• 제목/요약/키워드: Matrix Equations

검색결과 913건 처리시간 0.032초

3-D CFD Analysis of the CANDU-6 Moderator Circulation Under Nnormal Operating Conditions

  • Yoon, Churl;Rhee, Bo-Wook;Min, Byung-Joo
    • Nuclear Engineering and Technology
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    • 제36권6호
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    • pp.559-570
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    • 2004
  • A computational fluid dynamics model for predicting moderator circulation inside the Canada deuterium uranium (CANDU) reactor vessel has been developed to estimate the local subcooling of the moderator in the vicinity of the calandria tubes. The buoyancy effect induced by the internal heating is accounted for by the Boussinesq approximation. The standard $k-{\varepsilon}$ turbulence model with logarithmic wall treatment is applied to predict the turbulent jet flows from the inlet nozzles. The matrix of the calandria tubes in the core region is simplified to a porous media in which the anisotropic hydraulic impedance is modeled using an empirical correlation of pressure loss. The governing equations are solved by DFX-4.4, a commercial CFD code developed by AEA technology. The resultant flow patterns of the constant-z slices containing the inlet nozzles and the outlet port are "mined-type", as observed in the former 2-dimensional experimental investigations. With 103% full power for conservatism, the maximum temperature of the moderator is $82.9^{\circ}C$ at the top of the core region. Considering the hydrostatic pressure change, the minimum subcooling is $24.8^{\circ}C$.

Free vibration analysis of rectangular plate with arbitrary edge constraints using characteristic orthogonal polynomials in assumed mode method

  • Kim, Kook-Hyun;Kim, Byung-Hee;Choi, Tae-Muk;Cho, Dae-Seung
    • International Journal of Naval Architecture and Ocean Engineering
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    • 제4권3호
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    • pp.267-280
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    • 2012
  • An approximate method based on an assumed mode method has been presented for the free vibration analysis of a rectangular plate with arbitrary edge constraints. In the presented method, natural frequencies and their mode shapes of the plate are calculated by solving an eigenvalue problem of a multi-degree-of-freedom system matrix equation derived by using Lagrange's equations of motion. Characteristic orthogonal polynomials having the property of Timoshenko beam functions which satisfies edge constraints corresponding to those of the objective plate are used. In order to examine the accuracy of the proposed method, numerical examples of the rectangular plates with various thicknesses and edge constraints have been presented. The results have shown good agreement with those of other methods such as an analytic solution, an approximate solution, and a finite element analysis.

A Numerical and Experimental Study on Dynamics of A Towed Low-Tension Cable

  • 정동호;박한일
    • 한국해양공학회:학술대회논문집
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    • 한국해양공학회 2002년도 추계학술대회 논문집
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    • pp.191-196
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    • 2002
  • The paper presents a numerical and experimental investigation on dynamic behaviors of a towed low tension cable. In the numerical study, an implicit finite difference algorithm is employed for three-dimensional cable equations. Fluid and geometric non-linearity and bending stiffness are considered and solved by Newton-Raphson iteration. Block tri-diagonal matrix method is applied for the fast calculation of the huge size of matrices. In order to verify the numerical results and to see real physical phenomena, an experiment is carried out for a 6m cable in a deep and long towing tank. The cable is towed in two different ways; one is towed at a constant speed and the other is towed at a constant speed with top end horizontal oscillations. Cable tension and shear forces are measured at the top end. Numerical and experimental results are compared with good agreements in most cases but with some differences in a few cases. The differences are due to drag coefficients caused by vortex shedding. In the numerical modeling, non-uniform element length needs to be employed to cope with the sharp variation of tension and shear forces at near top end.

