• Transactions of the Korean Society of Mechanical Engineers
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• v.12 no.5
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• pp.1097-1103
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• 1988

This paper deals with surface crack behavior and the fatigue life prediction of notched specimens using the relation between surface crack length, a, and the cycle ratio, $N/N_{f}$. From the $a-N\;/\;N_{f}$ curves, UC(the upper limit curve), LC(the lower limit curve) and MC(the middle limit curve) were assumed and utilized to predict the fatigue life and crack growth rate. The data computed from the three assumed curves were compared with the experimental data. It has been found that in the stable crack growth region ($N/N_{f}=0.3-0.8$) fatigue life can be predicted within 20% errors. Using the characteristics of $a-N\;/\;N_{f}$ curve, it is possible to predict the $da/dN-K_{max}$ curve, the $da/dN-{\Delta}K_{{\varepsilon}_t}$ curve, and the $S-N_{f}$ curve.

• Bulletin of the Korean Mathematical Society
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• v.47 no.6
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• pp.1163-1170
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• 2010

We study finite type curve in $R^3$(-3) which lies in a cylinder $N^2$(c). Baikousis and Blair proved that a Legendre curve in $R^3$(-3) of constant curvature lies in cylinder $N^2$(c) and is a 1-type curve, conversely, a 1-type Legendre curve is of constant curvature. In this paper, we will prove that a 1-type curve lying in a cylinder $N^2$(c) has a constant curvature. Furthermore we will prove that a curve in $R^3$(-3) which lies in a cylinder $N^2$(c) is finite type if and only if the curve is 1-type.

• Kyungpook Mathematical Journal
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• v.58 no.1
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• pp.117-135
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• 2018

The orthogonal trajectories of the first tangents of the curve are called the involutes of x. The hyperspheres which have higher order contact with a curve x are known osculating hyperspheres of x. The centers of osculating hyperspheres form a curve which is called generalized evolute of the given curve x in n-dimensional Euclidean space ${\mathbb{E}}^n$. In the present study, we give a characterization of involute curves of order k (resp. evolute curves) of the given curve x in n-dimensional Euclidean space ${\mathbb{E}}^n$. Further, we obtain some results on these type of curves in ${\mathbb{E}}^3$ and ${\mathbb{E}}^4$, respectively.

• Communications of the Korean Mathematical Society
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• v.12 no.1
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• pp.17-25
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• 1997

We estimate the genus g(N) of modular curve $X_0^0(N)$ and show that g(N) = 0 if and only if $1 \leq N \leq 5$.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 2006.05a
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• pp.429-430
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• 2006

To estimate the fatigue life of flange-shaft assembly, fatigue test for flange material and bending fatigue test for flange-shaft assembly were conducted. Also, finite element analysis for flange-shaft assembly was conducted. Then, we have changed the obtained P-N curve to S-N curve using the finite element analysis results which were stress values at the location of fracture. The S-N curve of flange material itself was almost consistent with that of flange-shaft assembly, so it seems that the fatigue life of flange-shaft assembly could be estimated by using S-N curve for flange material and the stress at the location of fracture calculated by finite element methods.

• Kyungpook Mathematical Journal
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• v.56 no.3
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• pp.1003-1016
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• 2016

In this paper, we introduce a new kind of slant helix for null curves called null $W_n$-slant helix and we give a definition of new harmonic curvature functions of a null curve in terms of $W_n$ in (n + 2)-dimensional Lorentzian space $M^{n+2}_1$ (for n > 3). Also, we obtain a characterization such as: "The curve ${\alpha}$ s a null $W_n$-slant helix ${\Leftrightarrow}H^{\prime}_n-k_1H_{n-1}-k_2H_{n-3}=0$" where $H_n,H_{n-1}$ and $H_{n-3}$ are harmonic curvature functions and $k_1,k_2$ are the Cartan curvature functions of the null curve ${\alpha}$.

