• Journal of Korean Society of Steel Construction
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• v.22 no.1
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• pp.33-42
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• 2010

Patterning with a geodesic line is essential for economical or efficient usage of membrane materialsin fabric tension membrane structural engineering and analysis. The numerical algorithm to determine the geodesic line for membrane structures is generally classified into two. The first algorithm finds a non-linear shape using a fictitious geodesic element with an initial pre-stress, and the other algorithm is the geodesic line cutting or searching algorithm for arbitrarily curved 3D surface shapes. These two algorithms are still being used only for the three-node plane stress membrane element, and not for the four-node element. The lack of a numerical algorithm for geodesic lines with four-node membrane elements is the main reason for the infrequent use of the four-node membrane element in membrane structural engineering and design. In this paper, a modified numerical algorithm is proposed for the generation of a geodesic line that can be applied to three- or four-node elements at the same time. The explicit non-linear static Dynamic Relaxation Method (DRM) was applied to the non-linear geodesic shape-finding analysis by introducing the fictitiously tensioned 'strings' along the desired seams with the three- or four-node membrane element. The proposed algorithm was used for the numerical example for the non-linear geodesic shape-finding and patterning analysis to demonstrate the accuracy and efficiency, and thus, the potential, of the algorithm. The proposed geodesic shape-finding algorithm may improve the applicability of the four-node membrane element for membrane structural engineering and design analysis simultaneously in terms of the shape-finding analysis, the stress analysis, and the patterning analysis.

• Structural Engineering and Mechanics
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• v.39 no.1
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• pp.93-113
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• 2011

The explicit nonlinear dynamic relaxation method (DRM) is applied to the nonlinear geodesic shape finding analysis by introducing fictional tensioned 'strings' along the desired seams with a three or four-node membrane element. A number of results from the numerical example for the nonlinear geodesic shape finding and patterning analysis are obtained by the proposed method to demonstrate the accuracy and efficiency of the developed method. Therefore, the proposed geodesic shape finding algorithm may improve the applicability of a four-node membrane element to membrane structural engineering and design analysis simultaneously for the shape finding, stress, and patterning analysis.

• Proceedings of the Korean Society For Composite Materials Conference
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• 2003.10a
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• pp.179-182
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• 2003

This research aims to establish an optimal design method of filament wound structures. So far, most design and manufacturing of filament wound structures have been based on manufacturing experiences, and there is no established design rule. In this research, possible winding patterns considering the windability and the slippage between fiber and mandrel surface were calculated using the semi-geodesic path algorithm. In addition, finite element analyses using a commercial code, ABAQUS, were performed to predict the behavior of filament wound structures. On the basis of the semi-geodesic path algorithm and the finite element analysis method, filament wound structures were designed using the genetic algorithm.

• Proceedings of the Korean Society For Composite Materials Conference
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• 2000.04a
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• pp.211-214
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• 2000

Filament wound pressure vessels have been studied for the efficient design tool to consider the variation of fiber angles through-the thickness direction. Filament winding patterns were simulated from semi-geodesic fiber path equation to calculate fiber path on arbitrary surface. Finite element analyses were performed considering fiber angle variation in longitudinal and thickness directions by ABAQUS. For the finite element modeling of the pressure tank, the 3-dimensional layered solid element was utilized. From the stress results of pressure tanks, maximum stress criterion in transverse direction was applied to modify material properties for failed region. In the end of each load increment, resultant layer stresses were compared with a failure criterion and properties were reduced to 1/10 for a failed layer. Results of progressive failure analysis were compared with two experimental data.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2003.10a
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• pp.340-347
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• 2003

The aim of regularization of a structural configuration is to obtain a structure that consists of elements with identical or nearly identical length. And it is also possible to modify the configuration in a manner that the size of the elements vary in accordance with a specified pattern. For practical purpose, geodesic dome is cut off at a suitable place in order to make it fit on horizontal. Inevitably this pattern effects a change of element lengths. The purpose of this study is to verify a method for regularization of structural configuration by genetic algorithms and modify the element lengths of the dome. As a result of regularization of domes with various rise-span ratio, modified configurations have more regular element lengths and are more economical than initial configurations.

• The Pure and Applied Mathematics
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• v.30 no.1
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• pp.83-108
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• 2023

We find geodesics on a surface numerically by using Runge-Kutta method with Python.

• Composites Research
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• v.13 no.2
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• pp.51-60
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• 2000

Filament wound pressure vessels have been studied for the efficient design tool to consider the variation of fiber angles through-the thickness direction. Filament winding patterns were simulated from semi-geodesic fiber path equation to calculate fiber path on arbitrary surface. Finite element analyses were performed considering fiber angle variation in longitudinal and thickness directions by ABAQUS. For the finite element modeling of the pressure tank, the 3-dimensional layered solid element was utilized. From the stress results of pressure tanks, maximum stress criterion in transverse direction was applied to modify material properties for failed region. In the end of each load increment, resultant layer stresses were compared with a failure criterion and properties were reduced to 1/10 for a failed layer. Results of progressive failure analysis were compared with two experimental data.

• Communications of the Korean Mathematical Society
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• v.35 no.3
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• pp.917-925
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• 2020

It has been shown that the geometric mean A#B of positive definite Hermitian matrices A and B is the maximal element X of Hermitian matrices such that $$\(\array{A&X\\X&B}\)$$ is positive semi-definite. As an extension of this result for the 2 × 2 block matrix, we consider in this article the block matrix [[A#w_ijB]] whose (i, j) block is given by the Riemannian geodesics of positive definite Hermitian matrices A and B, where w_ij ∈ ℝ for all 1 ≤ i, j ≤ m. Under certain assumption of the Loewner order for A and B, we establish the equivalent condition for the parameter matrix ω = [w_ij] such that the block matrix [[A#w_ijB]] is positive semi-definite.

• Journal of the Institute of Electronics Engineers of Korea SP
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• v.37 no.1
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• pp.37-48
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• 2000

In this paper, we propose a new connected operator Using morphological grayscale reconstruction for region-based coding First, an effective method of reference-image creation lis proposed, which is based on the Size as well as the contrast. This improves the performance of simplification, because It preserves perceptually important components and removes unnecessary components The conventional connected operators are good for removing small regions, but have a serious drawback for low-contrast regions that are larger than the structuring element. That is, when the conventional connected operators are applied to tills region, the simplification becomes less effective or several meaningful regions are merged to one region to avoid this, the conventional geodesic dilation is modified to propose an adaptive operator to reduce the effect of inappropriate propagation, pixels reconstructed to the original values are excluded m the dilation operation Experimental results have shown that the proposed algorithm achieves better performance In terms of the reconstruction of flat zones. The Picture quality has also been improved by about 7dB, compared to the conventional methods.

• Proceedings of the Korean Society of Broadcast Engineers Conference
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• 1999.11b
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• pp.3-8
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• 1999

In this paper, we propose a new connected operator using morphological grayscale reconstruction for region-based coding. First, an effective method of reference-image creation is proposed, which is based on the size as well as the contrast. The conventional connected operators are good for removing small regions, but have a serious drawback for low-contrast regions that are larger than the structuring element. That is, when the conventional connected operators are applied to these regions. the simplification becomes less effective or several meaningful regions are merged to one region. To avoid this, the conventional geodesic dilation is modified to propose an adaptive operator. To reduce the effect of inappropriate propagation, pixels reconstructed to the original values are excluded in the dilation operation. Experimental results have shown that the proposed algorithm achieves better performance in terms of the reconstruction of flat zones. The picture quality has also been improved by about 7dB, compared to the conventional methods.