• 호남수학학술지
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• 제31권4호
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• pp.579-590
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• 2009

The precise form of singular functions, singular function representation and the extraction form for the stress intensity factor play an important role in the singular function methods to deal with the domain singularities for the Poisson problems with most common boundary conditions, e.q. Dirichlet or Mixed boundary condition [2, 4]. In this paper we give an elementary step to get the singular functions of the solution for Poisson problem with Neumann boundary condition or Robin boundary condition. We also give singular function representation and the extraction form for the stress intensity with a result showing the number of singular functions depending on the boundary conditions.

• Structural Engineering and Mechanics
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• 제51권5호
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• pp.773-792
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• 2014

In this paper, we study the inverse mode shape problem for an Euler-Bernoulli beam, using an analytical approach. The mass and stiffness variations are determined for a beam, having various boundary conditions, which has a prescribed polynomial second mode shape with an internal node. It is found that physically feasible rectangular cross-section beams which satisfy the inverse problem exist for a variety of boundary conditions. The effect of the location of the internal node on the mass and stiffness variations and on the deflection of the beam is studied. The derived functions are used to verify the p-version finite element code, for the cantilever boundary condition. The paper also presents the bounds on the location of the internal node, for a valid mass and stiffness variation, for any given boundary condition. The derived property variations, corresponding to a given mode shape and boundary condition, also provides a simple closed-form solution for a class of non-uniform Euler-Bernoulli beams. These closed-form solutions can also be used to check optimization algorithms proposed for modal tailoring.

• 한국전산구조공학회:학술대회논문집
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• 한국전산구조공학회 1994년도 봄 학술발표회 논문집
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• pp.128-136
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• 1994

In this study, dynamic boundary element method using mass matrix is derived, using fundamental solutions for the semi-infinite domain. In constituting boundary integral equations for the dynamic equilibrium condition, inertia term in the form of domain integral is transformed into boundary integral form. Corresponding system equations are derived, and a boundary element program is developed. In addition, equations for free vibration is formulated, and eigenvalue analysis is performed. The results from the dynamic boundary element analysis for a tunnel problem are compared with those from the finite element analysis. According to the comparison, boundary element method using mass matrix is consistent with the results of finite element method. Consequently, in tunnel vibration problems, it results in reasonable solution compared with other methods where relatively higher degree of freedoms are employed.

• 디자인학연구
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• 제18권3호
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• pp.171-180
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• 2005

본 연구의 목적은 21세기 디자인의 이슈인 인간중심의 디자인, 디지털리즘, 친환경디자인, 문화지향디자인에 부합하는 디자인의 방향성을 실내디자인에서 모색하고자 하는데 있다. 이러한 목적에 접근하는 방법으로써 먼저, 경계형태의 이론적 고찰을 통하여 공간에서 나타나는 경계구조 형태를 이해한다. 그리고 조형예술 및 타 장르에서 표현된 키네티시즘 특성을 조사하여 공간을 구성하는 인자로서의 경계 형태에 도입된 키네티시즘적 표현특성을 도출하고자 한다. 이러한 연구의 진행과정으로써 제 1장에서는 연구의 배경과 목적 및 방법을 설명하고, 제 2장에서는 공간의 경계형태 구조와 키네틱 아트의 전개 및 표현 특성을 살펴본다. 제 3장에서는 현대 건축공간의 동적 표현 양성을 실제적 움직임, 상대적 움직임, 연상적 움직임으로 나누어 고찰하고, 제 4장에서는 3장에서 언급한 세 가지 타입의 움직임 특성이 표현된 현대 공간사례를 조사하여 어떠한 경계구조에 도입되는지를 분석한다. 마지막으로 제 5장에서는 위와 같은 분석을 통해 나타난 결과로서 경계형태에 도입된 키네티시즘의 표현 특성을 도출하여 미래 실내디자인의 방향성을 제시한다.

• 대한수학회지
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• 제41권5호
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• pp.875-882
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• 2004

Let (M,g) be a compact m dimensional Einstein manifold with smooth boundary. Let $\Delta$$_{p}$,B be the realization of the p form valued Laplacian with a suitable boundary condition B. Let Spec($\Delta$$_{p}$,B) be the spectrum where each eigenvalue is repeated according to multiplicity. We show that certain geometric properties of the boundary may be spectrally characterized in terms of this data where we fix the Einstein constant.ant.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제9권1호
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• pp.31-37
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• 2002

In this paper, we find explicitly the eigenvalues and the eigenfunctions of Laplace operator on a triangle domain with a mixed boundary condition. We also show that a weaker form of the principle of spatial averaging holds for this domain under suitable boundary condition.

• Steel and Composite Structures
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• 제24권3호
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• pp.359-367
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• 2017

In this work, transient heat transfer analysis of functionally graded (FG) carbon nanotube reinforced nanocomposite (CNTRC) cylinders with various essential and natural boundary conditions is investigated by a mesh-free method. The cylinders are subjected to thermal flux, convection environments and constant temperature faces. The material properties of the nanocomposite are estimated by an extended micro mechanical model in volume fraction form. The distribution of carbon nanotube (CNT) has a linear variation along the radial direction of axisymmetric cylinder. In the mesh-free analysis, moving least squares shape functions are used for approximation of temperature field in the weak form of heat transform equation and the transformation method is used for the imposition of essential boundary conditions. Newmark method is applied for solution time depended problem. The effects of CNT distribution pattern and volume fraction, cylinder thickness and boundary conditions are investigated on the transient temperature field of the nanocomposite cylinders.

• 대한수학회논문집
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• 제10권2호
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• pp.357-363
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• 1995

We study non-existence of $L^2$-harmonic p-forms on a complete, non-compact Riemannian manifold without boundary as extension of results of K. Yano in the case of compact.

• 대한수학회보
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• 제32권1호
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• pp.19-23
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• 1995

We will estimate the lower bound of the first nonzero Neumann and Dirichlet eigenvalue of Laplacian equation on compact Riemannian manifold M with boundary. In case that the boundary of M has positive second fundamental form elements, Ly-Yau[3] gave the lower bound of the first nonzero neumann eigenvalue $\eta_1$. In case that the second fundamental form elements of $\partial$M is bounded below by negative constant, Roger Chen[4] investigated the lower bound of $\eta_1$. In [1], [2], we obtained the lower bound of the first nonzero Neumann eigenvalue is estimated under the condtion that the second fundamental form elements of boundary is bounded below by zero. Moreover, I realize that "the interior rolling $\varepsilon$ - ball condition" is not necessary when the first Dirichlet eigenvalue was estimated in [1].ed in [1].

• East Asian mathematical journal
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• 제33권5호
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• pp.495-509
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• 2017

With the accuracy of the nonlinearity guaranteed, plenty of time and large memory space are needed when we solve the finite element numerical solution of nonlinear partial differential equations. In this paper, we use the Group Element Method (GEM) to deal with the non-linearity of the BBM-Burgers Equation with Conservation form and perform a numerical analysis for two particular initial-boundary value (the Dirichlet boundary conditions and Neumann-Dirichlet boundary conditions) problems with the Finite Element Method (FEM). Some numerical experiments are performed to analyze the error between the exact solution and the FEM solution in MATLAB.