• 대한수학회보
• /
• 제51권5호
• /
• pp.1539-1549
• /
• 2014

The closed spacelike hypersurfaces with higher order mean curvature is discussed in a de Sitter space. The hypersurface is proved stable if and only if it is totally umbilical.

• 대한수학회보
• /
• 제39권4호
• /
• pp.681-685
• /
• 2002

It is shown that, an immersion of n-dimensional compact manifold without boundary into (n + 1)-dimensional Euclidean space, hyperbolic space or the open half spheres, is a totally umbilic immersion if for some r, r =2, 3, …, n the r-th mean curvature Hr does not vanish and there are nonnegative constants $C_1$, $C_2$, …, $C_{r}$ such that (equation omitted)d)

• 대한수학회지
• /
• 제61권1호
• /
• pp.41-63
• /
• 2024

In this paper, we study complete Riemannian immersions into a semi-Riemannian warped product obeying suitable curvature constraints. Under appropriate differential inequalities involving higher order mean curvatures, we establish rigidity and nonexistence results concerning these immersions. Applications to the cases that the ambient space is either an Einstein manifold, a steady state type spacetime or a pseudo-hyperbolic space are given, and a particular investigation of entire graphs constructed over the fiber of the ambient space is also made. Our approach is based on a parabolicity criterion related to a linearized differential operator which is a divergence-type operator and can be regarded as a natural extension of the standard Laplacian.

• 소성∙가공
• /
• 제21권8호
• /
• pp.479-484
• /
• 2012

The objective of this study is to compensate the elastic recovery in the flexible forming process using the predictive models. The target shape was limited to two-dimensional shape having only one curvature radius in the longitudinal-direction. In order to predict the shape error the regression and neural network models were established based on the finite element (FE) simulations. A series of simulations were conducted considering input variables such as the elastic pad thickness, the thickness of plate, and the objective curvature radius. Then, at sampling points in the longitudinal-direction, the shape errors between formed and objective shapes could be calculated from the FE simulations as an output variable. These shape errors were expressed to a representative error value by the root mean square error (RMSE). To obtain the correct objective shape the die shape was adjusted by the closed-loop using the neural network model since the neural network model shows a higher capability of estimating the shape error than the regression model. Finally the experimental result shows that the formed shape almost agreed with the objective shape.

• 대한기계학회논문집
• /
• 제9권4호
• /
• pp.403-413
• /
• 1985

본 논문에서는 수직벽 하류에 형성되는 박이 전단층의 발전과 재부착 그리고 재발전 경계층에 대해 평균 속도, 벽면의 압력 분포, 난류 강도, 레이놀즈 전단 압력 및 아직 수직벽에 대해서는 보고된바 없는 난류 떨림 속도 성분들의 3승곱 통계치를 측정하여 난류 구조의 변화를 분석하고 이를 수치적 계산 모델개발의 자 료로 제공하고자 함이 이 연구의 목적이다.

• 한국철도학회:학술대회논문집
• /
• 한국철도학회 2008년도 추계학술대회 논문집
• /
• pp.805-814
• /
• 2008

This study focused on the resilient modulus prediction model, which is the functions of mean effective principal stress and axial strain, for three types of railroad trackbed materials such as crushed stone, weathered soil, and crushed-rock soil mixture. The model is composed with the maximum Young's modulus and nonlinear values for higher strain in parallel with dynamic shear modulus. The maximum values is modeled by model parameters, $A_E$ and the power of mean effective principal stress, $n_E$. The nonlinear portion is represented by modified hyperbolic model, with the model parameters of reference strain, ${\varepsilon}_r$ and curvature coefficient, a. To assess the performance of the prediction models proposed herein, the elastic response of a test trackbed near PyeongTaek, Korea was evaluated using a 3-D nonlinear elastic computer program (GEOTRACK) and compared with measured elastic vertical displacement during the passages of freight and passenger trains. The material types of sub-ballasts are crushed stone and weathered granite soil, respectively. The calculated vertical displacements within the sub-ballasts are within the order of 0.6mm, and agree well with measured values with the reasonable margin. The prediction models are thus concluded to work properly in the preliminary investigation.

• Smart Structures and Systems
• /
• 제9권6호
• /
• pp.505-534
• /
• 2012

The present work deals with second order statistics of post buckling response of piezoelectric laminated composite cylindrical shell panel subjected to hygro-thermo-electro-mechanical loading with random system properties. System parameters such as the material properties, thermal expansion coefficients and lamina plate thickness are assumed to be independent of the temperature and electric field and modeled as random variables. The piezoelectric material is used in the forms of layers surface bonded on the layers of laminated composite shell panel. The mathematical formulation is based on higher order shear deformation shell theory (HSDT) with von-Karman nonlinear kinematics. A efficient $C^0$ nonlinear finite element method based on direct iterative procedure in conjunction with a first order perturbation approach (FOPT) is developed for the implementation of the proposed problems in random environment and is employed to evaluate the second order statistics (mean and variance) of the post buckling load of piezoelectric laminated cylindrical shell panel. Typical numerical results are presented to examine the effect of various environmental conditions, amplitude ratios, electrical voltages, panel side to thickness ratios, aspect ratios, boundary conditions, curvature to side ratios, lamination schemes and types of loadings with random system properties. It is observed that the piezoelectric effect has a significant influence on the stochastic post buckling response of composite shell panel under various loading conditions and some new results are presented to demonstrate the applications of present work. The results obtained using the present solution approach is validated with those results available in the literature and also with independent Monte Carlo Simulation (MCS).

