• 제목/요약/키워드: 포아송 방정식

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A Numerical Study on Thermo-hydro-mechanical Coupling in Continuum Rock Mass Based on the Biot's Consolidation Theory (Biot의 압밀 이론에 근거한 연속체 암반의 열-수리-역학 상호작용의 수치적 연구)

  • 이희석;양주호
    • Tunnel and Underground Space
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    • v.10 no.3
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    • pp.355-365
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    • 2000
  • As large underground projects such as radioactive waste disposal, hot water and heat storage, and geothermal energy become influential, the study, which consider all aspects of thermics, hydraulics and mechanics would be needed. Thermo-Hydro-Mechanical coupling analysis is one of the most complex numerical technique because it should be implemented with the combined three governing equations to analyze the behavior of rock mass. In this study, finite element code, which is based on Biot's consolidation theory, was developed to analyze the thermo-hydro-mechanical coupling in continuum rock mass. To verify the implemented program, one-dimensional consolidation model under the isothermal and non-isothermal conditions was analyzed and was compared with the analytic solution. The parametric study on two-dimensional consolidation was also performed and the effects of several factors such as poisson's ratio and hydraulic anisotropy on rock mass behavior were investigated. In the future, this program would be revised to be used for analysis of general discontinuous media with incorporating discrete joint model.

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Probabilistic Behavior of In-plane Structure due to Multiple Correlated Uncertain Material Constants (상호 상관관계가 있는 다중 재료상수의 불확실성에 의한 평면구조의 확률론적 거동)

  • Noh Hyuk-Chun
    • Journal of the Computational Structural Engineering Institute of Korea
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    • v.18 no.3
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    • pp.291-302
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    • 2005
  • Due to the importance of the parameter in structural response, the uncertain elastic modulus was located at the center of stochastic analysis, where the response variability caused by the uncertain system parameters is pursued. However when we analyze the so-called stochastic systems, as many parameters as possible must be included in the analysis if we want to obtain the response variability that can reach a true one, even in an approximate sense. In this paper, a formulation to determine the statistical behavior of in-plane structures due to multiple uncertain material parameters, i.e., elastic modulus and Poisson's ratio, is suggested. To this end, the polynomial expansion on the coefficients of constitutive matrix is employed. In constructing the modified auto-and cross-correlation functions, use is made of the general equation for n-th moment. For the computational purpose, the infinite series of stochastic sub-stiffness matrices is truncated preserving required accuracy. To demons4rate the validity of the proposed formulation, an exemplary example is analyzed and the results are compared with those obtained by means of classical Monte Carlo simulation, which is based on the local averaging scheme.

Mechanical Anisotropy of Pocheon Granite under Uniaxial Compression (일축압축하에서 포천화강암의 역학적 이방성)

  • Park Deok-Won
    • The Journal of Engineering Geology
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    • v.15 no.3
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    • pp.337-348
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    • 2005
  • Jurassic granite from Pocheon area were tested to investigate the effect of microcracks on mechanical properties of the granite. Three oriented core specimens were used for uniaxial compressive tests and each core specimen are perpendicular to the axes'R'(rift plane),'c'(grain plane) and'H'(hardway plane), respectively Among vacious elastic constants, the variation of Poisson's ratio as function of the directions was examined. From the related chart between ratio of failure strength and Poisson's ratio, H-specimen shows the highest range in Poisson's ratio and Poisson's ratio decreases in the order of C-specimen and R-specimen. The curve pattern is nearly linear in stage $I\simIII$ but the slope increases abruptly in stage H-3. As shown in the related chart, diverging point of a curve is formed when ratio of failure strength is $0.92\sim0.96$ Stage IV -3 is out of elastic region. The behaviour of rock in the four fracturing stages was analyzed in term of the stress-volumetric strain me. From the stress increment-volumetric strain equations governing the behaviour of rock, characteristic material constants, a, n, Q, m and $\varepsilon_v^{mcf}$, were determined. Among these, inherent microcrack porosity$(a, 10^{-3})$ and compaction exponent(n) in the microcrack closure region(stage I ) show an order of $a^R(3.82)>a^G(3.38)>a^H(2.32)\;and\;n^R(3.69)>n^G(2.79)>n^H(1.99)4, respectively. Especially, critical volumetric microcrack strain($\varepsilon_v^{mcf}$) in the stage W is highest in the H-specimen, normal to the hardway plane. These results indicate a strong correlation between two major sets of microcracks and mechanical properties such as Poisson's ratio and material constants. Correlation of strength anisotropy with microcrack orientation can have important application in rock fracture studies.

