• Title/Summary/Keyword: Quadratic Elements

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Horizontal 2-D Finite Element Model for Analysis of Mixing Transport of Heat Pollutant (열오염 혼합 거동 해석을 위한 수평 2차원 유한요소모형)

  • Seo, Il Won;Choi, Hwang Jeong;Song, Chang Geun
    • KSCE Journal of Civil and Environmental Engineering Research
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    • v.31 no.6B
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    • pp.507-514
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    • 2011
  • A numerical model has been developed by employing a finite element method to simulate the depth-averaged 2-D dispersion of the heat pollutant, which is an important pollutant material in natural streams. Among the finite element methods, the Streamline Upwind/Petrov Galerkin (SUPG) method was applied. Also both linear and quadratic elements can be applied so that irregular river boundaries can be easily represented. To show the movement of heat pollutants, the reaction term describing heat transfer was represented as an equation in which sink/source term is proportional to the difference between the equilibrium temperature and water surface temperature. The equation was expressed so that the water surface temperature changes according to the temperature transfer coefficient and the equilibrium temperature. For the calibration of the model developed, analytic and numerical results from a case of rectangular channel with full width continuous injection have been compared in a steady state. The comparisons showed that the numerical results were in good agreement with analytical solutions. The application site was selected from the downstream of Paldang dam to Jamsil submerged weir, and overall length of this site is about 22.5 km. The change of water temperature caused by the discharge from the Guri sewage treatment plant has been simulated, and results were similar to the observed data. Overall it is concluded that the developed model can represent the water temperature changes due to heat transport accurately. But the verification using observed data will further enhance the validity of the model.

A Study on the cognition for generality of solution in Algebra - Focusing on Quadratic equation - (대수 해법 일반성 인식에 관한 연구: 이차방정식 문항을 중심으로)

  • Kang, Jeong Gi
    • Communications of Mathematical Education
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    • v.28 no.1
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    • pp.155-178
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    • 2014
  • This study starts from the problem that although the solution premise the generality in algebra, a lot of students don't understand the generality of algebraic solution. We investigated this problem to understand cognitive characteristic of students. Moreover, we tried to find the elements which helping students understand the generality of algebraic solution. The purpose is to get the didactical implications. To do this, we had investigated the cognition of twenty middle school students for generality of solution. As result, 70 % of them didn't cognize the generality of solution. We had a personal interview with four students who showed a lack of sense of generality of algebraic solution. Putting into three action which we designed to help the change of their recognition, we observed and analyzed students cognizance change. Three action is the check of accordance for individual results, the check of solution accordance for different variables and the check of arbitrary variables. Based on the analysis, we discussed on the cognitive characteristic of students and the effect of three action. We finally discussed on the didactical implications to help students understand the generality of algebraic solution.

Development of FURA Code and Application for Load Follow Operation (FURA 코드 개발과 부하 추종 운전에 대한 적용)

  • Park, Young-Seob;Lee, Byong-Whi
    • Nuclear Engineering and Technology
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    • v.20 no.2
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    • pp.88-104
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    • 1988
  • The FUel Rod Analysis(FURA) code is developed using two-dimensional finite element methods for axisymmetric and plane stress analysis of fuel rod. It predicts the thermal and mechanical behavior of fuel rod during normal and load follow operations. To evaluate the exact temperature distribution and the inner gas pressure, the radial deformation of pellet and clad, the fission gas release are considered over the full-length of fuel rod. The thermal element equation is derived using Galerkin's techniques. The displacement element equation is derived using the principle of virtual works. The mechanical analysis can accommodate various components of strain: elastic, plastic, creep and thermal strain as well as strain due to swelling, relocation and densification. The 4-node quadratic isoparametric elements are adopted, and the geometric model is confined to a half-pellet-height region with the assumption that pellet-pellet interaction is symmetrical. The pellet cracking and crack healing, pellet-cladding interaction are modelled. The Newton-Raphson iteration with an implicit algorithm is applied to perform the analysis of non-linear material behavior accurately and stably. The pellet and cladding model has been compared with both analytical solutions and experimental results. The observed and predicted results are in good agreement. The general behavior of fuel rod is calculated by axisymmetric system and the cladding behavior against radial crack is used by plane stress system. The sensitivity of strain aging of PWR fuel cladding tube due to load following is evaluated in terms of linear power, load cycle frequency and amplitude.

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Upper Boundary Line Analysis of Rice Yield Response to Meteorological Condition for Yield Prediction I. Boundary Line Analysis and Construction of Yield Prediction Model (최대경계선을 이용한 벼 수량의 기상반응분석과 수량 예측 I. 최대경계선 분석과 수량예측모형 구축)

  • 김창국;이변우;한원식
    • KOREAN JOURNAL OF CROP SCIENCE
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    • v.46 no.3
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    • pp.241-247
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    • 2001
  • Boundary line method was adopted to analyze the relationships between rice yield and meteorological conditions during rice growing period. Boundary lines of yield responses to mean temperature($T_a$) and sunshine hour( $S_{h}$) and diurnal temperature range($T_r$) were well-fitted to hyperbolic functions of f($T_a$) =$$\beta$_{0t}$(1-EXP(-$$\beta$_{1t}$ $\times$ ($T_a$) ) and f( $S_{h}$)=$$\beta$_{0t}$((1-EXP($$\beta$_{1t}$$\times$ $S_{h}$)), to quadratic function of f($T_r$) =$\beta$$_{0r}$(1-($T_r$ 1r)$^2$), respectively. to take into account to, the sterility caused by low temperature during reproductive stage, cooling degree days [$T_c$ =$\Sigma$(20-$T_a$] for 30 days before heading were calculated. Boundary lines of yield responses to $T_c$ were fitted well to exponential function of f($T_c$) )=$\beta$$_{0c}$exp(-$$\beta$_{1c}$$\times$$T_c$ ). Excluding the constants of $\beta$$_{0s}$ from the boundary line functions, formed are the relative function values in the range of 0 to 1. And these were used as yield indices of the meteorological elements which indicate the degree of influence on rice yield. Assuming that the meteorological elements act multiplicatively and independently from each other, meteorological yield index (MIY) was calculated by the geometric mean of indices for each meteorological elements. MIY in each growth period showed good linear relationship with rice yield. The MIY's during 31 to 45 days after transplanting(DAT) in vegetative stage, during 30 to 16 days before heading (DBH) in reproductive stage and during 20 days after heading (DAH) in ripening stage showed greater explainablity for yield variation in each growth stage. MIY for the whole growth period was calculated by the following three methods of geometric mean of the indices for vegetative stage (MIVG), reproductive stage (HIRG) and ripening stage (HIRS). MI $Y_{I}$ was calculated by the geometric mean of meteorological indices showing the highest determination coefficient n each growth stage of rice. That is, (equation omitted) was calculated by the geometric mean of all the MIY's for all the growth periods devided into 15 to 20 days intervals from transplanting to 40 DAH. MI $Y_{III}$ was calculated by the geometric mean of MIY's for 45 days of vegetative stage (MIV $G_{0-45}$ ), 30 days of reproductive stage (MIR $G_{30-0}$) and 40 days of ripening stage (MIR $S_{0-40}$). MI $Y_{I}$, MI $Y_{II}$ and MI $Y_{III}$ showed good linear relationships with grain yield, the coefficients of determination being 0.651, 0.670 and 0.613, respectively.and 0.613, respectively.

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