• Proceedings of the Korean Society for Technology of Plasticity Conference
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• 한국소성가공학회 2003년도 제4회 박판성형 심포지엄
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• pp.53-57
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• 2003

In order to make a doubly curved sheet metal effectively, a sheet metal farming process has been developed by adopting the flexibility of the incremental forming process and the principle of bending deformation which causes slight deformation to thickness. The developed process is an unconstrained forming process with no holder. For this study, the experimental equipment is set up with the roll set which consists of two pairs of support rolls and one center roll. In the experiments using aluminum sheets, it is found that the curvature of the formed sheet metal is determined by controlling the distance between supporting rolls in pairs and the forming depth of the center roll and it also depends on the thickness of the sheet metal. In order to check the effect of process parameters on the generation of sheet metal curvatures in this process, the orthogonal array is adopted. From the experimental results, among the process parameters, the distance between supporting rolls in pairs along the same direction of one principle radius of curvature as well as the forming depth and the thickness of the material is shown to influence the generation of curvature in the same direction significantly. That is, the other distance between supporting rolls in pairs which are not located in the same direction of one principle radius of curvature, does not have an significant effect on the generation of the curvature in that direction. It just affects the generation of curvature in its own direction mainly with the forming depth and the thickness of the material.

• The Pure and Applied Mathematics
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• 제4권1호
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• pp.27-33
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• 1997

Let (M = B$\times$f F, g) be an ($n \geq3$ )-dimensional differential manifold with Riemannian metric g. We solve the following elliptic nonlinear partial differential equation (equation omitted). where $\Delta_{g}$ is the Laplacian in the $\Delta$g-metric and ($h(\chi)$) is the scalar curvature of g and ($H(\chi)$) is a function on M.

• Communications of the Korean Mathematical Society
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• 제38권4호
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• pp.1281-1298
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• 2023

Let (M^2m, 𝜑, g) be a B-manifold. In this paper, we introduce a new class of metric on (M^2m, 𝜑, g), obtained by a non-conformal deformation of the metric g, called a generalized Berger-type deformed metric. First we investigate the Levi-Civita connection of this metric. Secondly we characterize the Riemannian curvature, the sectional curvature and the scalar curvature. Finally, we study the proper biharmonicity of the identity map and of a curve on M with respect to a generalized Berger-type deformed metric.

• Transactions of the Korean Society of Mechanical Engineers A
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• 제27권6호
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• pp.1014-1019
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• 2003

A dynamic modeling method for beams undergoing overall rigid body motion is presented in this paper. Two special deformation variables are introduced to represent the stretching and the curvature and are approximated by the assumed mode method. Geometric constraint equations that relate the two special deformation variables and the cartesian deformation variables are incorporated into the modeling method. By using the special deformation variables, all natural as well as geometric boundary conditions can be satisfied. It is shown that the geometric nonlinear effects of stretching and curvature play important roles to accurately predict the dynamic response when overall rigid body motion is involved.

• Journal of Ocean Engineering and Technology
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• 제13권1호통권31호
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• pp.29-38
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• 1999

In this paper the forming simulation of circular bulge by using PAM-STAMP has been performed to estimate the sheet metal forning and the plastic deformation characteristic of circular bulge. The uniaxial tension tests adn bulge tests are carried out for studying the forming characteristics of materials, and also Moire experiment are carried out for measuring the radius of curvature of the bulge and the polar compressive thickness strain. In order to compare the simulation results with the experiment and Hills theory, the relationships between redius of curvature adn polar height of the bulge, between hydraulic pressure and polar height, and between polar compressive thickness strain and polar height, are used. According to this study, the results of simulation and Hills theory are good agreement to the experiment. So, the results of simulation by using PAM-STAMP and Hills theory will give engineers good information to assess the formagbility and plastic deformation characteristic of hydraulic circular bulge test.

• Journal of Welding and Joining
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• 제28권2호
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• pp.39-46
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• 2010

IIn this study, used is the equivalent loading method based on the inherent strain to predict the welding deformation of panel members. Equivalent loads are computed from the inherent strain distribution around weld line, and then applied for the linear finite element analysis. Thermal deformation of panel members can be, of course, carried out through the rigorous thermal elasto-plastic analysis procedure but it is not practical in applying to predicting the welding deformation of large structures such as blocks found in a ship structure from view of computing time. The present equivalent load approach has been applied to flat plate model to verify the present approach, and to several curved plate models having the curvature in the welding direction to investigate the effect of the longitudinal curvature upon the weld-induced deformation. The results are compared with those by thermal elasto-plastic analysis. As far as the present results are concerned, it can be said that the present approach shows good agreement with the results by welding experiment and the rigorous thermal elasto-plastic analysis. The present approach has been also applied to predict the welding deformation of panel block as for application illustration to practical model.

