• 한국CDE학회논문집
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• 제14권5호
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• pp.297-305
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• 2009

Automatic generation of the mid-surfaces of a CAD model is becoming a useful function in that it can help increase the efficiency of engineering analysis as far as it does not affect the result seriously. Several methods had been proposed previously to automatically generate the mid-surfaces, but they often failed to generate the mid-surfaces of complex CAD models. Due to the inherent difficulty of this mid-surface generation problem, it may not be possible to come up with a complete and general method to solve this problem. Since a method that can handle a specific case may not work for different cases, it seems that developing case-specific methods ends up with solving only a fraction of the problem. In this paper, therefore, we propose a method to generate mid-surfaces based on a divide-and-conquer paradigm. This method first decomposes a complex CAD model into simple volumes. The mid-surfaces of the simple volumes are automatically generated by the existing methods, and then they are converted into the mid-surfaces of the original CAD model.

• 대한기계학회논문집
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• 제19권7호
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• pp.1604-1618
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• 1995

In the process of mechanical assembly design, assembly modeling systems have been used mainly for the design verification before manufacturing by enabling to check the interference and/ or the dynamic and kinematic performance. However, the conventional assembly modeling systems have a shortcoming that they can not be used in the initial design stage but can be used only after the design is fully completed. In other words conventional assembly modeling systems provide bottom-up modeling which means that the detailed modeling of components must precede the definition of relationships between them. To resolve this problem, an assembly modeling system is proposed to provide a top-down modeling environment in which components and assembly can be modeled simultaneously. To this end, an assembly data structure suitable for top-down assembly modeling has been established. Feature positioning Module(FPM) using geometric constraints has been also developed. The Sekective Solving Method proposed for FPM is based on the priority between the constraint equations and enables the designer's intent expressed by geometric constraints to be maintained throughout the whole modeling process. Finally, the feature based modeling technique using two-level features has been developed. Two-level features include an abstract model and a detailed model in a merged form in non-manifold data frame.

• 지식경영연구
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• 제20권3호
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• pp.39-47
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• 2019

Response surface methodology (RSM) is a group of statistical modeling and optimization methods to improve the quality of design systematically in the quality engineering field. Its final goal is to identify the optimal setting of input variables optimizing a response. RSM is a kind of knowledge management tool since it studies a manufacturing or service process and extracts an important knowledge about it. In a real problem of RSM, it is a quite frequent situation that considers multiple responses simultaneously. To date, many approaches are proposed for solving (i.e., optimizing) a multi-response problem: process capability function approach, desirability function approach, loss function approach, and so on. The process capability function approach first estimates the mean and standard deviation models of each response. Then, it derives an individual process capability function for each response. The overall process capability function is obtained by aggregating the individual process capability function. The optimal setting is given by maximizing the overall process capability function. The existing process capability function methods usually use the arithmetic mean or geometric mean as an aggregation operator. However, these operators do not guarantee the Pareto optimality of their solution. Moreover, they may bring out an unacceptable result in terms of individual process capability function values. In this paper, we propose a maximin-based process capability function method which uses a maximin criterion as an aggregation operator. The proposed method is illustrated through a well-known multiresponse problem.

• 한국소성가공학회:학술대회논문집
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• 한국소성가공학회 2006년도 춘계학술대회 논문집
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• pp.99-104
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• 2006

A semi-Lagrangian finite element scheme with objective time stepping algorithm for solving viscoelastic flow problem is presented. The convection terms in the momentum and constitutive equations are treated using a quasi-monotone semi-Lagrangian scheme, in which characteristic feet on a regular grid are traced backwards over a single time-step. Concerned with the generalized midpoint rule type of algorithms formulated to exactly preserve objectivity, we use the geometric transformation such as pull-back, push-forward operation. The method is applied to the 4:1 planar contraction problem for an Oldroyd B fluid for both creeping and inertial flow conditions.

• 한국소음진동공학회:학술대회논문집
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• 한국소음진동공학회 2004년도 추계학술대회논문집
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• pp.954-957
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• 2004

Based on the authors' previous work, where a geometric constraint handling technique for stiffener layout optimization problem using geometry algorithms was proposed, stiffener layout optimization to maximize natural frequencies of a curved three-dimensional shell structure was performed with a projection method. The original geometry of the shell structure was first projected on a two-dimensional plane, and then the whole optimization process was performed with the projected geometry of the shell except that the original shell structure was used for the eigenproblem solving. The projection method can be applied to baseline structures with a one-to-one correspondence between original and projected geometries such as automobile hoods and roofs.

• 대한수학회지
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• 제54권4호
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• pp.1331-1343
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• 2017

A curve ${\gamma}$ immersed in the three-dimensional sphere ${\mathbb{S}}^3$ is said to be a slant helix if there exists a Killing vector field V(s) with constant length along ${\gamma}$ and such that the angle between V and the principal normal is constant along ${\gamma}$. In this paper we characterize slant helices in ${\mathbb{S}}^3$ by means of a differential equation in the curvature ${\kappa}$ and the torsion ${\tau}$ of the curve. We define a helix surface in ${\mathbb{S}}^3$ and give a method to construct any helix surface. This method is based on the Kitagawa representation of flat surfaces in ${\mathbb{S}}^3$. Finally, we obtain a geometric approach to the problem of solving natural equations for slant helices in the three-dimensional sphere. We prove that the slant helices in ${\mathbb{S}}^3$ are exactly the geodesics of helix surfaces.

