• Advances in biomechanics and applications
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• v.1 no.2
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• pp.85-93
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• 2014

In this paper, two procedures of enumerating the axial rotation are proposed using the unit sphere of the spherical rotation coordinate system specifying 3D rotation. If the trajectory of the movement is known, the integration of the axial component of the angular velocity plus the geometric effect equal to the enclosed area subtended by the geodesic path on the surface of the unit sphere. If the postures of the initial and final positions are known, the axial rotation is determined by the angular difference from the parallel transport along the geodesic path. The path dependency of the axial rotation of the three dimensional rigid body motion is due to the geometric effect corresponding to the closed loop discontinuity. Firstly, the closed loop discontinuity is examined for the infinitesimal region. The general closed loop discontinuity can be evaluated by the summation of those discontinuities of the infinitesimal regions forming the whole loop. This general loop discontinuity is equal to the surface area enclosed by the closed loop on the surface of the unit sphere. Using this quantification of the closed loop discontinuity of the axial rotation, the geometric effect is determined in enumerating the axial rotation. As an example, the axial rotation of the arm by the Codman's movement is evaluated, which other methods of enumerating the axial rotations failed.

• Journal of KIBIM
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• v.11 no.4
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• pp.42-52
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• 2021

Paneling building facades is one of the essential procedures in building construction. Traditionally, it has been an easy task of simply projecting paneling patterns drawn in drawing boards onto 3d building facades. However, as many organic or curved building shapes are designed and constructed in modern architectural practices, the traditional one-to-one projection is becoming obsolete for the building types of the kind. That is primarily because of the geometrical discrepancies between 2d drawing boards and 3d curved building surfaces. In addition, curved compound surfaces are often utilized to accommodate the complicated spatial programs, building codes, and zoning regulations or to achieve harmonious geometrical relationships with neighboring buildings in highly developed urban contexts. The use of the compound surface apparently makes the traditional paneling pattern projection more challenging. Various mapping technics have been introduced to deal with the inabilities of the projection methods for curved facades. The mapping methods translate geometries on a 2d surface into a 3d building façade at the same topological locations rather than relying on Euclidean or Affine projection. However, due to the intrinsic differences of the planar 2d and curved 3d surfaces, the mapping often comes with noticeable distortions of the paneling patterns. Thus, this paper proposes a practical method of drawing paneling patterns directly on a curved compound surface utilizing Geodesic, which is faithful to any curved surface, to minimize unnecessary distortions.

• Journal of Korean Association for Spatial Structures
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• v.23 no.4
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• pp.27-34
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• 2023

In this study, the seismic response characteristics of the three analysis model with or without TMD were investigated to find out the effective dome shape. The three analysis models are rib type, lattice type and geodesic type dome structure composed of space frame. The maximum vertical and horizontal displacements were evaluated at 1/4 point of the span by applying the resonance harmonic load and historical earthquake loads (El Centro, Kobe, Northridge earthquakes). The study of the effective TMD installation position for the dome structure shows that seismic response control was effective when eight TMDs were installed in all types of analysis model. The investigation of the efficiency of TMD according to dome shape presents that lattice dome and geodesic dome show excellent control performance, while rib dome shows different control performance depending on the historical seismic loads. Therefore, lattice and geodesic types are desirable for seismic response reduction using TMD compared to rib type.

• The Journal of the Acoustical Society of Korea
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• v.29 no.7
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• pp.431-438
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• 2010

The radiation pattern of conformal transducers installed on a curved surface is likely to be complicated depending on the array pattern on the curved surface. In this research, the acoustic sources constituting a conformal transducer are arrayed in equi-angle, equi-interval, and geodesic dome forms, and the radiation pattern function of each of the array geometries has been derived, and therewith the radiation pattern has been analyzed for each array geometry. Based on the analysis result, we have determined the equi-interval array geometry that provides the widest beam width with the lowest side lobe level among the three array geometries. Results of the present work are expected to be utilized to the design of conformal transducer structures.

• Kyungpook Mathematical Journal
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• v.13 no.1
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• pp.109-119
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• 1973

• Bulletin of the Korean Mathematical Society
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• v.14 no.1
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• pp.9-15
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• 1977

• Journal of Korean Association for Spatial Structures
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• v.12 no.4
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• pp.15-22
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• 2012

• 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

• 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.

• Bulletin of the Korean Mathematical Society
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• v.47 no.6
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• pp.1285-1296
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• 2010

We give criterions for a submanifold to be an extrinsic sphere and to be a totally geodesic submanifold by observing some Frenet curves of order 2 on the submanifold. We also characterize constant isotropic immersions into arbitrary Riemannian manifolds in terms of Frenet curves of proper order 2 on submanifolds. As an application we obtain a characterization of Veronese embeddings of complex projective spaces into complex projective spaces.