• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.5 no.1
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• pp.47-53
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• 2001

A problem of approximation by irrational splines is considered. These splines have a constant curvature between interpolation nodes and need only one additional boundary condition for derivatives, which should be set only at one of two boundary nodes, that is impossible for usual polynomial splines required boundary conditions at both boundary nodal points. Some estimations for numerical differentiation and rounding error analysis are presented.

• Journal of KIISE:Computer Systems and Theory
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• v.33 no.10
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• pp.768-776
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• 2006

Given an unstructured point set, we use an MLS (melting least-squares) approximation to estimate the local curvatures and their derivatives at a point by means of an approximation surface Then, we compute neighbor information using a Delaunay tessellation. feature points can then be detected as zero-crossings, and connected using curvature directions. Also this approach has a fast computation time than previous methods, which based on triangle meshes. We demonstrate our method on several large point-sampled models, rendered by point-splatting, on which the feature lines are rendered with line width determined from curvatures.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.19 no.4 s.74
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• pp.441-447
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• 2006

This paper deals with the application of the numerical differentiation in the structural analyses. Derivative values of the geometry of structure are definitely needed for analysing the structural behavior. In this study, free vibration problems of arches are chosen for verifying the numerical differential technique in the structural analyses. The curvature parameters composed with the derivatives of arch geometry obtained herein are quite agreed with those of analytical method. Also, natural frequencies with curvature parameters obtained by using the forward fifth polynomial method are quite agreed with those in the literature. The numerical differentiation technique can be practically utilized in the structural analyses.

• The Journal of Korean Association of Computer Education
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• v.11 no.4
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• pp.85-93
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• 2008

This paper proposes a method for generating low-level geometric models with retaining salient features during decimation. Our method employs feature extraction technique for extracting feature lines defined via curvature derivatives on the model (we divide features into ridges and valleys). We add the extraction method to simplification technique (Feature Quadric Error Metric) for making coarse model with features. This paper clearly shows that experimental results have better quality and smaller geometric error than previous methods.

• Journal of the Korean Mathematical Society
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• v.58 no.4
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• pp.895-920
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• 2021

In this paper, first we introduce the full expression of the Riemannian curvature tensor of a real hypersurface M in the complex quadric Q^m from the equation of Gauss and some important formulas for the structure Jacobi operator R_ξ and its derivatives ∇R_ξ under the Levi-Civita connection ∇ of M. Next we give a complete classification of Hopf real hypersurfaces with Reeb parallel structure Jacobi operator, ∇_ξR_ξ = 0, in the complex quadric Q^m for m ≥ 3. In addition, we also consider a new notion of 𝒞-parallel structure Jacobi operator of M and give a nonexistence theorem for Hopf real hypersurfaces with 𝒞-parallel structure Jacobi operator in Q^m, for m ≥ 3.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2008.04a
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• pp.216-221
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• 2008

Shape design optimization for linear elasticity problem is performed using isogeometric analysis method. In many design optimization problems for real engineering models, initial raw data usually comes from CAD modeler. Then designer should convert this CAD data into finite element mesh data because conventional design optimization tools are generally based on finite element analysis. During this conversion there is some numerical error due to a geometry approximation, which causes accuracy problems in not only response analysis but also design sensitivity analysis. As a remedy of this phenomenon, the isogeometric analysis method is one of the promising approaches of shape design optimization. The main idea of isogeometric analysis is that the basis functions used in analysis is exactly same as ones which represent the geometry, and this geometrically exact model can be used shape sensitivity analysis and design optimization as well. In shape design sensitivity point of view, precise shape sensitivity is very essential for gradient-based optimization. In conventional finite element based optimization, higher order information such as normal vector and curvature term is inaccurate or even missing due to the use of linear interpolation functions. On the other hands, B-spline basis functions have sufficient continuity and their derivatives are smooth enough. Therefore normal vector and curvature terms can be exactly evaluated, which eventually yields precise optimal shapes. In this article, isogeometric analysis method is utilized for the shape design optimization. By virtue of B-spline basis function, an exact geometry can be handled without finite element meshes. Moreover, initial CAD data are used throughout the optimization process, including response analysis, shape sensitivity analysis, design parameterization and shape optimization, without subsequent communication with CAD description.

• Journal of the Korean Association of Geographic Information Studies
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• v.21 no.1
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• pp.106-114
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• 2018

DEM(Digital Elevation Model) are now easily produced with advancing remote sensing technology. Depending on desired task, UAV can produce high resolution DEM. But high resolution comes with issues of data storage and processing time and cost. To check the effect of DEM resolution, this study compares six geomorphological parameters derived from different resolution DEM in a test area around Chuncheon, Korea. The comparison analysis was based on statistics of each derivatives of slope, curvature, flow direction, flow accumulation, flow length and basin. As a result, it was found that DEM remained unchanged and so did the flow accumulation area. However, slope, curvature, flow length and basin numbers were decreased with the normalization of increasing pixel size. DEM resolution should be carefully selected depending on the precision of application required.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.17 no.2 s.119
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• pp.185-193
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• 2007

This paper deals with the application of the numerical differentiation using the differential quadrature(DQ) in the curved member-like structural analysis. Derivative values of the geometry of structure are definitely needed for analyzing the structural behavior. For verifying the numerical differentiation using DQ, free vibration problems of arch are selected. Terms of curvature composed with the derivatives of arch geometry obtained herein are agreed quite well with exact values obtained explicitly. Natural frequencies subjected to terms of curvature obtained by DQ are agreed quite well with those in the literature. The numerical differentiation using DQ can be practically utilized in the structural analysis.

• Smart Structures and Systems
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• v.14 no.4
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• pp.569-594
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• 2014

Damage detection methods based on modal analysis have been widely studied in recent years. However the calculation of mode shapes in real structures can be time consuming and often requires dedicated software programmes. In the present paper the combined application of proper orthogonal decomposition and gapped smoothing method to structural damage detection is presented. The first is used to calculate the dynamic shapes of a damaged structural element using only the time response of the system while the second is used to derive a reference baseline to which compare the data coming from the damaged structure. Experimental verification is provided for a beam case while numerical analyses are conducted on plates. The introduction of a stiffener on a plate is investigated and a method to distinguish its influence from that of a defect is presented. Results highlight that the derivatives of the proper orthogonal modes are more effective damage indices than the modes themselves and that they can be used in damage detection when only data from the damaged structure are available. Furthermore the stiffened plate case shows how the simple use of the curvature is not sufficient when analysing complex components. The combined application of the two techniques provides a possible improvement in damage detection of typical aeronautical structures.