• Title/Summary/Keyword: plate equations

검색결과 1,089건 처리시간 0.032초

지수 및 멱 법칙 점진기능재료 판의 3차원 자유진동해석 (3-D Free Vibration Analysis of Exponential and Power-law Functionally Graded Material(FGM) Plates)

  • 이원홍;한성천;안진희;박원태
    • 한국전산구조공학회논문집
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    • 제28권5호
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    • pp.553-561
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    • 2015
  • 지수 함수 및 멱 법칙 함수를 이용한 점진기능재료(FGM) 판의 전단 및 두께 방향 변형을 고려한 이론을 정식화하여 동적 평형방정식을 유도하였다. 지수 함수 및 멱 법칙 함수는 두께 방향으로 재료의 변화를 고려할 수 있고 3차원 해석방법은 전단 및 두께 방향 변형을 고려함으로써 점진기능재료의 정확한 구조적 특성을 고려할 수 있다. Pasternak탄성지반 위에 놓인 4변이 단순 지지되고 전단 및 두께 방향 변형이 고려된 점진기능재료 판의 지배방정식을 풀기 위해 Navier 방법을 사용하였다. 거듭제곱 지수와 3차원 해석의 효과를 나타내기 위한 지수 및 멱 법칙 점진기능재료 판의 동적 해석결과를 제시하였다. 기존의 2차원 고차전단변형 이론 및 3차원 이론과의 관계를 수치해석 결과를 통하여 고찰하였다. 또한 (i) 거듭제곱 지수, (ii) 폭-두께 비, 그리고 (iii) 탄성지반 계수, 등이 점진기능재료 판의 자유진동수에 미치는 효과에 대하여 관찰하였다. 본 연구의 결과를 검증하기 위해 참고문헌의 결과들과 비교 분석하였다.

할선탄성계수를 이용한 반복하중 하 지반의 영구변형 해석 (Analysis of Permanent Deformation under Repetitive Load Based on Degraded Secant Modulus)

  • 안재훈;오정호;신호성
    • 한국지반공학회논문집
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    • 제29권2호
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    • pp.15-21
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    • 2013
  • 일반적으로 도로 포장체 영구변형의 해석은, 먼저 포장체를 층이 진 탄성체로 가정하고 회복탄성계수를 통해 포장체의 회복변형률을 계산하고, 이로부터 다시 실내시험을 통해 얻어진 방정식을 이용하여 영구변형률을 산정하게 된다. 회복탄성계수를 통하여 포장체 내의 응력을 산정할 경우, 포장 내 노상토 상부의 응력은 반복하중으로 인한 노상토의 영구변형 증가를 고려하지 않은 회복탄성계수로부터 결정되므로, 영구변형이 지반 및 포장체에 미치는 영향은 응력 산정 시에 고려되지 않는다. 또한, 토목섬유 등으로 보강된 포장체 등의 거동은 해석에 한계가 있다. 본 논문에서는 기존에 회복탄성계수를 사용하여 포장체의 탄성거동을 계산하는 방식과 달리 하중반복회수의 함수인 할선탄성계수를 사용하여 영구변형을 측정할 수 있도록 새로운 모델을 제안하고, 본 모델 적용과 모델계수 산정의 예를 보인다. 제안된 할선탄성계수를 통한 해석은 비포장 도로 상의 교통으로 인한 영구변형의 예측이나 아스팔트 포장 전 노상토나 기층상부에 가해지는 공사차량으로 인한 영구변형의 산정에 적용가능 할 것으로 판단한다.

Ibuprofen Racemate의 HPLC 분리실험과 FEMLAB 전산모사 연구 (Experimental and FEMLAB Simulation Study of Ibuprofen Racemate Separation in HPLC)