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Analysis of trusses by total potential optimization method coupled with harmony search

  • Toklu, Yusuf Cengiz;Bekdas, Gebrail;Temur, Rasim
    • Structural Engineering and Mechanics
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    • 제45권2호
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    • pp.183-199
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    • 2013
  • Current methods of analysis of trusses depend on matrix formulations based on equilibrium equations which are in fact derived from energy principles, and compatibility conditions. Recently it has been shown that the minimum energy principle, by itself, in its pure and unmodified form, can well be exploited to analyze structures when coupled with an optimization algorithm, specifically with a meta-heuristic algorithm. The resulting technique that can be called Total Potential Optimization using Meta-heuristic Algorithms (TPO/MA) has already been applied to analyses of linear and nonlinear plane trusses successfully as coupled with simulated annealing and local search algorithms. In this study the technique is applied to both 2-dimensional and 3-dimensional trusses emphasizing robustness, reliability and accuracy. The trials have shown that the technique is robust in two senses: all runs result in answers, and all answers are acceptable as to the reliability and accuracy within the prescribed limits. It has also been shown that Harmony Search presents itself as an appropriate algorithm for the purpose.

Effect of Circuit Parameters on Stability of Voltage-fed Buck-Boost Converter in Discontinuous Conduction Mode

  • Feng, Zhao-He;Gong, Ren-Xi;Wang, Qing-Yu
    • Journal of Electrical Engineering and Technology
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    • 제9권4호
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    • pp.1283-1289
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    • 2014
  • The state transition matrix are obtained by solving state equations in terms of Laplace inverse transformation and Cayley-Hamilton theorem, and an establishment of a precise discrete-iterative mapping of the voltage-fed buck-boost converter operating in discontinuous conduction mode is made. On the basis of the mapping, the converter bifurcation diagrams and Lyapunov exponent diagrams with the input voltage, the resistance, the inductance and the capacitance as the bifurcation parameters are obtained, and the effect of the parameters on the system stability is deeply studied. The results obtained show that they have a great influence on the stability of the system, and the general trend is that the increase of either the voltage-fed coefficient, input voltage or the load resistance, or the decrease of the filtering inductance, capacitance will make the system stability become poorer, and that all the parameters have a critical value, and when they are greater or less than the values, the system will go through stable 1T orbits, stable 2T orbits, 4T orbits, 8T orbits and eventually approaches chaos.

용탕주조법을 이용한 금속복합재료 제조공정의 열전달 해석 (Numerical Modeling of Heat Transfer for Squeeze Casting of MMCs)

  • 정창규;정성욱;남현욱;한경섭
    • 대한기계학회논문집A
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    • 제26권10호
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    • pp.2104-2113
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    • 2002
  • A finite element model is developed for the process of squeeze casting of metal matrix composites (MMCs) in cylindrical molds. The fluid flow and the heat transit. are fundamental phenomena in squeeze casting. To describe heat transfer in the solidification of molten aluminum, the energy equation is written in terms of temperature and enthalpy are applied in an axisymmetric model which is similar to the experimental system. A one dimensional flow model simulates the transient metal flow. A direct iteration technique was used to solve the resulting nonlinear algebraic equations, using a computer program to calculate the enthalpy, temperature and fluid velocity. The cooling curves and temperature distribution during infiltration and solidification were calculated fer pure aluminum. Experimentally, the temperature was measured and recorded using thermocouple wire. The measured time-temperature data were compared with the calculated cooling curves. The resulting agreement shows that the finite element model can accurately estimate the solidification time and predict the cooling process.

끝단질량과 크랙을 가진 유체유동 회전 외팔 파이프의 동적 안정성 (Dynamic Stability of Rotating Cantilever Pipe Conveying Fluid with Tip mass and Crack)

  • 손인수;윤한익;김동진
    • 한국소음진동공학회논문집
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    • 제18권1호
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    • pp.101-109
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    • 2008
  • The stability of a rotating cantilever pipe conveying fluid with a crack and tip mass is investigated by the numerical method. That is, the effects of the rotating angular velocity, mass ratio, crack severity and tip mass on the critical flow velocity for flutter instability of system are studied. The equations of motion of rotating pipe are derived by using the Euler-Bernoulli beam theory and the extended Hamilton's principle. The crack section of pipe is represented by a local flexibility matrix connecting two undamaged pipe segments. Also, the crack is assumed to be in the first mode of fracture and always opened during the vibrations. When the tip mass and crack are constant, the critical flow velocity for flutter is proportional to the rotating angular velocity of pipe. In addition, the stability maps of the rotating pipe system as a rotating angular velocity and mass ratio ${\beta}$ are presented.