• Restorative Dentistry and Endodontics
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• 제26권5호
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• pp.418-435
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• 2001

Root canal preparation process is of utmost importance in successful treatment of root canal. Also, one of the most important purpose of the root canal preparation is to enlarge the root canal three dimensionally without changing the curvature of the root canal However as the curvature of the root canal increases, there are many difficulties involved in formation of optimum root canal. Therefore in order to solve the above mentioned problems, new developments in methods of root canal preparation and equipments for such purposes were made. Recently, vigorous studies about newly introduced engine-driven nickel-ti-tanium rotary file are conducted. As shown in research results to dates, it is well established that the use of nickel-titanium file is better suited for curved root canal than stainless steel file in maintaining the curvature or root canal and reducing the deformation of root canal. However it is also acknowledged that there are a few discrepancies in research results according to protocol, due to failure to remove variables in experiments. In addition, although it is recommended by the manufacturer that the GT rotary file should maintain a low rotational speed of 150~350rpm and 'light pressure' as light as not to break the lead of a pencil, academic studies about the vertical force which is not yet standardized are not sufficiently explored. Therefore, this research devised and utilized a special research equipment to standardize the appropriate range of vertical force for GT rotary file through experiments by breaking of the lead of a pencil as expressed by the manufacturer and to accurately measure factors involved through repeating and recreating the environment of root canal preparation. Forming nine experimental groups by varying the vertical forces (150g. 220g, 300g) and rpm (150rpm, 250rpm, 350rpm), the effects of changing vertical forces and rpm on working efficiency were measured in terms of time expended in root canal preparation by crown-down method using a transparent resin block with 35 degree curvature and GT rotary file (z-test). The following research using this special research equipment that involved nine experimental groups and varying the vertical force for root canal preparation from 300g which is within the normal vertical force range to 700g and 1000g which fall outside the normal rpm range. The results were as follows : 1. Analysis of the experiment results revealed that the time spent in root canal preparation decreased as the vertical forces and rpm increased (p<0.05). Also, the effects of rpm were greater than those of the vertical forces within the normal vertical force range ($\beta$-weight test). 2. Observation of the deformation of GT rotary file revealed that deformation increases in a direct correlation with the vertical force increase and in a reverse correlation with the rpm decrease. In the case of the vertical forces close to the normal range, the probability of GT rotary file deformation were quite different depending on the rpm changes. In the case of greater vertical forces, the occurrences of deformation of the file were more frequent regardless of the rpm changes. 3. Deformation and breakage of file were also commonly observed in the expended time measurement experiments and GT rotary file deformation experiments in which low speed rpm (150rpm) was used and at the curved portion of the resin block.

• Journal of Korean Society of Steel Construction
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• 제9권4호통권33호
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• pp.673-682
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• 1997

The main purpose of this paper is to investigate the effects of rotatory inertia and shear deformation on the natural frequencies of arches with variable curvature. The differential equations are derived for the in-plane free vibration of linearly elastic arches of uniform stiffness and constant mass per unit length. The governing equations are solved numerically for parabolic, circular and elliptic geometries with hinged-hinged, hinged-clamped and clamped-clamped end constraints. For each cases, the four lowest frequency parameters are presented as functions of the two dimensionless system parameters; the arch rise to span length ratio, and the slenderness ratio.

• Journal of the Korea Academia-Industrial cooperation Society
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• 제7권6호
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• pp.1040-1046
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• 2006

This paper is aimed to investigate the deformation caused by ununiform contraction of injection molding with highly big differences of thickness by the continuity of various curvature radius. By CAE analysis, the uniform cooling structure and optimum molding conditions are found for Jars made of SAN and PMMA materials and applied to the design of chill. In order toevaluate the molding pressure, resin temperature, molding temperature, cooling conditions, Moldflow program is applied. As results of experiments, the deformation and inferiority phenomena in Jars are analyzed for each factor and proposed the injection molding conditions to minimize the cooling structure and reduce the cycle time.

• Honam Mathematical Journal
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• 제33권1호
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• pp.121-127
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• 2011

In this paper, when N is a compact Riemannian manifold, we discuss the nonexistence of conformal deformations on space-times $M = (a,\infty){\times}_fN$ with prescribed scalar curvature functions.