• Bulletin of the Korean Mathematical Society
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• v.40 no.1
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• pp.63-76
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• 2003

In this article, we establish relations between the sectional curvature and the shape operator and also between the k-Ricci curvature and the shape operator for a slant submanifold in a Sasakian space form of constant $\varphi-sectional$ curvature with arbitrary codimension.

• Journal of the Korean Mathematical Society
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• v.41 no.5
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• pp.795-808
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• 2004

In this article, we establish sharp relations between the sectional curvature and the shape operator and also between the k-Ricci curvature and the shape operator for a totally real submanifold in a locally conformal Kaehler space form of constant holomorphic sectional curvature with arbitrary codimension. mean curvature, sectional curvature, shape operator, k-Ricci curvature, locally conformal Kaehler space form, totally real submanifold.

• Bulletin of the Korean Mathematical Society
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• v.42 no.1
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• pp.189-201
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• 2005

In this article, we establish relations between the sectional curvature function K and the shape operator, and also relationship between the k-Ricci curvature and the shape operator for slant submanifolds in generalized complex space forms with arbitrary codimension.

• Communications of the Korean Mathematical Society
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• v.34 no.3
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• pp.863-879
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• 2019

In this paper we study the Myers' theorem for orientable Riemannian hypersurfaces under some restrictions on the mean curvature, the second-order mean curvature, or the divergence of the shape operator and give some estimates for the diameter of such hypersurfaces.

• Journal of the Korean Mathematical Society
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• v.44 no.3
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• pp.647-659
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• 2007

Relationships between the Ricci curvature and the squared mean curvature and between the shape operator associated with the mean curvature vector and the sectional curvature function for slant submanifolds of an S-space-form are proved, particularizing them to invariant and anti-invariant submanifolds tangent to the structure vector fields.

• Journal of the Korean Society for Precision Engineering
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• v.30 no.8
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• pp.815-823
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• 2013

The hot curvature forming of large aluminum plates is a process used to produce spherical liquefied natural gas (LNG) tanks. In this study, we describe a method to determine the optimum shape of blanks to minimize the root gap in the forming process. The method proposed in this study was applied to a small-scale model for thick plates with a curvature of 1500 mm and thickness of 6 mm. First, the shape of the curved shells was determined as the target shape, and then a coordinate transform was used to determine the optimum blank shape, which was then iteratively modified using the results of finite element method (FEM) simulations, including heat transfer, until the shape error was minimized. Experiments in forming using Al5083 thick plate were carried out, showing that the method can determine the optimum blank shape within an allowable root gap of 0.1 mm.

• Proceeding of EDISON Challenge
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• 2016.03a
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• pp.228-233
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• 2016

Auxetic material is a material which has negative Poisson's ratio(NPR). Auxetic material shows some distinctive property like high energy absorbing property and high shear modulus. Among these, synclastic curvature is very interesting characteristic. When synclastic-curvature-material bends, it changes its shape like dome, contrary to non-auxetic material which changes its shape like saddle(anticlastic). This distinctive property could make it easy to manufacture curved structure like nose cone or wing panel in aerospace engineering. In this study, we studied a quantitative analysis about synclastic curvature of re-entrant panel with finite element model. We suggested a concept 'Degree of Synclasticity(DOS)', which means a ratio of curvature of load-direction and load-orthogonal direction. We studied the variation of DOS with two factor, unit cell inner angle(${\theta}$) and load position angle(${\phi}$). DOS decreases as ${\theta}$ increases because the unit cell goes out of auxetic-shape. As ${\phi}$ varies, DOS changes in a large range. So proper optimization of ${\phi}$ would be needed for application.

• Journal for History of Mathematics
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• v.11 no.1
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• pp.42-46
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• 1998

Using Fermi coordinates and the principle curvature on the tubula hypersurfaces, we characterize space of constant sectional curvature by analysing the shape operator on the tubular hypersurfaces.

• Advances in Computational Design
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• v.7 no.1
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• pp.81-98
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• 2022

This study presents the application of two indices for the locating of cracks in Reinforced Concrete (RC) structures, as well as the development of their modified forms to overcome limitations. The first index is based on mode shape curvature and the second index is based on the fourth derivative of the mode shape. In order to confirm the indices' effectiveness, both eigenvalues coupled with nonlinear static analyses were carried out and the eigenvectors for two different damage locations and intensities of load were obtained from the finite element model of RC beams. The values of the damage-locating indices derived using both indices were then compared. Generally, the mode shape curvature-based index suffered from insensitivity when attempting to detect the damage location; this also applied to the mode shape fourth derivative-based index at lower modes. However, at higher modes, the mode shape fourth derivative-based index gave an acceptable indication of the damage location. Both the indices showed inconsistencies and anomalies at the supports. This study proposed modification to both indices to overcome identified flaws. The results proved that modified forms exhibited better sensitivity for identifying the damage location. In addition, anomalies at the supports were eliminated.

• Proceedings of the KSME Conference
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• 2001.06c
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• pp.94-99
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• 2001

Theoretical analysis using finite element method are peformed in order to clarify the formation of the flare-shape defect for multi-step tube sinking process. The parameters of concern were the friction between the tube and the die, and geometrical parameters, such as the die inclination angle, the diameters of the die entrance and exit, and the curvature at the corner of the die exit. The effect of the curvature at the comer of the die exit is dominant for determining the flare-shape defect. In order to minimize the flare-shape defect the curvature at the corner of the die exit should be increased up to a certain level(120mm). Using three-step tube sinking die sets which have different curvatures at the comer of the die exit, several numbers of tests were performed and its results are compared with that of theoretical analysis.