공분산구조분석을 이용한 자체충족률 모형 검증 (Formulating Regional Relevance Index through Covariance Structure Modeling)

  • 장혜정;김창엽
    • 보건행정학회지
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    • 제11권2호
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    • pp.123-140
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    • 2001
  • Hypotheses In health services research are becoming increasingly more complex and specific. As a result, health services research studies often include multiple independent, intervening, and dependent variables in a single hypothesis. Nevertheless, the statistical models adopted by health services researchers have failed to keep pace with the increasing complexity and specificity of hypotheses and research designs. This article introduces a statistical model well suited for complex and specific hypotheses tests in health services research studies. The covariance structure modeling(CSM) methodology is especially applied to regional relevance indices(RIs) to assess the impact of health resources and healthcare utilization. Data on secondary statistics and health insurance claims were collected by each catchment area. The model for RI was justified by direct and indirect effects of three latent variables measured by seven observed variables, using ten structural equations. The resulting structural model revealed significant direct effects of the structure of health resources but indirect effects of the quantity on RIs, and explained 82% of correlation matrix of measurement variables. Two variables, the number of beds and the portion of specialists among medical doctors, became to have significant effects on RIs by being analyzed using the CSM methodology, while they were insignificant in the regression model. Recommendations for the CSM methodology on health service research data are provided.

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The effect of carbon nanotubes agglomeration on vibrational response of thick functionally graded sandwich plates

  • Tahouneh, Vahid
    • Steel and Composite Structures
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    • 제24권6호
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    • pp.711-726
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    • 2017
  • In the present work, by considering the agglomeration effect of single-walled carbon nanotubes, free vibration characteristics of functionally graded (FG) nanocomposite sandwich plates resting on Pasternak foundation are presented. The volume fractions of randomly oriented agglomerated single-walled carbon nanotubes (SWCNTs) are assumed to be graded in the thickness direction. To determine the effect of CNT agglomeration on the elastic properties of CNT-reinforced composites, a two-parameter micromechanical model of agglomeration is employed. In this research work, an equivalent continuum model based on the Eshelby-Mori-Tanaka approach is employed to estimate the effective constitutive law of the elastic isotropic medium (matrix) with oriented straight CNTs. The 2-D generalized differential quadrature method (GDQM) as an efficient and accurate numerical tool is used to discretize the equations of motion and to implement the various boundary conditions. The proposed rectangular plates have two opposite edges simply supported, while all possible combinations of free, simply supported and clamped boundary conditions are applied to the other two edges. The benefit of using the considered power-law distribution is to illustrate and present useful results arising from symmetric and asymmetric profiles. The effects of two-parameter elastic foundation modulus, geometrical and material parameters together with the boundary conditions on the frequency parameters of the laminated FG nanocomposite plates are investigated. It is shown that the natural frequencies of structure are seriously affected by the influence of CNTs agglomeration. This study serves as a benchmark for assessing the validity of numerical methods or two-dimensional theories used to analysis of laminated plates.

Buckling response with stretching effect of carbon nanotube-reinforced composite beams resting on elastic foundation

  • Khelifa, Zoubida;Hadji, Lazreg;Daouadji, Tahar Hassaine;Bourada, Mohamed
    • Structural Engineering and Mechanics
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    • 제67권2호
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    • pp.125-130
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    • 2018
  • This study deals with buckling analysis with stretching effect of functionally graded carbon nanotube-reinforced composite beams resting on an elastic foundation. The single-walled carbon nanotubes (SWCNTs) are aligned and distributed in polymeric matrix with different patterns of reinforcement. The material properties of the CNTRC beams are estimated by using the rule of mixture. The significant feature of this model is that, in addition to including the shear deformation effect and stretching effect it deals with only 4 unknowns without including a shear correction factor. The equilibrium equations have been obtained using the principle of virtual displacements. The mathematical models provided in this paper are numerically validated by comparison with some available results. New results of buckling analyses of CNTRC beams based on the present theory with stretching effect is presented and discussed in details. the effects of different parameters of the beam on the buckling responses of CNTRC beam are discussed.