• Korean Journal of Mathematics
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• v.5 no.2
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• pp.113-118
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• 1997

According to the Bernoulli-Euler theory of elastic rods the bending energy of the wire is proportional to the total squared curvature of ${\gamma}$, which we will denote by $F({\gamma})=\int_{\gamma}k^2ds$. If the result of J.Langer and D.Singer [3] extend to knotted elastic curve, then we obtain the following. Let {${\gamma},M$} be a closed knotted elastic curve. If the curvature of ${\gamma}$ is nonzero for everywhere, then ${\gamma}$ lies on torus.

• Journal of Ocean Engineering and Technology
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• v.10 no.2
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• pp.98-105
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• 1996

A method is proposed to evaluate the elastic-plastic fracture resistance curve only with load displacement records without the crack length measurement in CT specimen. This method is based on the idea that the effect of plastic deformation and the crack growth can be measured only by using a load-displacement record. If we know the reference-load curve representing the hardening of specimen, then the crack extension can be calculated by the elastic compliance determined from the load ratio. The results of this proposed method were compared to those of the elastic-plastic fracture resistance curve for the ASTM standard unloading compliance method. The experimental results for two kinds of ductile materials showed that the proposed method well simulates the material J-R curves. This method is currently applied for CT specimens. but it can be extended to the other specimen geometries.

• Structural Engineering and Mechanics
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• v.60 no.1
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• pp.21-30
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• 2016

In this paper two procedures for determination of the elastic curve of the simply and multiple supported beams are developed. Determination of the elastic curve is complex as it requires to solve a strong nonlinear differential equation with given boundary conditions. For numerical solution the initial guess of the slope at the end of the beam is necessary. Two procedures for obtaining of the initial guess are developed: one, based on transformation of the supported beam into a clamped-free one, and second, on the linearization of the problem. Procedures are applied for calculating of elastic curve of a simply supported beam and a beam with three supports. Obtained results are compared. Advantages and disadvantages of both methods are discussed. It is proved that both suggested procedures give us technically accurate results.

• Proceedings of the Korean Institute of Electrical and Electronic Material Engineers Conference
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• 2005.07a
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• pp.375-376
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• 2005

탄소나노튜브는 캔틸레버처럼 주어진 압력에 의해 elastic curve를 형성하게 되는데, 이러한 성질은 탄소나노튜브가 가지고 있는 young's modulus와 구조적인 형태에서 기인한다. 따라서 탄소나노튜브의 변위와 인가된 analyte의 농도에 따른 압력 사이의 관계를 이용해 가스센서로의 적용이 가능하다. 이 번 연구에서는 시뮬레이션을 통해 길이가 30nm 이고 반경이 1.5nm로 모델링 된 단일 벽 탄소나노튜브가 3000ppm와 1000ppm ethanol의 농도에 의해 형성된 elastic curve의 최대변위를 구하고, 농도와 단일 벽 탄소나노튜브의 elastic curve의 최대변위가 비례함을 보였다.

• Honam Mathematical Journal
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• v.39 no.4
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• pp.637-647
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• 2017

Elastica is known as classical curve that is a solution of variational problem, which minimize a thin inextensible wire's bending energy. Studies on elastica has been conducted in Euclidean space firstly, then it has been extended to Riemannian manifold by giving different characterizations. In this paper, we focus on energy of the elastic curve in a Lie group. We attepmt to compute its energy by using geometric description of the curvature and the torsion of the trajectory of the elastic curve of the trajectory of the moving particle in the Lie group. Finally, we also investigate the relation between energy of the elastic curve and energy of the same curve in Frenet vector fields in the Lie group.

• Structural Engineering and Mechanics
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• v.68 no.6
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• pp.713-720
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• 2018

In this paper a new numerical method to determine the elastic curve of the simply supported beams of variable cross-section is demonstrated. In general case it needs to solve linear or small nonlinear second order differential equations with prescribed boundary conditions. For numerical solution the initial values of the slope and the deflection of the end cross-section of the beam is necessary. For obtaining the initial values a lively procedure is developed: it is a special application of the shooting method because boundary value problems can be transformed into initial value problems. As a result of these transformations the initial values of the differential equations are obtained with high accuracy. Procedure is applied for calculating of elastic curve of a simply supported beam of variable cross-section. Results of these numerical procedures, analytical solution of the linearized version and finite element method are compared. It is proved that the suggested procedure yields technically accurate results.

• Honam Mathematical Journal
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• v.42 no.1
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• pp.187-195
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• 2020

In this paper, we investigate the vectorial moments of Bäcklund transformations of a space curve in 𝔼³. Firstly, it is obtained the vectorial moments which named α𝓖 dual curve, β𝓖 dual curve, and γ𝓖 dual curve of Bäcklund transformations. Then we give the Euler elastic bending energies of these curves. Finally, we provide some examples of α𝓖 dual, β𝓖 dual, and γ𝓖 dual, and their Euler elastic bending energies.

• Proceedings of the KSME Conference
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• 2004.04a
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• pp.132-137
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• 2004

In this work, effects of hyper-elastic rubber material properties on the indentation load-deflection curve and subindenter deformation are first examined via [mite element (FE) analyses. An optimal data acquisition spot is selected, which features maximum strain energy density and negligible frictional effect. We then contrive two normalized functions. which map an indentation load vs. deflection curve into a strain energy density vs. first invariant curve. From the strain energy density vs. first invariant curve, we can extract the rubber material properties. This new spherical indentation approach produces the rubber material properties in a manner more effective than the common uniaxial tensile/compression tests. The indentation approach successfully measures the rubber material properties and the corresponding nominal stress.strain curve with an average error less than 3%.

• Journal of the Korean Society of Safety
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• v.12 no.3
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• pp.45-51
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• 1997

To evaluate the elastic-plastic fracture toughness by this modified offset method, the origin of J-R curve is set with drawing the blunting line on the maximum point of the negative crack growth and R curve is modified by adding the blunting factor of the experimented point on the R curve. The elastic-plastic fracture toughness $J_{IC]$ of A5083-H112 material by the modified offset method we 44kN/m on the smooth CT specimens.

• Journal of Ocean Engineering and Technology
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• v.7 no.2
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• pp.91-102
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• 1993

The elastic-plastic fracture thoughness J sub(IC) of Nuclear Reactor Vessel Steel(SA 508-3) which has high toughness was discussed at temperatures RT, $-20^{\circ}C$, $200^{\circ}C$ and 1/2/CT specimen was used for this study. Especially the two methods recommended in ASTM and JSME were compared. It was difficult to find J sub(IC) by ASTM R-curve method with the specimen used for this research, while JSME R-curve method yielded good result. The stretched zone width menthod gave slightly larger J sub(IC) values than those by the R-curve method for SA 508-3 steel.