• Journal of Ocean Engineering and Technology
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• v.25 no.2
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• pp.67-72
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• 2011

This study had the goal of investigating the effect of the curvature along the heating line on the transverse angular distortion of plates having an initial curvature from line heating. A thermo-elasto-plastic analysis was carried out using 54 models with various radii of curvature, plate thicknesses, and heating speeds. The results show the effect of the curvature along the heating line on the angular distortion in relation to changes in the magnitudes of the curvature, heating speed, and plate thickness. The present numerical results show that the time history of the angular distortion after cooling and reaching the final deformed shape for a plate having an initial curvature is quite different from that of a flat plate. This emphasized the importance of considering the curvature effect on the transverse angular distortion. From the viewpoint of the curvature effect on the deformation, it has been seen that the curvature does not affect the transverse shrinkage. In this study the predicting formula for the transverse angular distortion was derived through a regression analysis. It showed that as the curvature increased, the angular distortion was reduced because of the higher bending rigidity at the same heat input parameter, and the peak points moved toward the origin as the curvature increased.

• Journal of Ocean Engineering and Technology
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• v.20 no.4 s.71
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• pp.24-30
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• 2006

Different methods exist for the estimation of thermaldeformation of plates in the line heating process. These are based on the assumption of residual strains in the heat-affected zone, known as the method of inherent strains, or simulated relations between heating conditions and residual deformations. The purpose of this paper is to develop a simulator of thermal deformation in the line heating, using the artificial neural network. Curvature deformations for the plate-forming are investigated, which can be used as a prime deformation parameter in the process. The curvature of plates are calculated using the approximation of plate surface by NURBS. Line heating experiments for 11 specimens of different thickness and heating conditions were performed. Two neural networks predicting the maximum temperature and curvature deformations at the heating line are studied. It was concluded that the thermal deformations predicted by the neural network can be used in a line heating simulator, which is considered an attractive and practical alternative to the existing methods.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.22 no.8
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• pp.1173-1182
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• 1998

A throughflow analysis program for axial flow turbines is constructed, which can handle not only the two-dimensional multi-streamline (streamline curvature) method but also the one-dimensional mean line method. Calculations are performed for single stage and multi-stage axial flowturbines. For a wide operating range, the performance and flow field calculated by the present streamline curvature method are close enough to the test data. It is also revealed for the single stage turbine that the present analysis leads to far better correspondence with the experiment than other researchers" throughflow analyses. A special focus is put on the comparison of the results between the streamline curvature analysis and the mean line analysis. It is found that the mean line analysis can not predict the performance for highly off-designed conditions as accurately as the streamline curvature method, which shows the importance of considering the spanwise variation of loss and flow.

• Journal of the Chungcheong Mathematical Society
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• v.34 no.4
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• pp.379-385
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• 2021

We consider the local uniqueness of a catenoid under the condition for the Gaussian curvature analogous to Bianchi surfaces. More precisely, if a nonplanar minimal surface in ℝ³ has the Gaussian curvature $K={\frac{1}{(U(u)+V(v))^2}}$ for any functions U(u) and V (v) with respect to a line of curvature coordinate system (u, v), then it is part of a catenoid. To do this, we use the relation between a conformal line of curvature coordinate system and a Chebyshev coordinate system.

• Journal of Ocean Engineering and Technology
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• v.19 no.1 s.62
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• pp.33-38
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• 2005

It has been well documented that plate forming is one of the most important processes in shipbuilding. In the most shipyards, the line heating method is primarily used for plate forming. Since the heating process is carried out for the curved plate and not for the flat plate, a curvature effect on the final deformation must be considered in deriving the simplified prediction models for deformation. This paper investigates the effect of curvature along the heating line on the deformation of the plate. First of all, results of numerical analysis are compared with these of a line-heating test, to justify the elasto-plastic analysis procedure for the present study, which shows good agreement. Then, the present numerical procedure is applied to flat and curved plate models, to investigate the curvature effect on the heat transfer characteristics and deformation by line heating.

