• Journal of applied mathematics & informatics
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• v.39 no.3_4
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• pp.327-338
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• 2021

In this paper, we have introduced a new notion of recurrent structure Jacobi of real hypersurfaces in complex hyperbolic two-plane Grassmannians G^*₂(ℂ^m+2). Next, we show a non-existence property of real hypersurfaces in G^*₂(ℂ^m+2) satisfying such a curvature condition.

• Journal of the Chungcheong Mathematical Society
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• v.34 no.1
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• pp.37-53
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• 2021

In this paper we define scaled visual curvature and visual Frenet frame that can be visually accepted for discrete space curves. Scaled visual curvature is relatively simple compared to multi-scale visual curvature and easy to control the influence of noise. We adopt scaled minimizing directions of height functions on each neighborhood. Minimizing direction at a point of a curve is a direction that makes the point a local minimum. Minimizing direction can be given by a small noise around the point. To reduce this kind of influence of noise we exmine the direction whether it makes the point minimum in a neighborhood of some size. If this happens we call the direction scaled minimizing direction of C at p ∈ C in a neighborhood Br(p). Normal vector of a space curve is a second derivative of the curve but we characterize the normal vector of a curve by an integration of minimizing directions. Since integration is more robust to noise, we can find more robust definition of discrete normal vector, visual normal vector. On the other hand, the set of minimizing directions span the normal plane in the case of smooth curve. So we can find the tangent vector from minimizing directions. This lead to the definition of visual tangent vector which is orthogonal to the visual normal vector. By the cross product of visual tangent vector and visual normal vector, we can define visual binormal vector and form a Frenet frame. We examine these concepts to some discrete curve with noise and can see that the scaled visual curvature and visual Frenet frame approximate the original geometric invariants.

• International Journal of Ocean System Engineering
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• v.2 no.3
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• pp.195-199
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• 2012

This paper reports a new analytical method to calculate the planar displacement of structures. The cross-sections were assumed to remain in plane and the deflection curve was evaluated using the curvature values geometrically, despite being solved with differential equations. The deflection curve was parameterized with the arc-length of the curvature values, and was taken as an assembly of chains of circular arcs. Fast and accurate solutions of complex deflections can be obtained easily. This paper includes a comparison of the nonlinear displacements of an elastic tapered cantilever beam with a uniform moment distribution among the proposed analytical method, numerical method of the theory and large deflection FEM solutions.

• Transactions of the Korean Society of Mechanical Engineers
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• v.17 no.12
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• pp.3020-3027
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• 1993

Curved beam element has received attention because of its own usefulness and its bearing on general curved elements like shells. In conventional curved beam elements stiffness matrix is overestimated and eigensolutions are poor. To avoid this phenomenon it is necessary to use a large number of elements and, as a result, the total number of degrees of freedom is increased. In this paper the two-noded, with three degrees of freedom at each node, in-plane curvature-based curbed beam element is employed in eigen-analysis of curved beam. It is shown that the curvature-based beam element is very efficient in vibration analysis and also that it is applicable to both thin and thick curved beams.

• Transactions of the Korean Society of Automotive Engineers
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• v.4 no.6
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• pp.27-38
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• 1996

A two-dimensional FEM program, which considers bending effects in the membrane fromulation, was developed under plane strain assumption for analyzing forming processes of an arbitrarily shaped draw-die of automotive panels. For the evaluation of bending effects with membrane elements, the bending equivalent forces and stiffnesses are calculated from the bending moment computed using the changes in curvature of the formed shape of two membrane ones. The curves depicted with 3 nodes are described by a circle, a quadratic equation, and a cubic equation, respectively, and in the simulation of the stretch/draw sections of an automotive inner panel, three different description results are compared each other. Also, the bending results are compared with membrane results and measurements in order to verify the validity of the developed program.

• Proceedings of the KSR Conference
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• 2007.11a
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• pp.107-114
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• 2007

In this paper, the equations of motion by which the natural vibration of rotating thick ring can be analyzed accurately are presented. These equations are derived from the theory of finite deformation and the principle of virtual work. The effects of variation in curvature across the ring cross-section can be considered in these equations. The ring models are called as thick ring model and thin ring model respectively as the effects of variation in curvature are considered or neglected. The radial displacement of ring which is rotating at constant angular velocity is determined by a non-linear equation derived from the principle of virtual work. The equations of the in-plane and out-of-plane vibrations at disturbed state are also formulated from the principle of virtual work. They can be expressed as the combination of the radial displacement at the steady state and the disturbed displacements about the steady state. The natural vibrations of rings with different thickness are analyzed by using the presented ring models and 3-dimensional finite element method to verify accuracy of the presented equations of motion. Its results are compared and discussed.

• Journal of the Korean Society of Surveying, Geodesy, Photogrammetry and Cartography
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• v.13 no.2
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• pp.285-289
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• 1995

This paper describes the determination of geoid using height data measured by GPS and Spirit Levelling. The GPS data of the 88 stations were used to determine the geoid undulation (N) which can be easily obtained by subtracting the orthometric height(H) from the ellipsoidal height(h). From the geoid undulation (N) calculated at each station mentioned above, geoid plots with a contour interval of 0.25 m were drawn using two interpolation methods. The following interpolation methods were applied and compared with each other: Minimum Curvature Method and Least Squares Fitted Plane. Comparison between geometric geoid and gravimetric geoid undulation by FFT technique was carried out.

• Structural Engineering and Mechanics
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• v.39 no.2
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• pp.169-186
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• 2011

This paper is devoted to the development of the equations which describe the elastic response of a curved laminate subjected to in-plane loads and bending moments. Similar to the classic $6{\times}6$ ABD matrix constitutive relation of a flat laminate, a new $6{\times}6$ matrix constitutive relation between force resultants, moment resultants, mid-plane strains and deformed curvatures for a curved laminate is formulated. This curved lamination theory will provide the fundamental basis for the analyses of curved laminated structures. The stress predictions by the present curved lamination theory are compared to those by the curved laminate analysis that neglected the nonlinear terms in the derivation of the constitutive relation. The results show that the curved laminate analysis that neglected the nonlinear terms cannot reflect the effect of curvature and can no longer predict the stresses accurately as the curvature becomes noticeable. In this paper, a curved lamination theory that retains the nonlinear terms and, therefore, accounts for the effect of the non-flat geometry of the structure will be developed.

• Journal of the Korean Society for Precision Engineering
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• v.34 no.1
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• pp.65-72
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• 2017

The goal of this paper is to investigate the effects of out-of-plane deposition angle on product characteristics of a UV photo-curing process. Specimens are manufactured from a commercialized UV photo-curing machine, the NOBEL V1.0. The influence of the out-of-plane deposition angle of the specimen on surface characteristics, including morphology of the sloped surface, pick-to-pick distance of convex region, and roughness of the sloped surface, is examined via the observation of the sloped surface. In addition, the influence of the radius of curvature of the specimen on the surface roughness of the sloped surface is evaluated. The effects of the out-of-plane deposition angle on impact strength of specimens are investigated via Izod impact experiments. Finally, we discuss the influence of the out-of-plane deposition angle on failure characteristics of specimens for impact loads.

• Journal of the Korean Mathematical Society
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• v.43 no.5
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• pp.1129-1142
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• 2006

In this paper, we estimate area of tube in a CBA(0)-space with extendible geodesics. As its application, we obtain an upper bound of systole in a nonsimply connected space of nonpositive curvature. Also, we determine a relative growth of a ball in a CBA(0)-space to the corresponding ball in Euclidean plane.