• Title/Summary/Keyword: geodesic line

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Geodesic Shape Finding Algorithm for the Pattern Generation of Tension Membrane Structures (막구조물의 재단도를 위한 측지선 형상해석 알고리즘)

  • Lee, Kyung-Soo;Han, Sang-Eul
    • 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.

A CHARACTERIZATION OF MAXIMAL SURFACES IN TERMS OF THE GEODESIC CURVATURES

  • Eunjoo Lee
    • Journal of the Chungcheong Mathematical Society
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    • v.37 no.2
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    • pp.67-74
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    • 2024
  • Maximal surfaces have a prominent place in the field of differential geometry, captivating researchers with their intriguing properties. Bearing a direct analogy to the minimal surfaces in Euclidean space, investigating both their similarities and differences has long been an important issue. This paper is aimed to give a local characterization of maximal surfaces in 𝕃3 in terms of their geodesic curvatures, which is analogous to the minimal surface case presented in [8]. We present a classification of the maximal surfaces under some simple condition on the geodesic curvatures of the parameter curves in the line of curvature coordinates.

A Study on Cutting Pattern Generation of Membrane Structures by Using Geometric Line (막 구조물의 측지선을 이용한 재단도 생성에 관한 연구)

  • Ahn, Sang-Gil;Shon, Su-Deok;Kim, Seung-Deog
    • Proceeding of KASS Symposium
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    • 2005.05a
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    • pp.125-132
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    • 2005
  • Membrane structures, a kind of lightweight soft structural system, are used for spatial structures. The material property of the membrane has strong axial stiffness, but little bending stiffness. The design procedure of membrane structures are needed to do shape finding, stress-deformation analysis and cutting pattern generation. In shape finding, membrane structures are unstable structures initially. These soft structures need to be introduced initial stresses because of its initial unstable state, and it happens large deformation phenomenon. And also there are highly varied in their size, curvature and material stiffness. So, the approximation inherent in cutting pattern generation methods is quite different. Therefore, in this study, to find the structural shape after large deformation caused by Initial stress, we need the shape analysis considering geometric nonlinear ten And the geodesic line on surface of initial equilibrium shape and the cutting pattern generation using the geodesic line is introduced.

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A Study on The Search of Geodesic Line and Cuting Pattern Generation of Membrane Structures (막 구조물의 측지선 탐색과 재단도 작성에 관한 연구)

  • Jeon Jin-Hyung;Jeong Eul-Seok;Shon Su-Deok;Kim Seung-Deog
    • Proceedings of the Computational Structural Engineering Institute Conference
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    • 2006.04a
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    • pp.325-332
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    • 2006
  • Membrane structures, a kind of lightweight soft structural system, are used for spatial structures. The design procedure of membrane structures are needed to do shape finding, stress-deformation analysis and cutting pattern generation, because the material property has strong axial stiffness, but little bending stiffness. The problem of cutting pattern is highly varied in their size, curvature and material stiffness. So, the approximation inherent in cutting pattern generation methods is quite different. Therefore the ordinary computer software of structural analysis & design is not suitable for membrane structures. In this study, we develop the program for cutting pattern generation using geodesic line, and investigate the result of example's cutting pattern in detail.

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A Study on the Geodesic Line Algorithms for Cutting Pattern Generation of Membrane Structures (막 구조물의 재단도 생성을 위한 지오데식 라인 알고리즘에 관한 연구)

  • 배종효;한상을
    • Proceedings of the Computational Structural Engineering Institute Conference
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    • 2000.04b
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    • pp.357-364
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    • 2000
  • The three main processes involved in the design of stressed membrane surface are surface form-finding, stress analysis and cutting pattern generation. The last process, cutting pattern generation, is considered as a very important procedure in the aspect of the practical design for the fabric membrane surface. In this paper, The cutting pattern generation technique using the geodesic line algorithms is first introduced. And the numerical examples resulting from this technique are presented. Cable elements are used for the approximating membrane surface and two kinds of model, square line and central line model, are used in pattern generation. Finally, a number of different cutting pattern generation for the same membrane surface is carried out and the numerical results are compared each