• 대한토목학회논문집
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• 제6권2호
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• pp.1-15
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• 1986

본(本) 연구(硏究)에서는 전(全) 해석과정(解析過程)을 two-Levels로 나누었다. Level 1 에서는 two-phases로 나누어 단면(斷面)을 최적화(最適化)하고, Level 2 에서는 트러스의 절점좌표(節點座標)를 변수(變數)로 하여 형상(形狀)을 최적화(最適化)하는 알고리즘을 제시(提示)한 것이다. 이 알고리즘의 Level 1 에서는 유도(誘導)된 비선형계획문제(非緣形計劃問題)를 SUMT 문제(問題)로 변환(變換)시켜 Modified Newton-Raphson Method에 의한 SUMT 법(法)을 채택하고, Leve1 2 에서는 Powell Method의 일방향(一方向) 탐사기법(探査技法)에 의해 목적함수(目的凾數)만이 최소(最小)가 되도록 하는 기법(技法)을 도입하여 최적화(最適化)알고리즘을 제시(提示)하였다. 제시(提示)된 알고리즘을 트러스의 형태(形態), 설계제약조건(設計制約條件), 재하조건(載荷條件) 등을 변화(變化)시켜 가면서 수종의 트러스에 적용(適用)하여 수치계산(數値計算)을 실시하고, 그 결과(結果)를 다른 알고리즘의 결과(結果)와 비교(比較)하므로서 알고리즘의 타당성(妥當性), 안전성(安全性), 적용성(適用性)을 검토하였다. 연구결과(硏究結果)의 two-Level 알고리즘은 트러스의 설계조건(設計條件)에 구애받지 않고 트러스의 형상최적화(形狀最適化)에 적용(適用)할 수 있으며, 안정성(安定性) 있게 비교적(比較的) 빠른 속도(速度)로 최적해(最適解)에 수렴(收斂)한다는 사실이 확인되었다.

• 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.

• 한국수학교육학회지시리즈E:수학교육논문집
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• 제24권3호
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• pp.503-523
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• 2010

현재 우리나라의 수학과 교육과정의 체제는 '가. 성격' '나. 목표', '다. 내용', '라. 교수 학습 방법', '라. 평가'로 구성되어 있다. 학교에서 구체적으로 학습해야 할 수학 성취기준은 '다. 내용'에 학년별로 제시되어 있다. '다. 내용'은 초등학교의 경우 수와 연산, 도형, 측정, 확률과 통계, 규칙성과 문제해결의 5개 하위 영역으로 구성되어 있으며, 중학교와 고등학교의 경우에는 수와 연산, 문자와 식, 함수, 확률과 통계, 기하의 5개 하위 영역으로 구성되어 있다. 이와 같은 하위 영역들은 초등학교의 규칙성과 문제해결 영역에서의 문제해결을 제외하고는 모두 수학적 주제들을 다루는 내용 영역이라고 할 수 있다. 이 글에서는 수학과 교육과정의 '다. 내용'에 5개의 내용 영역 이외에 '수학적 과정'이라는 하위 영역을 신설하여 추가하는 방안에 대해 살펴보고자 한다.

• Advances in nano research
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• 제16권5호
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• pp.473-487
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• 2024

The current study employs the nonlocal Timoshenko beam (NTB) theory and von-Kármán's geometric nonlinearity to develop a non-classic beam model for evaluating the nonlinear free vibration of bi-directional functionally-graded (BFG) nanobeams. In order to avoid the stretching-bending coupling in the equations of motion, the problem is formulated based on the physical middle surface. The governing equations of motion and the relevant boundary conditions have been determined using Hamilton's principle, followed by discretization using the differential quadrature method (DQM). To determine the frequencies of nonlinear vibrations in the BFG nanobeams, a direct iterative algorithm is used for solving the discretized underlying equations. The model verification is conducted by making a comparison between the obtained results and benchmark results reported in prior studies. In the present work, the effects of amplitude ratio, nanobeam length, material distribution, nonlocality, and boundary conditions are examined on the nonlinear frequency of BFG nanobeams through a parametric study. As a main result, it is observed that the nonlinear vibration frequencies are greater than the linear vibration frequencies for the same amplitude of the nonlinear oscillator. The study finds that the difference between the dimensionless linear frequency and the nonlinear frequency is smaller for CC nanobeams compared to SS nanobeams, particularly within the α range of 0 to 1.5, where the impact of geometric nonlinearity on CC nanobeams can be disregarded. Furthermore, the nonlinear frequency ratio exhibits an increasing trend as the parameter µ is incremented, with a diminishing dependency on nanobeam length (L). Additionally, it is established that as the nanobeam length increases, a critical point is reached at which a sharp rise in the nonlinear frequency ratio occurs, particularly within the nanobeam length range of 10 nm to 30 nm. These findings collectively contribute to a comprehensive understanding of the nonlinear vibration behavior of BFG nanobeams in relation to various parameters.