• Proceedings of the KSME Conference
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• 2001.06a
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• pp.217-222
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• 2001

For the life evaluating of notched members, it is the best way that performing the real fatigue test of structure containing notch. But this method required generally much times and costs to evaluate fatigue life. So, generally we use the modified S-N curve or several methods to predict fatigue life. In this study, crack initiation life was evaluated by fatigue testing the SAE keyhole specimen and smooth specimen made of Al 7075-T6 alloys using the constant load then obtained S-N curve of smooth specimen and P-N curve of SAE keyhole specimen. And, fatigue lives of keyhole specimen are predicted using some life prediction methods (Nominal range I method, Nominal range II method, FEM analysis) for investigating experimented results, and that were compared with experimental data. Predicted fatigue lives by FEM analysis were corresponded with experimental data between 1/3times and 3times on the whole, and predicted fatigue lives using modified S-N curve (Nominal range I method, Nominal range II method) were nonconservative compared with that of FEM analysis.

• Structural Engineering and Mechanics
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• v.53 no.5
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• pp.881-896
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• 2015

In this study, a method for fatigue performance estimation of deepwater steel catenary riser (SCR) under short-term vortex-induced vibration was investigated for selected S-N curves. General tendency between S-N curve capacity and fatigue performance was analysed. SCRs are generally used to transport produced oil and gas or to export separated oil and gas, and are exposed to various environmental loads in terms of current, wave, wind and others. Current is closely related with VIV and it affects fatigue life of riser structures significantly. In this regards, the process of appropriate S-N curve selection was performed in the initial design stage based on the scale of fabrication-related initial imperfections such as welding, hot spot, crack, stress concentration factor, and others. To draw the general tendency, the effects of stress concentration factor (SCF), S-N curve type, current profile, and three different sizes of SCRs were considered, and the relationship between S-N curve capacity and short-term VIV fatigue performance of SCR was derived. In case of S-N curve selection, DNV (2012) guideline was adopted and four different current profiles of the Gulf of Mexico (normal condition and Hurricane condition) and Brazil (Amazon basin and Campos basin) were considered. The obtained results will be useful to select the S-N curve for deepwater SCRs and also to understand the relationship between S-N curve capacity and short-term VIV fatigue performance of deepwater SCRs.

• Korean Journal of Computational Design and Engineering
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• v.11 no.4
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• pp.246-255
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• 2006

Ribs and fans are interesting geometric entities that are derived from an ordinary $B\'{e}zier$ curve or surface. A rib itself is a $B\'{e}zier$ curve or surface with a lower degree than the given curve or surface. A fan is a vector field whose degree is also lower than its origin. First, we present methods to transform the control points of a $B\'{e}zier$ curve or surface into the control points and vectors of its ribs and fans. Then, we show that a $B\'{e}zier$ curve of degree n is decomposed into a rib of degree (n-1), a fan of degree (n-2), and a scalar function of degree 2. We also show that a $B\'{e}zier$ surface of degree (m, n) is decomposed into a rib of degree (m-1, n-1) and three fans of degrees (m-1, n-2), (m-2, n-1), and (m-2, n-2), respectively. In addition, the lengths of the fans are further controlled by scalar functions of degree 2 and (2, 2). We present relevant notations and definitions, introduce theories, and present some of design examples.

• Journal of KIISE:Computer Systems and Theory
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• v.36 no.1
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• pp.21-25
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• 2009

In this paper, we study the problem to fit a piecewise-quadratic polynomial curve to points in the plane. The curve consists of quadratic polynomial segments and two points are connected by a segment. But it passes through a subset of points, and for the points not to be passed, the error between the curve and the points is estimated in $L^{\infty}$ metric. We consider two optimization problems for the above problem. One is to reduce the number of segments of the curve, given the allowed error, and the other is to reduce the error between the curve and the points, while the curve has the number of segments less than or equal to the given integer. For the number n of given points, we propose $O(n^2)$ algorithm for the former problem and $O(n^3)$ algorithm for the latter.