 2 차 하중의 크기 변수에 대한 유한요소 해석을 수행 하였고 유한요소 해석 결과를 이용해 각 코드의 J-적분 평가법에 대한 정량적인 비교를 하였다. R6 코드는 $L_r=1$ 부근에서 보수적으로 평가 되었으며 RCC-MR A16 코드의 경우 기계하중이 작은 영역에서 보수적으로 평가되었다. 이와 같은 결과를 토대로 본 논문에서는 원주방향 균열이 있는 배관에 대하여 각 코드의 J-적분 계산을 보완할 수 있는 방법을 제시하였다. 그 결과로 보완된 J-적분 계산이 유한요소해석 결과와 잘 일치하는 것을 확인 하였다.

• 전기학회논문지
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• 제66권5호
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• pp.806-811
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• 2017

This paper considers the delay-dependent stability of linear systems with a time-varying delay in the frame work of Lyapunov-Krasovskii functional(LKF) approach. In this approach, an integral inequality is essential to estimate the upper bound of time-derivative of LKF, and a less conservative one is needed to get a less conservative stability result. In this paper, based on free weighting matrices, an improved integral inequality encompassing well-known results is proposed and then a stability result in the form of linear matrix inequality is derived based on an augmented LKF. Finally, two well-known numerical examples are given to demonstrate the usefulness of the proposed result.

• Nuclear Engineering and Technology
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• 제52권3호
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• pp.552-559
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• 2020

This paper presents an observer-based chattering free robust optimal control scheme to regulate the total power of a nuclear reactor. The non-linear model of nuclear reactor is linearized around a steady state operating point to obtain a linear model for which an optimal second order integral sliding mode controller is designed. A second order integral sliding mode observer is also designed to estimate the unmeasurable states. In order to avoid the chattering effect, the discontinuous input of both observer and controller are designed using the super-twisting algorithm. The proposed controller is realized by combining an optimal linear tracking controller with a second order integral sliding mode controller to ensure minimum control effort and robustness of the closed-loop system in the presence of uncertainties. The condition for the selection of gains of discontinuous control based on the super-twisting algorithm is derived using a strict Lyapunov function. Performance of the proposed observer based control scheme is demonstrated through non-linear simulation studies.

• 한국전산구조공학회:학술대회논문집
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• 한국전산구조공학회 1996년도 봄 학술발표회 논문집
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• pp.62-69
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• 1996

In this study, an equivalent domain integral (EDI) method is presented to estimate the track-till integral parameter, J-value, for two dimensional cracked elastic bodies which may quantify the severity of the crack-tit) stress fields. The conventional J-integral method based on line integral has been converted to equivalent area or domain integrals by using the divergence theorem. It is noted that the EDI method is very attractive because all the quantities necessary for computation of the domain integrals are readily available in a finite element analysis. The details and its implementation are extened to both h-version finite element model with 8-node isoparametric element and p-version finite element model with high order hierarchic element using Legendre type shape fuctions. The variations with respect to the different path of domain integrals from the crack-tip front and the choice of 5-function have been tested by several examples.

• Journal of Mechanical Science and Technology
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• 제14권1호
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• pp.30-38
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• 2000

This paper presents a framework how to estimate crack driving forces in terms of crack-tip opening displacement and J-integral for mismatched dissimilar joints with interface cracks. The mismatch in elastic, thermal, and plastic hardening properties is not considered, but the mismatch in plastic yield strengths is emphasized here. The main outcome of the present work is that the existing methods to estimate crack driving forces for homogeneous materials can be used with slight modification. Such modification includes (i) mismatch- corrected limit load solutions, and (ii) evaluating the contribution of each material in dissimilar joints to the total crack driving force, which depends on the strength mismatch of the dissimilar joints.