• 한국지반공학회:학술대회논문집
• /
• 한국지반공학회 2008년도 추계 학술발표회
• /
• pp.1404-1414
• /
• 2008

In the mechanistic-empirical trackbed design of railways, the resilient modulus is the key input parameter. This study focused on the resilient modulus prediction model, which is the functions of mean effective principal stress and axial strain, for three types of railroad trackbed materials such as crushed stone, weathered soil, and crushed-rock soil mixture. The model is composed with the maximum Young's modulus and nonlinear values for higher strain in parallel with dynamic shear modulus. The maximum values is modeled by model parameters, $A_E$ and the power of mean effective principal stress, $n_E$. The nonlinear portion is represented by modified hyperbolic model, with the model parameters of reference strain, ${\varepsilon}_r$ and curvature coefficient, a. To assess the performance of the prediction models proposed herein, the elastic response of a test trackbed near PyeongTaek, Korea was evaluated using a 3-D nonlinear elastic computer program (GEOTRACK) and compared with measured elastic vertical displacement during the passages of freight and passenger trains. The material types of sub-ballasts are crushed stone and weathered granite soil, respectively. The calculated vertical displacements within the sub-ballasts are within the order of 0.6mm, and agree well with measured values with the reasonable margin. The prediction models are thus concluded to work properly in the preliminary investigation.

• 한국초전도ㆍ저온공학회논문지
• /
• 제24권3호
• /
• pp.62-67
• /
• 2022

Liquid hydrogen (LH₂) has a higher density than gaseous hydrogen, so it has high transport efficiency and can be stored at relatively low pressure. In order to use efficient bulk hydrogen in the industry, research for the LH₂ supply system is needed. In the high-pressure hydrogen station based on LH₂ currently being developed in Korea, a heat exchanger is used to heat up supercritical hydrogen at 700 bar and 60 K, which is pressurized by a cryogenic high-pressure pump, to gas hydrogen at 700 bar and 300 K. Accordingly, the heat exchanger used in the hydrogen station should consider the design of high-pressure tubes, miniaturization, and freezing prevention. A helical heat exchanger generates secondary flow due to the curvature characteristics of a curved tube and can be miniaturized compared to a straight one on the same heat transfer length. This paper evaluates the heat transfer performance through parametric study on the distance between coils, guide effect, and anti-icing design of helical heat exchanger. The helical heat exchanger has better heat transfer performance than the straight tube exchanger due to the influence of the secondary flow. When the distance between the coils is uniform, the heat transfer is enhanced. The guide between coils increases the heat transfer performance by increasing the heat transfer length of the shell side fluid. The freezing is observed around the inlet of distribution tube wall, and to solve this problem, an anti-icing structure and a modified operating condition are suggested.

• 대한토목학회논문집
• /
• 제29권2C호
• /
• pp.71-79
• /
• 2009

본 연구에서는 국내 철도 토공노반 재료로 가장 흔히 사용되는 입도조정쇄석, 화강풍화토, 암버럭-토사 혼합 재료에 대해 평균유효주응력과 축변형률의 함수로 표현되는 회복탄성계수 예측모델을 결정하였다. 회복탄성계수 예측모델은 대표적인 동적물성치인 변형률에 따른 전단탄성계수 감소곡선의 표현과 같이 최대영탄성계수와 정규화 영탄성계수 감소곡선으로 구성된다. 평균유효주응력의 함수로 표현되는 최대영탄성계수의 모델인자는 $A_E$와 $n_E$이고, 비선형 영역의 정규화 영탄성계수 감소곡선은 기준변형률(${\varepsilon}_r$)과 곡률계수(a)를 모델인자로 하는 수정 쌍곡선 모델로 표현된다. 제안된 회복탄성계수 예측모델을 검증하기 위해 3차원 다층탄성해석 프로그램(GEOTRACK)을 이용하여 평택 시험 철도노반의 탄성거동을 평가하였고, 화물열차 및 여객열차가 시험구간을 통과할 때 계측한 노반의 수직 탄성변위와 비교하였다. 현장계측은 자갈도상 아래의 재료가 각각 입도조정쇄석과 양질의 화강풍화토인 두 개소에서 수행되었다. 자갈도상 아래에서 계산된 수직 탄성변위는 대략 0.6mm 이내였고 계측 결과와 잘 일치하였다. 본 연구를 통해 제안된 회복탄성계수 예측모델이 열차하중에 의한 노반의 탄성거동을 적절히 표현하고 있음을 확인하였다.