• Steel and Composite Structures
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• 제21권6호
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• pp.1347-1368
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• 2016

In this article, an exact analytical solution for mechanical buckling analysis of symmetrically cross-ply laminated plates including curvature effects is presented. The equilibrium equations are derived according to the refined nth-order shear deformation theory. The present refined nth-order shear deformation theory is based on assumption that the in-plane and transverse displacements consist of bending and shear components, in which the bending components do not contribute toward shear forces and, likewise, the shear components do not contribute toward bending moments The most interesting feature of this theory is that it accounts for a parabolic variation of the transverse shear strains across the thickness and satisfies the zero traction boundary conditions on the top and bottom surfaces of the plate without using shear correction factors. Buckling of orthotropic laminates subjected to biaxial inplane is investigated. Using the Navier solution method, the differential equations have been solved analytically and the critical buckling loads presented in closed-form solutions. The sensitivity of critical buckling loads to the effects of curvature terms and other factors has been examined. The analysis is validated by comparing results with those in the literature.

• 대한수학회보
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• 제50권4호
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• pp.1061-1067
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• 2013

In this paper, we study surfaces of revolution without parabolic points in 3-Euclidean space $\mathbb{R}^3$, satisfying the condition ${\Delta}^{II}G=f(G+C)$, where ${\Delta}^{II}$ is the Laplace operator with respect to the second fundamental form, $f$ is a smooth function on the surface and C is a constant vector. Our main results state that surfaces of revolution without parabolic points in $\mathbb{R}^3$ which satisfy the condition ${\Delta}^{II}G=fG$, coincide with surfaces of revolution with non-zero constant Gaussian curvature.

• ETRI Journal
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• 제29권6호
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• pp.817-819
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• 2007

A low-stress organic polymer membrane is proposed as a deformable mirror that can be incorporated into a cellular phone camera to achieve auto focusing without motor-type moving parts. It is demonstrated that our fabricated device has an optical power of 20 diopters and can switch focus in 14 ms. The surface roughness of the organic membrane is measured around 15 nm, less than ${\lambda}$/20 of the visible light. With curve fitting, we found that the actuated membrane is almost parabolic in shape, which leads to less aberration than spherical surfaces. It is suitable for reflective-optics systems.

• 설비공학논문집
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• 제3권1호
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• pp.11-25
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• 1991

The steady, incompressible developing 3-dimensional turblent flow in a square sectioned curved duct has been investigated by using partially-parabolic equation and Finite Analytic Method. The calculation of turbulent flow field is performed using 2-equation K-$\epsilon$ turbulence model, modified wall function, simpler algorithm and numerically generated body fitted coordinates. Iso-mean velocity contours at the various sections are compared with the existing experimental data and elliptic solutions by other authors. In the region of $0^{\circ}<{\theta}<71^{\circ}$, present results agree with the experimental data much better than the elliptic solution for the similar number of grid points. Furthermore, for the same tolerance, the present solution converges four times faster than the elliptic solution.

• 한국자동차공학회논문집
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• 제11권1호
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• pp.193-200
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• 2003

This paper proposes a novel algorithm to recognize the curve of a structured road. The proposed algorithm uses an LCF (Lane Curve Function) obtained by the transformation of a parabolic function defined on world coordinate into image coordinate. Unlike other existing methods, the algorithm needs no transformation between world coordinate and image coordinate owing to the LCF. In order to search for an LCF describing the lane best, the differential comparison between the slope of an assumed LCF and the phase angle of edge pixels in the LROI (Lane Region Of Interest) constructed by the LCF is implemented. As finding the true LCF, the lane curve is determined. The proposed method is proved to be efficient through various kinds of images, providing the reliable curve direction and the valid curvature compared to the real road.