  • 이은;장상목;김종민;김우식;김인호
    • KSBB Journal
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    • 제21권3호
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    • pp.224-229
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    • 2006
  • 전산모사 프로그램인 FEMLAB을 이용하여 chiral center를 가지고 있는 racemate인 ibuprofen의 R-form과 S-form의 분리 전산모사 결과와 Kromasil KR100-5CHI-TBB 칼럼을 사용하여 HPLC를 통한 실험데이터를 비교 분석하였다. Hexane/t-BME/acetic acid(45:55:1 v/v%)의 이동상의 조건에서 이론단수(number of theoretical plates), 이론단높이(HETP; Height Equivalent to a Theoretical Plate)을 구하여 축방향 확산계수($Deff_i$)를 계산하였다. PIM(Pulsed Input Method)을 사용하여 분석한 결과 ibuprofen의 농도가 증가할수록 Langmuir 등온흡착식을 따르는 비선형 거동을 보였고, 각 농도에서의 체류시간($t_R$)과 phase ratio를 이용하여 비경쟁적 Langmuir 등온흡착식의 매개변수를 추산하였고, 이 매개변수를 이용하여 경쟁적 Langmuir 등온흡착식을 결정하였다. 실험을 통해 얻은 데이터를 FEMLAB 적용하여 등온흡착식의 변화에 따른 용리띠의 변화와 두 성분이 컬럼을 이동하는 동안 두 성분간 분리 과정을 관찰하였다. Ibuprofen의 농도, 유속을 변화시키면서 실험결과와 전산모사결과를 비교한 결과 실험결과와 전산모사결과가 비슷한 경향성을 보였다. 이와 같이 FEMLAB 전산모사 프로그램의 실험적용 가능성을 확인하였고. 실험과 일치하는 전산모사데이터를 얻기 위해서 고정상내의 세공에서의 물질전달을 포함하는 물질수지식의 적용과 비선형 흡착평형식에 대한 좀 더 정확한 식이 요구된다.

SPH 기법 기반의 파동수조 시뮬레이션 (SPH-Based Wave Tank Simulations)

  • 이상민;김무종;고권환;홍정욱
    • 한국전산구조공학회논문집
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    • 제34권1호
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    • pp.59-69
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    • 2021
  • 최근 친환경 에너지 개발에 대한 관심의 증가로 해상 및 연안 지역에서 대규모 해양구조물들이 건설되고 있다. 해양구조물은 항상 파랑 하중에 노출되어 있으므로 구조적인 안전성을 확보하기 위해서는 파랑에 대한 정확한 이해와 분석이 필수적이다. 실해역에서 수행되는 실험은 해양파를 이해하기 위한 가장 정확한 방법이지만, 변수의 통제가 어렵고 비용과 규모 측면에서 실험이 제한되는 경우가 많다. 본 연구에서는 수치파동수조를 이용하여 다양한 조건의 파를 생성하고 및 이론식과 비교를 통해 파랑 생성 능력을 검증하였다. 입자 기반 수치해석법인 SPH(Smoothed Particle Hydrodynamics) 기법을 이용하여 3차원 수조 및 피스톤 조파기를 모델링하였으며, 반사파에 대한 영향을 최소화하기 위해 수로 끝단에 질량 가중 감쇠 영역을 설정하여 안정적인 파고 및 유속 계산이 수행될 수 있게 하였다. 목표 파랑 조건에서,상대 수심이 2 이하를 만족하는 경우 파형경사에 관계없이 파고와 유속을 계산한 결과가 이론값과 높은 정확도를 보였다. 그러나 상대수심과 파형경사의 목표값이 증가하고, 측정 위치가 멀어짐에 따라서 최대 10% 이상의 오차가 발생하였다. 수치해석을 이용하여 정확한 계산이 가능한 파랑 범위를 무차원 변수를 이용하여 제안하였으며, 차후 수치해석을 이용한 수치파동수조 검증기준과 유체-구조물 상호작용 해석분야 연구에 효과적으로 활용될 수 있다.

해양환경에 노출된 강부재의 표면염분과 부식량 상관관계 (Correlation of Surface Chloride and Corrosion Amount for Steel Member Exposed in Marine Environment)

  • 하민균;허창재;유훈;안진희
    • 한국구조물진단유지관리공학회 논문집
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    • 제27권4호
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    • pp.45-53
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    • 2023
  • 본 연구에서는 해양환경에 노출된 강부재의 표면염분과 부식량의 상관관계를 분석하기 위하여 해상강교량의 보강형 거더 부재와 강박스 실험체를 대상으로 표면염분량과 평균부식두께를 부재단위로 평가하였다. 표면염분은 월단위로 1년간 Bresle method를 활용하여 계측하였고, 부식량은 실험용 모니터링 강판에 발생한 부식생성물로 인한 중량감소량을 평균부식두께으로 환산하여 분석하였다. 표면염분과 부식량을 계측한 결과, 강부재의 형상이나 설치위치에 따라 상대적인 표면염분량과 평균부식두께의 차이가 나타났으며, 동일한 교량 내에 설치된 동일한 형상의 부재라도 부식량이 국부적으로 급격히 증가하는 것을 확인하였다. 표면염분과 부식량의 상관관계를 분석하기 위하여 표면염분에 따른 부식량 발생 경향을 평가하였으며, 부식량을 평가할 수 있는 평가식을 부재의 형상별로 분석하였다. 표면염분과 부식량의 상관관계 분석 결과, 표면염분의 영향으로 강부재에서 발생하는 부식량은 부재의 형상에 따라 약 1.15배까지 변화하는 것으로 나타났다.

