• Bulletin of the Korean Mathematical Society
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• v.54 no.6
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• pp.2119-2139
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• 2017

Here, certain Ricci flow for Finsler n-manifolds is considered and deformation of Cartan hh-curvature, as well as Ricci tensor and scalar curvature, are derived for spaces of scalar flag curvature. As an application, it is shown that on a family of Finsler manifolds of constant flag curvature, the scalar curvature satisfies the so-called heat-type equation. Hence on a compact Finsler manifold of constant flag curvature of initial non-negative scalar curvature, the scalar curvature remains non-negative by Ricci flow and blows up in a short time.

• Communications of the Korean Mathematical Society
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• v.21 no.1
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• pp.145-149
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• 2006

We demonstrate a novel almost Kahler deformation on $\mathbb{R}^4$ which diffuses the scalar curvature.

• Communications of the Korean Mathematical Society
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• v.37 no.3
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• pp.865-879
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• 2022

Let (M^m, g) be an m-dimensional Riemannian manifold. In this paper, we introduce a new class of metric on (M^m, g), obtained by a non-conformal deformation of the metric g. First we investigate the Levi-Civita connection of this metric. Secondly we characterize the Riemannian curvature, the sectional curvature and the scalar curvature. In the last section we characterizes some class of proper biharmonic maps. Examples of proper biharmonic maps are constructed when (M^m, g) is an Euclidean space.

• The Journal of Korea Robotics Society
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• v.17 no.1
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• pp.68-75
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• 2022

In this paper, we considered the deformation shape of the soft rotation actuator as a double curvature shell and proceeded with the analytical development. Since the response of the hyperelastic material has a large nonlinear deformation, the analytical approach is very complicated and the solution cannot be easily obtained. it is assumed that the behavior of the flexible body, which is a superelastic material, takes the form of a double curvature shell, and the formulas for calculating the deformation are simplified. In this process, equilibrium equations in the related coordinate system representing a double curvature shell were derived. In addition, assuming a thin shell, the stress component in the thickness direction was ignored, and the equation was developed by adding the assumption of free rotation without load. In order to verify the analytically calculated value in this way, an experiment was conducted and the results were compared.

• Structural Engineering and Mechanics
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• v.9 no.4
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• pp.339-347
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• 2000

The creep deformation of pure bending (hold constant moment for a period of time) tests were conducted in this paper. Thin-walled tubes of 304 stainless steel were used in this investigation. The curvature-ovalization measurement apparatus, designed by Pan et al. (1998), was used for conducting the present experiments. It has been found that as soon as the creep deformation is started, the magnitudes of the tube curvature and ovalization of tube cross-section quickly increase. The magnitudes of the creep curvature and ovalization of tube cross-section increase fast with a higher hold moment than that with a lower one. Owing to the continuously increasing curvature during the creep deformation, the tube specimen buckles eventually.

• 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 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.

• Proceedings of the Korea Committee for Ocean Resources and Engineering Conference
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• 2006.11a
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• pp.201-204
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• 2006

A three-dimensional finite element (FEM) model has been developed to simulate the deformation due to bead on plate welding of curved plates with curvature in the weld direction. By using traditional method such as thermal-elastic-plastic FEM, the weld-induced deformation can be predicted accurately. However, this method is not practical approach to analyze the deformation of large and complex structures such as ship hull structures in view of time and cost. This study is classified from the aspect of equivalent load based on inherent strain near the weld line. Therefore, the residual deformation can be simply computed by elastic analysis. Further more, a practical solution is proposed to consider the contact between the plate and the positioning jig by judging the reaction forces of the jig at calculation step and the effect of the longitudinal curvature is closely considered.

• Tunnel and Underground Space
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• v.6 no.1
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• pp.10-18
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• 1996

Arched openings are generally excavated in underground construction works. Since stress distribution around openings depends on geological structure in rock mass, any shape of arched openings fully conformed with in-situ stress condition should be recommended to maintain mechanical safety of structures. Shape of arched openings is specified by both roof curvature and height-width ratio, and especially this report presents deformation behaviors related with roof curvature. Scale model tests and numerical studies of various shaped openings are conducted, where rectangular opening shows the greatest convergence. Through the anlayses of various arched opengings, as radius of roof curvature is increased, roof lowering and sidewall closure are remarkably increased, whereas floor heaving is increased little by little. By the way, it is useful that displacements of openings are roughly estimated in the stage of preliminary investigation. To find out elastic displacements of arched openings with any roof curvature, regressional formula and charts by least square method are represented. In addition elastoplastic deformation behavoirs of arched openings concerning associated adn non-associated flow rule are discussed.

• Journal of the Society of Naval Architects of Korea
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• v.44 no.5
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• pp.474-481
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• 2007

A three-dimensional finite element model has been used to simulate the bead on plate welding of curved steel plates having curvature in the welding direction. By using traditional method such as thermal-elastic-plastic(TEP) finite element analysis. the weld-induced deformation can be accurately predicted. However, three-dimensional finite element analysis is not practical in analyzing the weld-induced deformation of large and complex structures such as ship structures in view of computing time and cost. In this study, used is the equivalent loading method based on inherent strain to illustrate the effect of the longitudinal curvature upon the weld-induced deformation of curved plates.