• 한국전자파학회논문지
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• 제19권6호
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• pp.612-620
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• 2008

본 논문은 UWB 통신을 위한 포물선 엣지(egde) 형태의 평면 모노폴 안테나에 대한 것이다. 평면 모노폴과 그라운드의 엣지를 포물선 구조로 하여 구조적으로 광대역 속성을 갖도록 하였다. 모노폴과 그라운드 엣지의 곡률을 변화시키면서 자기 상보(self-complementary) 구조에 가깝도록 설계하였다. 안테나는 모노폴과 그라운드가 동일 평면상에 존재하며, 동축 케이블 급전을 하였다. 유전 상수가 4.4인 FR4 유전체 기판을 사용하였고, 그 크기는 $26{\times}31{\times}1.6mm$이다. $3.1{\sim}10.6GHz$에서 10 dB 이상의 반사 손실을 얻을 수 있었다. 복사 패턴은 모든 주파수에서 다이폴 안테나의 복사 패턴과 비슷한 결과를 보이고 있으며, 측정한 결과에서 E-plane의 경우 최대 이득은 $1.37{\sim}6.02dBi$의 값을 갖는다.

• 한국전자파학회논문지
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• 제20권11호
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• pp.1225-1232
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• 2009

본 논문은 디지털 TV 실내 수신을 위한 포물선 엣지 형태의 평면 모노폴 안테나를 제안한다. 평면 모노폴과 그라운드의 엣지를 포물선 구조로 하여 광대역 특성을 갖도록 한다. 모노폴과 그라운드 엣지의 곡률을 변화시키면서 자기 상보(self-complementary) 구조에 가깝도록 설계한다. 안테나는 모노폴과 그라운드가 동일 평면상에 존재하며, coplanar waveguide 급전을 사용한다. 유전 상수가 4.4인 FR4 유전체 기판을 사용하였고, 크기는 $200\;mm{\times}40\;mm{\times}1.6\;mm$이다. 470~806 MHz의 디지털 TV 수신 전 대역에서 10 dB 이상의 반사 손실을 얻을 수 있었다. E 평면의 최대 이득은 600 MHz일 때 1.86 dBi, H평면의 최대 이득은 600 MHz일 때 3.86 dBi였다.

• 대한수학회지
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• 제49권3호
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• pp.585-604
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• 2012

In this paper we consider the evolution of the rolling stone with a rotationally symmetric nonconvex compact initial surface ${\Sigma}_0$ under the Gauss curvature flow. Let $X:S^n{\times}[0,\;{\infty}){\rightarrow}\mathbb{R}^{n+1}$ be the embeddings of the sphere in $\mathbb{R}^{n+1}$ such that $\Sigma(t)=X(S^n,t)$ is the surface at time t and ${\Sigma}(0)={\Sigma}_0$. As a consequence the parabolic equation describing the motion of the hypersurface becomes degenerate on the interface separating the nonconvex part from the strictly convex side, since one of the curvature will be zero on the interface. By expressing the strictly convex part of the surface near the interface as a graph of a function $z=f(r,t)$ and the non-convex part of the surface near the interface as a graph of a function $z={\varphi}(r)$, we show that if at time $t=0$, $g=\frac{1}{n}f^{n-1}_{r}$ vanishes linearly at the interface, the $g(r,t)$ will become smooth up to the interface for long time before focusing.

• 한국강구조학회 논문집
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• 제9권4호통권33호
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• pp.673-682
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• 1997

이 논문에서는 회전관성과 전단변형이 변화곡률 아치의 고유진동수에 미치는 영향을 분석하였다. 임의의 변화곡률을 갖는 등단면 아치의 자유진동을 지배하는 미분방정식을 유도하였으며, 유도된 미분방정식에 회전-회전, 회전-고정 및 고정-고정의 단부조건을 갖는 포물선, 원호 및 타원 아치를 적용하여 수치해석하였다. 해석결과로서 무차원 변수인 아치높이 지간길이비 및 세장비 변화에 따론 최저차 4개의 무차원 고유진동수를 산출하였다.

• 대한수학회보
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• 제52권3호
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• pp.925-933
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• 2015

It is well-known that the area of parabolic region between a parabola and any chord $P_1P_2$ on the parabola is four thirds of the area of triangle ${\Delta}P_1P_2P$. Here we denote by P the point on the parabola where the tangent is parallel to the chord $P_1P_2$. In the previous works, the first and third authors of the present paper proved that this property is a characteristic one of parabolas. In this paper, with respect to triangles ${\Delta}P_1P_2PQ$ where Q is the intersection point of two tangents to X at $P_1$ and $P_2$ we establish some characterization theorems for parabolas.