투수계수 산정을 위한 균질화 해석법의 적응 (Application of the Homogenization Analysis to Calculation of a Permeability Coefficient)

  • 채병곤
    • 한국지하수토양환경학회지:지하수토양환경
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    • 제9권1호
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    • pp.79-86
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    • 2004
  • 암석 내 균열을 따른 수리전도도는 균열의 기하학적 요소, 즉 방향, 간극, 거칠기 그리고 상호 연결도에 주로 좌우된다. 따라서, 균열 내 투수계수를 정확하게 계산하기 위해서는 이와 같은 기하 요소들을 최대한 계산모델에 반영할 필요가 있다. 이 연구에서는 균열 기하양상을 최대한 정확히 반영한 균열모델에서 기존 수치해석과는 다른 새로운 방법인 균질화 해석법(homogenization analysis method)을 이용하여 균열을 따른 투수계수를 구하기 위해 수치해석을 수행하였다. 먼저, 공초점 레이저 스캔 현미경(Confocal Laser Scanning Microscope)을 이용하여 암석시료의 균열 조도와 균열에 가한 수직압축력의 변화에 따른 간극 변화량을 직접 측정하고, 이와 같이 획득한 자료는 균열모델 재현을 위한 입력자료로 사용되었다. 재현된 균열모델을 토대로 한 균질화 해석법은 미시규모(microscale) 매질특성과 거시규모(macroscale) 매질특성을 동시에 고려하여 투수계수를 계산할 수 있는 것이다. 즉, 균질화 해석법은 주기적 미세구조(microstructure)를 갖는 미소 불균질 물질의 거동특성을 구명하기 위해 개발된 새로운 형태의 섭동(perturbation) 이론이다. 이는 균질한 미시규모에서 미시 투수특성을 계산한 후, 거시규모에서의 균질화 투수계수를 계산하게 된다. 그러므로, 이 방법은 균열 기하양상의 국부적 영향을 고려한 투수특성을 정확히 해석할 수 있다. 균질화법을 이용한 투수계수 산정결과를 기존 연구에서 제안한 경험식과 비교하여 그 타당성을 검증하기 위해 전술한 2차원 균열모델을 이용한 투수계수 계산을 수행하였다. 균열모델은 거칠기(roughness)를 반영하고 동일한 간극을 할당한 평행판 모델을 가정하였다. 계산결과에 의하면, 균질화 해석법에 의해 계산한 C-투수계수는 실내투수시험에 의해 구한 투수계수와 같은 범위의 값을 가지거나 $10^1$ 정도의 차이를 보여, 그 계산결과는 타당하다고 볼 수 있다. 그러나, 균질화 해석법은 국부적으로 불균질한 균열 기하양상과 물질특성이 미시규모와 거시규모에서 모두 고려되므로, 이들 특성을 정확히 알고 있을 경우 기존에 제안된 경험식들에 의한 계산결과 보다 균질화 해석법의 결과가 훨씬 정확함을 주목하여야 한다.

에폭시 수지 모르터의 특성에 관한 실험적 연구 (Experimental Studies on the Properties of Epoxy Resin Mortars)

