• 한국전산구조공학회:학술대회논문집
• /
• 한국전산구조공학회 2007년도 정기 학술대회 논문집
• /
• pp.415-420
• /
• 2007

In analyzing the nano-scale behavior of nano devices or materials, QC method is efficient because it does not treat all the atoms. But for more accurate analysis in QC method, it is important to consider temperature and surface effects. In finite temperature, free energy is considered instead of potential energy. Because the surface area to volume ratio increases as the length scale of a body decreases, the surface effects are more dominant. In this paper, temperature related Cauchy-Born rule and surface Cauchy-Born rule are proposed to configurate the strain energy density. This method is applied to small and homogeneous deformation in two dimensional problem using finite element simulation.

• 한국해양공학회지
• /
• 제4권1호
• /
• pp.62-70
• /
• 1990

Cauchy의 적분공식을 복소속도(complex velocity)에 적용하여 포텐시얼 유동을 해석하는 복소경계요소법이 개발되었다. 이 결과로 얻어지는 적분방정식은 경계면에서의 접선속도(tangential velocity)와 법선속도(normal velocity)의 함수로 주어진다. 자유수면에서의 접선속도의 시간변화(evolution of tangential velocity)를 수식화하기 위하여 새로운 비선형 동역학적 자유수면경계조건(nonlinear dynamic free surface boundary condition)을 유도하였다. 복소포텐시얼 대신 복소속도를 이용하는 이 방법은 유장내의 특이점(field singularity)을 용이하게 고려할 수 있으며, 수치미분없이 직접 경계면에서의 유속을 해로서 구하게 된다. 그러나 자유수면이 존재하는 문제의 경우에는, 자유수면에서의 동역학적 경계조건을 만족 시키기 위한 계산과정에 접선 벡타의 변화량을 추정하는 것이 포함되게 되어, 계산과정이 다소 복잡하게 된다.

• 대한수학회보
• /
• 제50권2호
• /
• pp.441-444
• /
• 2013

It is shown that any two-dimensional globally hyperbolic spacetime with noncompact Cauchy surfaces has no null cut points.

• 한국해양공학회지
• /
• 제14권1호
• /
• pp.1-5
• /
• 2000

A numerical analysis for wave motion in the shallow water is presented. The method is based on potential theory. The fully nonlinear free surface boundary condition is assumed in an inner domain and this solution is matched along an assumed common boundary to a linear solution in outer domain. In two-dimensional problem Cauchy's integral theorem is applied to calculate the complex potential and its time derivative along boundary.

• International Journal of CAD/CAM
• /
• 제9권1호
• /
• pp.103-109
• /
• 2010

Recently, various conformal geometric methods have been presented for non-rigid surface matching and registration. This work proposes to improve the robustness of conformal geometric methods to the boundaries by incorporating the symmetric information of the input surface. We presented two symmetric conformal mapping methods, which are based on solving Riemann-Cauchy equation and curvature flow respectively. Experimental results on geometric data acquired from real life demonstrate that the symmetric conformal mapping is insensitive to the boundary occlusions. The method outperforms all the others in terms of robustness. The method has the potential to be generalized to high genus surfaces using hyperbolic curvature flow.

• 한국해양공학회지
• /
• 제19권5호
• /
• pp.78-82
• /
• 2005

The motion response results of a submerged submarine section in waves are presented. The numerical method is based on Cauchy's integral and 3 degrees-of-freedom motions of submarine sections are calculated in two dimensions, in regular waves. The fully nonlinear free surface and body boundary conditions are applied to the present problem, and the viscous effects on the submarine are modeled by Morison's formulas. The motions of submarine sections in beam sea are directly simulated and the effects of wave frequency, snorkel depth, and bridge are discussed.

• 대한수학회지
• /
• 제60권1호
• /
• pp.71-90
• /
• 2023

We construct generalized Cauchy-Riemann equations of the first order for a pair of two ℝ-valued functions to deform a minimal graph in ℝ³ to the one parameter family of the two dimensional minimal graphs in ℝ⁴. We construct the two parameter family of minimal graphs in ℝ⁴, which include catenoids, helicoids, planes in ℝ³, and complex logarithmic graphs in ℂ². We present higher codimensional generalizations of Scherk's periodic minimal surfaces.

• Interaction and multiscale mechanics
• /
• 제4권2호
• /
• pp.123-137
• /
• 2011

We review a series of crack problems arising in the general deformations of a linearly elastic solid (Mode-I, Mode-II and Mode-III crack) and, perhaps more significantly, when the contribution of surface effects are taken into account. The surface mechanics are incorporated using the continuum based surface/interface model of Gurtin and Murdoch. We show that the deformations of an elastic solid containing a single crack can be decoupled into in-plane (Mode-I and Mode-II crack) and anti-plane (Mode-III crack) parts, even when the surface mechanics is introduced. In particular, it is shown that, in contrast to classical fracture mechanics (where surface effects are neglected), the incorporation of surface elasticity leads to the more accurate description of a finite stress at the crack tip. In addition, the corresponding stress fields exhibit strong dependency on the size of crack.

• International Journal of Ocean System Engineering
• /
• 제1권1호
• /
• pp.28-31
• /
• 2011

An attempt was made to compute the free surface deformation due to the impact of a water droplet. The Cauchy Poisson, i.e. the initial value problem, was solved with the kinematic and dynamic free surface boundary conditions linearized. The zero order Hankel transformation and Laplace transform were applied to the related equations. The initial condition for the free surface profile was derived from a captured video image. The effect of the surface tension was not significant with the water mass used in this investigation. The computed and observed free surface deformations were compared.

• 대한조선학회논문집
• /
• 제30권2호
• /
• pp.86-97
• /
• 1993

수치방법은 포텐셜 유동의 가정하에서 Semi-Lagrangian 기법을 사용하여 2차원 쇄기의 비선형운동과 축대칭 물체의 강제 상하동요 운동에 대해서 개발되었다. 2차원에서 Cauchy 이론은 경계를 따라서 복소포텐셜과 그것의 미분치를 계산하기 위해 적용되었고, 3차원에서 Rankinering 쏘오스가 사용되고 대수방정식을 풀기위해서 그린 제2정리를 이용하였다. 해는 완전한 사유표면 조건을 수치적분함으로서 시간전진시킨다. 수치계산 예는 정속도로 입수하는 쇄기형 주상체와 정지 상태로 부터 강제상하동요하는 문제를 택하였다. 쇄기입수 문제는 Chapman [4], Kim[11]의 계산결과와 비교된다. 위에서 적용된 기법을 이용하여 구한 시간영역에서 힘을 Fourier 변환함으로서 부가질량계수, 감쇄계수, 2차조화력등이 얻어지고 Yamashita[5]의 실험치와 비교된다.