• 대한수학교육학회지:학교수학
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• 제10권2호
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• pp.181-197
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• 2008

Bertrand's Paradox는 '임의의 현(random chord)'의 의미가 분명하지 않기 때문에 구하는 방법에 따라 그 결과가 다르게 나오는 paradox(역설)로 알려져 있다. 본 논문에서는 현의 임의성에 대한 구체적인 제시의 부재로 인해 발생하는 다양한 풀이 방법에 대해 분석하였다. 또한 세 가지 풀이의 수학적 계산과 현실 세계에서의 물리적 실험의 결과에서 발생하는 차이를 알아보고, '임의의 현'의 실제적인 의미에 대한 공리적인 정의를 통하여 보편 타당한 답을 구하고자 하였다. 이를 구하는 과정에서 적분기하학의 기본개념인 측도와 적분과 연관이 있는 기하학적 확률지도가 Laplace의 고전적 관점을 기본으로 하는 현 교육과정에 적합한 요소인가에 대한 반성과 그의 위상에 관해 논하였다.

• 대한수학교육학회지:학교수학
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• 제14권1호
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• pp.151-163
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• 2012

2006개정 교육과정에서 초등수학과의 교수 학습방법으로 학습자의 조작 활동을 통한 탐구방식의 학습이나 교사와 학생이 함께 학습활동 등으로 학습자의 능동적이고 적극적인 활동주의 학습 원리에 따른 학습 효과를 극대화 할 수 있는 방법을 요구하고 있다. 이에 본 연구에서는 초등학교 1학년에서 6학년까지의 수학교과서에 제시된 모든 학습내용에 따른 학습 활동을 10가지의 유형으로 조사한 후에 이를 수와 연산, 도형, 확률과 통계, 측정 그리고 규칙성과 문제해결의 5대 내용영역과 저 중 고학년군의 3개로 나누어 특징을 분석하였다. 그리고 이 결과를 교사들이 단원에 따라 개대되는 활동유형과 비교하고 분석하여 학습지도에 효과적으로 활용하도록 하였다.

• 한국CDE학회논문집
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• 제17권2호
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• pp.123-131
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• 2012

The requirements for computational resources to perform the structural analysis are increasing rapidly. The size of the current analysis problems that are required from practical industry is typically large-scale with more than millions degrees of freedom (DOFs). These large-scale analysis problems result in the requirements of high-performance analysis codes as well as hardware systems such as supercomputer systems or cluster systems. In this paper, the pre- and post-processing system for supercomputing based large-scale structural analysis is presented. The proposed system has 3-tier architecture and three main components; geometry viewer, pre-/post-processor and supercomputing manager. To analyze large-scale problems, the ADVENTURE solid solver was adopted as a general-purpose finite element solver and the supercomputer named 'tachyon' was adopted as a parallel computational platform. The problem solving performance and scalability of this structural analysis system is demonstrated by illustrative examples with different sizes of degrees of freedom.

• Structural Engineering and Mechanics
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• 제48권6호
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• pp.757-774
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• 2013

An integrated simulation tool for multilayer stepped pyramidal structures is presented. The tool, based on a semi-analytical mathematical strategy, is able to calculate the temperature distributions and thermal stresses at the interfaces between the layers of such structures. The core of the thermal solver is the analytical simulator for power electronic devices, DJOSER, which has been supplemented with a mechanical solver based on the finite-element method. To this end, a new ele-ment is proposed whose geometry is defined by its mean surface and thickness, just as in a plate. The resulting mechanical model is fully three-dimensional, in the sense that the deformability in the direction orthogonal to the mean surface is taken into account. The dedicated finite element code developed for solving the equilibrium problem of structures made up of two or more superimposed plates subjected to thermal loads is applied to some two-layer samples made of silicon and copper. Comparisons performed with the results of standard finite element analyses using a large number of brick elements reveal the soundness of the strategy employed and the accuracy of the tool developed.

• 대한기계학회논문집A
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• 제24권2호
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• pp.496-505
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• 2000

A semi-infinite parallel crack propagated with constant velocity in two bonded anisotropic strip under anti-plane clamped displacement is analyzed. Using Fourier integral transform a Wiener-Hopf equation is derived. By solving this equation the asymptotic stress and displacement fields near the crack tip are determined, where the results give the more general expression applicable to the extent of the anisotropic material having one plane of elastic symmetry for the parallel crack. The dynamic stress intensity factor and energy release rate are also obtained as a closed form, which are the results applicable to the problem both of dynamic and static crack under the same geometry as this study. The stress intensity factor approaches zero at the critical crack velocity which is less than the shear wave velocity, but in typical case of isotropic or orthotropic material agrees with the velocity of shear wave. Also a circular shear stress around crack tip is considered, from which the stress is shown to be approximately symmetric about the horizontal axis. Referring to the maximum stress criteria, it could be shown that a brenched crack is formed by crack growth as crack velocity increases.