Charge Trap Flash 메모리 소자 프로그램 동작 시 전하수송 메커니즘

  • Yu, Ju-Tae;Kim, Dong-Hun;Kim, Tae-Hwan
    • Proceedings of the Korean Vacuum Society Conference
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    • 2011.08a
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    • pp.273-273
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    • 2011
  • 현재 사용되고 있는 플로팅 게이트를 이용한 플래시 메모리 소자는 비례축소에 의해 발생하는 단 채널 효과, 펀치스루 효과 및 소자간 커플링 현상과 같은 문제로 소자의 크기를 줄이는데 한계가 있다. 이러한 문제를 해결하기 위하여 silicon nitride와 같은 절연체를 전자의 트랩층으로 사용하는 charge trap flash (CTF) 메모리 소자에 대한 연구가 활발히 진행되고 있다. CTF 메모리 소자의 전기적 특성에 대한 연구는 활발히 진행 되었지만, 수치 해석 모델을 사용하여 메모리 소자의 전하수송 메커니즘을 분석한 연구는 매우 적다. 본 연구에서는 수치 해석 모델을 적용하여 개발한 시뮬레이터를 사용하여 CTF 메모리 소자의 프로그램 동작 시 전하수송 메커니즘에 대한 연구를 하였다. 시뮬레이터에 사용된 모델은 연속방정식, 포아송 방정식과 Shockley-Read-Hall 재결합 모델을 수치해석적 방법으로 계산하였다. 또한 CTF 소자 프로그램 동작 시 트랩 층으로 주입되는 전자의 양은 Wentzel-Kramers-Brillouin 근사 법을 이용하여 계산하였다. 트랩 층에 트랩 되었던 전자의 방출 모델은 이온화 과정을 사용하였다. 게이트와 트랩 층 사이의 터널링은 Fowler-Nordheim (FN) tunneling 모델, Direct tunneling 모델, Modified FN tunneling 모델을 적용하였다. FN tunneling 만을 적용했을때 보다 세가지 모델을 적용했을 때가 더 실험치와의 오차가 적었다. 그 이유는 시뮬레이션 결과를 통해 인가된 전계에 의해 Bottom Oxide 층의 에너지 밴드 구조가 변화하여 세가지 tunneling 모델의 구역이 발생하는 것을 확인 할 수 있었다. 계산된 결과의 전류-전압 곡선을 통해 CTF 메모리 소자의 프로그램 동작 특성을 관찰하였다. 트랩 층의 전도대역과 트랩 층 내부에 분포하는 전자의 양을 시간에 따라 계산하여 트랩 밀도가 시간이 지남에 따라 일정 값에 수렴하고 많은 전하가 트랩 될 수록 전하 주입이 줄어듬을 관찰 하였다. 이와 같은 시뮬레이션 결과를 통해 CTF 메모리의 트랩층에서 전하의 이동에 대해 더 많이 이해하여 CTF 소자가 가진 문제점 해결에 도움을 줄 것이다.

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Optimal Release Problems based on a Stochastic Differential Equation Model Under the Distributed Software Development Environments (분산 소프트웨어 개발환경에 대한 확률 미분 방정식 모델을 이용한 최적 배포 문제)

  • Lee Jae-Ki;Nam Sang-Sik
    • The Journal of Korean Institute of Communications and Information Sciences
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    • v.31 no.7A
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    • pp.649-658
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    • 2006
  • Recently, Software Development was applied to new-approach methods as a various form : client-server system and web-programing, object-orient concept, distributed development with a network environments. On the other hand, it be concerned about the distributed development technology and increasing of object-oriented methodology. These technology is spread out the software quality and improve of software production, reduction of the software develop working. Futures, we considered about the distributed software development technique with a many workstation. In this paper, we discussed optimal release problem based on a stochastic differential equation model for the distributed Software development environments. In the past, the software reliability applied to quality a rough guess with a software development process and approach by the estimation of reliability for a test progress. But, in this paper, we decided to optimal release times two method: first, SRGM with an error counting model in fault detection phase by NHPP. Second, fault detection is change of continuous random variable by SDE(stochastic differential equation). Here, we decide to optimal release time as a minimum cost form the detected failure data and debugging fault data during the system test phase and operational phase. Especially, we discussed to limitation of reliability considering of total software cost probability distribution.

