• Steel and Composite Structures
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• v.21 no.6
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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.

• Bulletin of the Korean Mathematical Society
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• v.50 no.4
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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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• v.29 no.6
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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.

• Korean Journal of Air-Conditioning and Refrigeration Engineering
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• v.3 no.1
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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.

• Transactions of the Korean Society of Automotive Engineers
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• v.11 no.1
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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.

• The Journal of Korean Institute of Electromagnetic Engineering and Science
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• v.19 no.6
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• pp.612-620
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• 2008

In this parer, parabolic edge planar monopole antenna for UWB communication is presented. The antenna have broadband property structurally through planar monopole and ground which have parabolic edge. It is designed close to self-complementary structure as changing curvature of edge of monopole and ground. Monopole and ground of proposed antenna exist on coplanar plane, and excite as coaxial feeding. It used FR4 dielectric substrate of ${\varepsilon}_r=4.4$, and the size is $26{\times}31{\times}1.6mm$. Return loss is more than 10 dB in $3.1{\sim}10.6GHz$. Radiation pattern is about the same that of dipole antenna at all frequency. At measured result, max gain is $1.37{\sim}6.02dBi$ at E-plane.

• The Journal of Korean Institute of Electromagnetic Engineering and Science
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• v.20 no.11
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• pp.1225-1232
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• 2009

In this paper, a parabolic edge planar monopole antenna for indoor DTV reception is presented. The antenna has broadband property with the planar monopole and ground of parabolic edges. It is designed close to self-complementary structure as changing curvature of edges of monopole and ground. Monopole and ground conductors of the antenna are on the same plane, and excited through CPW feeding. It is fabricated on an FR4 dielectric substrate of $\varepsilon_r=4.4$, and the dimension is $40\;mm{\times}200\;mm{\times}1.6\;mm$. Return loss is larger than 10 dB in 470~806 MHz. Maximum gain is 1.86 dBi on E-plane at 810 MHz and 3.86 dBi on H-plane at 600 MHz.

• Journal of the Korean Mathematical Society
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• v.49 no.3
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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.

• Journal of Korean Society of Steel Construction
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• v.9 no.4 s.33
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• pp.673-682
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• 1997

The main purpose of this paper is to investigate the effects of rotatory inertia and shear deformation on the natural frequencies of arches with variable curvature. The differential equations are derived for the in-plane free vibration of linearly elastic arches of uniform stiffness and constant mass per unit length. The governing equations are solved numerically for parabolic, circular and elliptic geometries with hinged-hinged, hinged-clamped and clamped-clamped end constraints. For each cases, the four lowest frequency parameters are presented as functions of the two dimensionless system parameters; the arch rise to span length ratio, and the slenderness ratio.

• Bulletin of the Korean Mathematical Society
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• v.52 no.3
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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.