• Journal of the Korean Society of Clothing and Textiles
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• v.33 no.1
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• pp.68-79
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• 2009

It is inevitable to have cutting line to get the 2D pattern from 3D body surface. In this paper the efficiency of curvature plot as a cutting line in the process of flattening 3D surface was investigated. As reference, basic clothing construction line was adopted to divide the 3D surface into small blocks to make the flattening process easy. Female dummy as well as human body were scanned and surface of the upper body was segmented using curvature plot and basic constructing line. 2D tight-fit pattern was developed using three software, the RapidForm 2004, 2C-AN and Yuka CAD. Gap between clothes and body, and the clothing pressure on the body was observed to determine the fit of the clothes. As results, clothes constructed with blocks divided by curvature plot displayed a similar level of tight fit as compared with those by basic construction line. It was found that curvature plot is effective method as a segmentation of the 3D surface even for the actual body which does not have any previous reference line. It is expected that application of curvature plot will be expanded in 3D apparel technology.

• Nonlinear Functional Analysis and Applications
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• v.26 no.2
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• pp.225-236
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• 2021

In this paper, we determine position vector of a line of curvature of a regular surface which is relatively normal-slant helix, with respect to Darboux frame. Then, a vector differential equation is established by means Darboux formulas, in the case of the geodesic torsion is vanishes. In terms of solution, we determine the parametric representation of a line of curvature which is relatively normal-slant helix, with respect to standard frame in Euclidean 3-space. Thereafter, we apply this result to find the position vector of a line of curvature which is isophote curve.

• Journal of the Korean Mathematical Society
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• v.56 no.2
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• pp.421-437
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• 2019

We establish some Hessian comparison theorems and volume comparison theorems for Riemann-Finsler manifolds under various line radial integral curvature bounds. As their applications, we obtain some results on first eigenvalue, Gromov pre-compactness and generalized Myers theorem for Riemann-Finsler manifolds under suitable line radial integral curvature bounds. Our results are new even in the Riemannian case.

• 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.

• Journal of Oral Medicine and Pain
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• v.20 no.2
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• pp.361-376
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• 1995

The purpose of this study was to investigate the relationship between the head and neck postre and the cervical curvature, especially in forward head postrue(FHP). Sixty patients with craniomandibular disorders and thirty dental students without any signs and symptoms of craniomandibular disordres participated in this study as patient groups and sa control group, respectively. The author evaluated the head and neck posture of all subjects by plumb line and CROM( Cervical Ragne of Motion), and had taken cephaograph in natural head position. On the cephalograph the angle of cervical inclination formed by true horizntal plane and 4th cervical vertebra(C4) and the radius of cervical curvature from C1 to C5 were measured. A specially designed ruler was used for measuring cervical curvature. Occlusal contac number and force with T-scan system, electromygraphic activity of cervical muscles with Bio-EMG, and distance of freeway space with Bio-ECN were recorded, respectively. The collected data were processed by SAS/STAT progrm. The obtained results were as follows : 1. In subjects with longer radius which was less cervical curvature, head positioned more anteriorly than subjects with smaller radius, and they showed slightly straight cervical vertebra. 2. Between the patients and the control group, there were no differences in cervical curvature, in forward head position by plumb line and in CROM. But the patient group had a greater cervical inclination than the control group had. 3. There were positive correlation between cervical curvature and forward head position by plumbline,between forward head position y plumb line and that by CROM in patient group. The cervical inclination, however, had negative correlation with cervical curvature, and with forward head postion by plumb line, respectively. 4. In case of showing more cervical curvature and more forward head position by plumb line the head position was defined as forward head posture. In patient group, subjects without forward head posture showed greater posterior teeth contact force than subjects with forward head posture, but in control group, there were no difference between the two subjects. 5. There were higher electromyographic activity in almost all muscles and smaller freeway space in induced forward head posture than those in natural head position in subjects without forward head posture. In conclusion, head position of patients with craniomandibular disorders were not more anterior than that of normal control person, but they had tendency to head extension. From the result of this study, forward head posture could be defined as posterior rotation of upper cervical segment with a straight lower cercial segment due to loss of normal lordosis.