• 한국학교수학회논문집
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• 제13권1호
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• pp.105-124
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• 2010

본 연구의 목적은 아동들의 수학적 의사소통 능력 중 말하기 능력과 쓰기 능력에 대해서 심도 깊게 알아보고, 말하기 능력과 쓰기 능력에서 어떤 차이점이 있는지를 조사하는 것이다. 3명의 5학년 아동들이 본 연구에 참여하였고 도형 영역에서 그들의 말하기 능력과 쓰기 능력이 분석되었다. 아동들은 자신이 알고 있는 수학적 개념이나 문제 해결 과정을 말 또는 글로 설명하기 위해서 적절한 수학적 언어를 선택하여 사용하는데 어려움을 나타내고 있었다. 본 연구에 참여한 아동들의 경우에는 말하기 능력이 쓰기 능력보다 좋은 것으로 나타났다.

• 제어로봇시스템학회논문지
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• 제9권2호
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• pp.117-123
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• 2003

Rotational machines such as optical disk drives, hard disk drives, and so on are subject to periodic disturbances caused by their mechanical characteristics. In the meanwhile, it is well known that repetitive control rejects periodic disturbance effectively. This paper presents a practical application of repetitive control to the track-following servo of an optical disk drive. The repetitive control system is composed of two repetitive controllers which compensate for periodic disturbances generated by track geometry and eccentric rotation of disk and a feedback controller stabilizing the feedback loop. A robust stability for all plant uncertainties is proved using linear matrix inequalities (LMIs). In the controller design, a weighting function is introduced for the feedback controller to ensure a minimum loop gain and a sufficient phase margin. The repetitive controllers and the feedback controller are designed by solving an optimization problem which can consider the robust stability condition and the system performance. The developed repetitive control system is implemented in the digital control system with a 16-bit fixed-point digital signal processor (DSP). Through simulation and experiment. The feasibility of the proposed repetitive control system is verified.

• Structural Engineering and Mechanics
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• 제47권2호
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• pp.227-245
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• 2013

The term "constructability" in regard to cast-in-place concrete construction refers mainly to the ease of reinforcing steel placement. Bar congestion complicates steel placement, hinders concrete placement and as a result leads to improper consolidation of concrete around bars affecting the integrity of the structure. In this paper, a multi-objective approach, based on the non-dominated sorting genetic algorithm (NSGA-II) is developed for optimal design of reinforced concrete cantilever retaining walls, considering minimization of the economic cost and reinforcing bar congestion as the objective functions. The structural model to be optimized involves 35 design variables, which define the geometry, the type of concrete grades, and the reinforcement used. The seismic response of the retaining walls is investigated using the well-known Mononobe-Okabe analysis method to define the dynamic lateral earth pressure. The results obtained from numerical application of the proposed framework demonstrate its capabilities in solving the present multi-objective optimization problem.

• 대한기계학회논문집
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• 제17권2호
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• pp.277-284
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• 1993

본 연구에서는 적분변환에 의한 해법을 사용하여 폐형으로 주어지는 엄밀해를 얻었다. 먼저 평면에 수직한 방향의 변위를 도입하여 주어진 문제를 Mellin 변환하 고 수식화 하면 Wiener-Hopf 방정식이 주어진다.이 방정식을 푼 다음 변위에 관한 적분 표현식을 점근(asymptotic)전개하여 평가하면 균열선단 부근의 변위가 결정된다. 이로부터 폐형(closed form)으로 구성되는 균열선단부근의 응력확대계수(stress in- tensity factor)를 얻었다. 이 결과를 가지고 특정한 경우에 해당되는 기존의 연구 결과와 비교하였다. 특별히 가해진 하중이 자기평형(self equilibrium)을 이루는 경 우에 한정하여 계면에 인접한 재료의 결과와 동일함을 무한고체물에 대한 해석에서 보 인 바 있는데, 이와같은 정성적인 결과가 본문제와 같이 계면방향 표면균열을 지니는 반무한 크기의 고체물에서도 유지되는가를 검토하였다. 아울러 본 연구와 동일한 모 양의 균열이라면 고체물표면 혹은 균열면에 임의로 분포하는 비평면하중문제에 대한 응력확대계수는 본 연구의 결과를 가지고 간단한 적분을 수행함으로써 용이하게 계산 됨을 보였다.

• Nuclear Engineering and Technology
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• 제43권3호
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• pp.243-256
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• 2011

This paper considers the concept of analog computing based on a cellular neural network (CNN) paradigm to simulate nuclear reactor dynamics using a time-dependent second order form of the neutron transport equation. Instead of solving nuclear reactor dynamic equations numerically, which is time-consuming and suffers from such weaknesses as vulnerability to transient phenomena, accumulation of round-off errors and floating-point overflows, use is made of a new method based on a cellular neural network. The state-of-the-art shows the CNN as being an alternative solution to the conventional numerical computation method. Indeed CNN is an analog computing paradigm that performs ultra-fast calculations and provides accurate results. In this study use is made of the CNN model to simulate the space-time response of scalar flux distribution in steady state and transient conditions. The CNN model also is used to simulate step perturbation in the core. The accuracy and capability of the CNN model are examined in 2D Cartesian geometry for two fixed source problems, a mini-BWR assembly, and a TWIGL Seed/Blanket problem. We also use the CNN model concurrently for a typical small PWR assembly to simulate the effect of temperature feedback, poisons, and control rods on the scalar flux distribution.