A Study of the Threshold Voltage of a Symmetric Double Gate Type MOSFET (대칭형 이중 게이트 MOSFET에 대한 문턱전압 연구)

  • Lee, Jeong-Ihll;Shin, Jin-Seob
    • The Journal of the Institute of Internet, Broadcasting and Communication
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    • v.10 no.6
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    • pp.243-249
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    • 2010
  • In this thesis, in order to a equivalent circuit-analytical study for a symmetric double gate type MOSFET, we slove analytically the 2D Poisson's equation in a a silicon body. To solve the threshold voltage in a symmetric double gate type MOSFET from the derived expression for the surface potential which the two-dimensional potential distribution of a symmetric double gate type MOSFET is assumed approximately. This thesis can use short and long channel in a silicon body we introduce a new the threshold voltage model in a symmetric double gate type MOSFET and measure it the distance about the range of channel length up to 0.1 [${\mu}m$].

AN EFFICIENT ALGORITHM FOR INCOMPRESSIBLE FREE SURFACE FLOW ON CARTESIAN MESHES (직교격자상에서 효율적인 비압축성 자유표면유동 해법)

  • Go, G.S.;Ahn, H.T.
    • Journal of computational fluids engineering
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    • v.19 no.4
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    • pp.20-28
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    • 2014
  • An efficient solution algorithm for simulating free surface problem is presented. Navier-Stokes equations for variable density incompressible flow are employed as the governing equation on Cartesian meshes. In order to describe the free surface motion efficiently, VOF(Volume Of Fluid) method utilizing THINC(Tangent of Hyperbola for Interface Capturing) scheme is employed. The most time-consuming part of the current free surface flow simulations is the solution step of the linear system, derived by the pressure Poisson equation. To solve a pressure Poisson equation efficiently, the PCG(Preconditioned Conjugate Gradient) method is utilized. This study showed that the proper application of the preconditioner is the key for the efficient solution of the free surface flow when its pressure Poisson equation is solved by the CG method. To demonstrate the efficiency of the current approach, we compared the convergence histories of different algorithms for solving the pressure Poisson equation.

Node Activation Technique for Finite Element Model : Ⅱ. Computation (유한요소 모델의 절점 활성화 기법 : Ⅱ. 계산)

  • Kim, Do Nyeon;Kim, Seung Jo;Ji, Yeong Beom;Jo, Jin Yeon
    • Journal of the Korean Society for Aeronautical & Space Sciences
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    • v.31 no.4
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    • pp.35-43
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    • 2003
  • In this paper, an efficient computational algorithm for the implementation of the newly proposed node activation technique is presented, and its computational aspects are thoroughly investigated. To verify the validity, convergence, and efficiency of the node activation technique, various numerical examples are worked out including the problems of Poisson equation, 2D elasticity problems, and 3D elasticity problems. From the numerical tests, it is verified that one can arbitrarily activate and handle the nodal points of interest in finite element model with very little loss of the numerical accuracy.

A Study on the Correction Method for Deviations and Variations of Digital Magnetic Compass (디지털 자기 컴퍼스의 자차와 편차 수정에 관한 연구)

  • Yim, Jeong-Bin;Saha, Rampadha
    • Proceedings of KOSOMES biannual meeting
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    • 2006.11a
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    • pp.137-141
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    • 2006
  • To consider the practical use of a ship's Digital Compass in earth's magnetic field high accurate Deviation and 얘 nation are required to obtain ship's true bearing. Variation can be obtain with World Magnetic Model (WMM) using the Earth's spherical harmonic model of the main field and of the secular variation at any location around the earth. Deviation can be obtain with deviation analysis and synthesis method based on the Poisson equations. As results of deviation and variation corrections to the Digital Compass, high accurate true bearing is obtained. This experiments are carried out during in the navigation of training ship 'SAE-NU-RI'.

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Analysis of Subthreshold Swings Based on Scaling Theory for Double Gate MOSFET (이중게이트 MOSFET의 스켈링 이론에 대한 문턱전압이하 스윙분석)

  • Jung, Hakkee
    • Journal of the Korea Institute of Information and Communication Engineering
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    • v.16 no.10
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    • pp.2267-2272
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    • 2012
  • This study has presented the analysis of subthreshold swings based on scaling theory for double gate MOSFET. To solve the analytical potential distribution of Poisson's equation, we use Gaussian function to charge distribution. The scaling theory has been used to analyze short channel effect such as subthreshold swing degradation. These scaling factors for gate length, oxide thickness and channel thickness has been modified with the general scaling theory to include effects of double gates. We know subthreshold swing degradation is rapidly reduced when scaling factor of gate length is half of general scaling factor, and parameters such as projected range and standard projected deviation have greatly influenced on subthreshold swings.