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A Study on The Cutting Pattern Generation of Membrane Structures and Loss Ratio of Febrics According to the Curvature (막구조물의 재단도 작성과 곡률 변화에 따른 손실률에 관한 연구)

  • Jeon, Jin-Hyung;Jeong, Eul-Seok;Shon, Su-Deok;Kim, Seung-Deog
    • Proceeding of KASS Symposium
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    • 2006.05a
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    • pp.205-213
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    • 2006
  • Membrane structures, a kind of lightweight soft structural system, are used for spatial structures. The design procedure of membrane structures are needed to do shape finding, stress-deformation analysis and cutting pattern generation, because the material property has strong axial stiffness, but little bending stiffness. The problem of cutting pattern is highly varied in their size, curvature and material stiffness. So, the approximation inherent in cooing pattern generation methods is quite different. Therefore the ordinary computer software of structural analysis & design is not suitable for membrane structures. In this study, we develop the program for cutting pattern generation using geodesic line, and investigate the result of example's cutting pattern in detail.

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A STUDY OF THE TUBULAR SURFACES ACCORDING TO MODIFIED ORTHOGONAL FRAME WITH TORSION

  • Gulnur SAFFAK ATALAY
    • Honam Mathematical Journal
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    • v.46 no.2
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    • pp.279-290
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    • 2024
  • In this study, tubular surfaces were introduced according to the modified orthogonal frame defined at the points where the torsion is different from zero in the 3-dimensional Euclidean space. First, the relations between the Frenet frame and the modified orthogonal frame with torsion are given. Then, the singularity, Gaussian curvature, mean curvature and basic forms of the tubular surface given according to the modified orthogonal frame with torsion were calculated. In addition, the conditions for the parameter curves of the tubular surface to be geodesic, asymptotic and line of curvature were examined. Finally, tubular surface examples based on both the Frenet frame and the modified orthogonal frame with torsion were given to support the study.

A Study on The Cutting Pattern Generation of Membrane Structures and The Loss-Ratio of Material (막 구조물의 재단도 작성과 막재의 손실률에 관한 연구)

  • Shon, Su-Deok;Jeong, Eul-Seok;Kim, Seung-Deog
    • Journal of Korean Association for Spatial Structures
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    • v.6 no.1 s.19
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    • pp.117-127
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    • 2006
  • Membrane structures, a kind of lightweight soft structural system, are used for spatial structures. The design procedure of membrane structures are needed to do shape finding, stress-deformation analysis and cutting pattern generation, because the material property has strong axial stiffness, but little bending stiffness. The problem of cooing pattern is highly varied in their size, curvature and material stiffness. So, the approximation inherent in cutting pattern generation methods is quite different. Therefore the ordinary computer software of structural analysis & design is not suitable for membrane structures. In this study, we develop the program for cooing pattern generation using geodesic line, and investigate the result of example's cooing pattern in detail.

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METRIC FOLIATIONS ON HYPERBOLIC SPACES

  • Lee, Kyung-Bai;Yi, Seung-Hun
    • Journal of the Korean Mathematical Society
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    • v.48 no.1
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    • pp.63-82
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    • 2011
  • On the hyperbolic space $D^n$, codimension-one totally geodesic foliations of class $C^k$ are classified. Except for the unique parabolic homogeneous foliation, the set of all such foliations is in one-one correspondence (up to isometry) with the set of all functions z : [0, $\pi$] $\rightarrow$ $S^{n-1}$ of class $C^{k-1}$ with z(0) = $e_1$ = z($\pi$) satisfying |z'(r)| ${\leq}1$ for all r, modulo an isometric action by O(n-1) ${\times}\mathbb{R}{\times}\mathbb{Z}_2$. Since 1-dimensional metric foliations on $D^n$ are always either homogeneous or flat (that is, their orthogonal distributions are integrable), this classifies all 1-dimensional metric foliations as well. Equations of leaves for a non-trivial family of metric foliations on $D^2$ (called "fifth-line") are found.