• Journal of the Korean Mathematical Society
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• v.43 no.2
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• pp.413-424
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• 2006

Let $\Gamma$ be a bounded rotation (BR) curve without cusps in the complex plane $\mathbb{C}$ and let G := int $\Gamma$. We prove that the rate of convergence of the interpolating polynomials based on the zeros of the Faber polynomials $F_n\;for\;\bar G$ to the function of the reflexive Smirnov-Orlicz class $E_M (G)$ is equivalent to the best approximating polynomial rate in $E_M (G)$.

• Journal of the Korean Mathematical Society
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• v.40 no.6
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• pp.977-998
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• 2003

Let k be an imaginary quadratic field, η the complex upper half plane, and let $\tau$ $\in$ η $textsc{k}$, p = $e^{{\pi}i{\tau}}$. In this article, using the infinite product formulas for g2 and g3, we prove that values of certain infinite products are transcendental whenever $\tau$ are imaginary quadratic. And we derive analogous results of Berndt-Chan-Zhang ([4]). Also we find the values of (equation omitted) when we know j($\tau$). And we construct an elliptic curve E : $y^2$ = $x^3$ ＋ 3 $x^2$ ＋ {3-(j/256)}x ＋ 1 with j = j($\tau$) $\neq$ 0 and P = (equation omitted) $\in$ E.

• Structural Engineering and Mechanics
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• v.13 no.6
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• pp.713-730
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• 2002

This paper presents a finite element approach for determining the natural frequencies for planar inclined arches of various shapes vibrating in three-dimensional space. The profile of inclined arches, represented by undeformed centriodal axis of cross-section, is defined by the equation of plane curves expressed in the rectangular coordinates which are : circular, parabolic, sine, elliptic, and catenary shapes. In free vibration state, the arch is slightly displaced from its undeformed position. The linear relationship between curvature-torsion and axial strain is expressed in terms of the displacements in three-dimensional space. The finite element discretization along the span length is used rather than the total are length. Numerical results for arches of various shapes are given and they are in good agreement with those reported in literature. The natural frequency parameters and mode shapes are reported as functions of two nondimensional parameters: the span to cord length ratio (e) and the rise to cord length ratio (f).

• Journal of Ocean Engineering and Technology
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• v.21 no.5
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• pp.25-32
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• 2007

The piled-raft foundation, a new design concept, is one of the most effective kinds of foundation for reducing settlement of structures. An alternative piled-raft system with disconnection cap and a sand cushion between the pile and raft was also investigated to compare the influence of ultimate bearing capacity and settlement. Load-settlement relation curves were used to evaluate the ultimate bearing capacity. In the numerical analyses, a plane strain elasto-plastic finite element model (Mohr-Coulomb model) was used to present the response of the piled-raft foundation.

• Proceedings of the Korean Society For Composite Materials Conference
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• 2003.10a
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• pp.71-74
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• 2003

The cell modeling homogenization method to derive the constitutive equation considering the microstructures of the fiber reinforced composites has been previously developed for composites with simple microstructures such as 2D plane composites and 3D rectangular shaped composites. Here, the method has been further extended for 3D circular braided composites, utilizing B-spline curves to properly describe the more complex geometry of 3D braided composites. For verification purposes, the method has been applied for orthotropic elastic properties of the 3D circular braided glass fiber reinforced composite, in particular for the tensile property. Prepregs of the specimen have been fabricated using the 3D braiding machine through RTM (resin transfer molding) with epoxy as a matrix. Experimentally measured uniaxial tensile properties agreed well with predicted values obtained fer two volume fractions.

• Journal of the Korean Society of Manufacturing Technology Engineers
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• v.8 no.3
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• pp.100-106
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• 1999

Owing to the complexity of electrical discharge machining (EDM) phenomenon, it is very difficult to determine optimal machining parameters fer improving machining performance. This paper proposes a methodology for determining optimal electrical discharge machining parameters, which is maintaining suitable current density for increasing productivity or improving surface roughness. Machining area is closely related on optimal machining parameters in electrical discharge machining process, so calculation of machining area is needed in order to determine optimal machining parameters. In this study machining area, which is corresponding to the machining position, is calculated from intersection curves between the tool surface and a horizontal plane.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 2001.04a
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• pp.426-429
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• 2001

Many various products are manufactured which have sculptured surfaces recently. Constructing surface of these models is required technique called reverse engineering. In reverse engineering, a product which has sculptured surfaces is measured and we create surface model to acquire complete model data of object. Measured point data needs preprocess and sampling. Next a set of point data in a plane fit section curve. At last, surface is generated by fitting to section curves. Here we uses sweep surface. Sweep surface is compatible fitting CAD model to drawing. This paper discusses converting approximation of NURBS surface as a standard surface.

• Journal of the Korean Society for Precision Engineering
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• v.24 no.8 s.197
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• pp.97-107
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• 2007

The present CNC machining system if without any CAM software has been limited to 2D or 2.5D plane cut using lines, arcs and curves. If the CNC is equipped with a surface interpolation module and a surface reorganizing module inside it, we can easily try 3D surface machining without aid of CAM software. The existing NURBS surface interpolator is simple and direct to use for a unit surface. However, it enables only machining of each reference surface individually even when machining a simple composite surface. In this paper, we propose a method which can unify and reorganize various reference surfaces with a newly defined NURBS surface cycle command: a multi-repetitive cycle command such as in a CNC turning center. We also introduce a reorganizing rule for reference surfaces using NURBS properties. The usefulness of the proposed method is verified through computer simulation.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2000.06a
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• pp.319-324
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• 2000

Sound insulation effect of periodically arranged circular rods is studied by numerical method (BEM) and model experiment in anechoic room. Five different cylinder groups of diameter from 48 mm to 27 mm are arranged, where each group consists of 5 rows of identical rods and area ratio is kept almost the same as 60%. Comparisons of results by BEM and experiment show the band gap frequency ranges are qualitatively in agreement, while experiments gives higher attenuations. Frequency shifted attenuations (BEM results) by first group (${\phi}$48), third group (${\phi}$34) and fifth group (${\phi}$27) show that attenuation curves are in reasonable agreements for both plane wave and point source.

• Journal of the Korean Society of Safety
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• v.15 no.4
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• pp.15-19
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• 2000

The exact estimation of the ductile crack growth in a thin sheet would be needed in part of the commercial transport aircraft industry fields. A 2-dimensional elastic plastic finite element analysis was carried out to simulate a stable crack extension in a thin sheet 2024 aluminium alloy. Two kinds of crack modeling were used to evaluate curves of the stable crack extension. And then CTOA(crack tip opening angle) and CTED(crack tip energy density) were calculated in order to determine whether they can be used as useful crack extension criterions in a thin sheet. Results indicate that stable crack extension behaviors were simulated well and CTED is more admirable even though CTOA also is reasonable as a criterion for a stable crack extension in a thin 2024 aluminium alloy sheet.