  • 연규석;강신업
    • 한국농공학회지
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    • 제26권1호
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    • pp.52-72
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    • 1984
  • This study was performed to obtain the basic data which can be applied to the use of epoxy resin mortars. The data was based on the properties of epoxy resin mortars depending upon various mixing ratios to compare those of cement mortar. The resin which was used at this experiment was Epi-Bis type epoxy resin which is extensively being used as concrete structures. In the case of epoxy resin mortar, mixing ratios of resin to fine aggregate were 1: 2, 1: 4, 1: 6, 1: 8, 1:10, 1 :12 and 1:14, but the ratio of cement to fine aggregate in cement mortar was 1 : 2.5. The results obtained are summarized as follows; 1.When the mixing ratio was 1: 6, the highest density was 2.01 g/cm$^3$, being lower than 2.13 g/cm$^3$ of that of cement mortar. 2.According to the water absorption and water permeability test, the watertightness was shown very high at the mixing ratios of 1: 2, 1: 4 and 1: 6. But then the mixing ratio was less than 1 : 6, the watertightness considerably decreased. By this result, it was regarded that optimum mixing ratio of epoxy resin mortar for watertight structures should be richer mixing ratio than 1: 6. 3.The hardening shrinkage was large as the mixing ratio became leaner, but the values were remarkably small as compared with cement mortar. And the influence of dryness and moisture was exerted little at richer mixing ratio than 1: 6, but its effect was obvious at the lean mixing ratio, 1: 8, 1:10,1:12 and 1:14. It was confirmed that the optimum mixing ratio for concrete structures which would be influenced by the repeated dryness and moisture should be rich mixing ratio higher than 1: 6. 4.The compressive, bending and splitting tensile strenghs were observed very high, even the value at the mixing ratio of 1:14 was higher than that of cement mortar. It showed that epoxy resin mortar especially was to have high strength in bending and splitting tensile strength. Also, the initial strength within 24 hours gave rise to high value. Thus it was clear that epoxy resin was rapid hardening material. The multiple regression equations of strength were computed depending on a function of mixing ratios and curing times. 5.The elastic moduli derived from the compressive stress-strain curve were slightly smaller than the value of cement mortar, and the toughness of epoxy resin mortar was larger than that of cement mortar. 6.The impact resistance was strong compared with cement mortar at all mixing ratios. Especially, bending impact strength by the square pillar specimens was higher than the impact resistance of flat specimens or cylinderic specimens. 7.The Brinell hardness was relatively larger than that of cement mortar, but it gradually decreased with the decline of mixing ratio, and Brinell hardness at mixing ratio of 1 :14 was much the same as cement mortar. 8.The abrasion rate of epoxy resin mortar at all mixing ratio, when Losangeles abation testing machine revolved 500 times, was very low. Even mixing ratio of 1 :14 was no more than 31.41%, which was less than critical abrasion rate 40% of coarse aggregate for cement concrete. Consequently, the abrasion rate of epoxy resin mortar was superior to cement mortar, and the relation between abrasion rate and Brinell hardness was highly significant as exponential curve. 9.The highest bond strength of epoxy resin mortar was 12.9 kg/cm$^2$ at the mixing ratio of 1:2. The failure of bonded flat steel specimens occurred on the part of epoxy resin mortar at the mixing ratio of 1: 2 and 1: 4, and that of bonded cement concrete specimens was fond on the part of combained concrete at the mixing ratio of 1 : 2 ,1: 4 and 1: 6. It was confirmed that the optimum mixing ratio for bonding of steel plate, and of cement concrete should be rich mixing ratio above 1 : 4 and 1 : 6 respectively. 10.The variations of color tone by heating began to take place at about 60˚C, and the ultimate change occurred at 120˚C. The compressive, bending and splitting tensile strengths increased with rising temperature up to 80˚ C, but these rapidly decreased when temperature was above 800 C. Accordingly, it was evident that the resistance temperature of epoxy resin mortar was about 80˚C which was generally considered lower than that of the other concrete materials. But it is likely that there is no problem in epoxy resin mortar when used for unnecessary materials of high temperature resistance. The multiple regression equations of strength were computed depending on a function of mixing ratios and heating temperatures. 11.The susceptibility to chemical attack of cement mortar was easily affected by inorganic and organic acid. and that of epoxy resin mortar with mixing ratio of 1: 4 was of great resistance. On the other hand, when mixing ratio was lower than 1 : 8 epoxy resin mortar had very poor resistance, especially being poor resistant to organicacid. Therefore, for the structures requiring chemical resistance optimum mixing of epoxy resin mortar should be rich mixing ratio higher than 1: 4.

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태양에너지를 이용한 곡물건조시스템의 시뮬레이션에 관한 연구 (Simulation of Drying Grain with Solar-Heated Air)

  • 금동혁;김용운
    • Journal of Biosystems Engineering
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    • 제4권2호
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    • pp.65-83
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    • 1979
  • Low-temperature drying systems have been extensively used for drying cereal grain such as shelled corn and wheat. Since the 1973 energy crisis, many researches have been conducted to apply solar energy as supplemental heat to natural air drying systems. However, little research on rough rice drying has been done in this area, especially very little in Korea. In designing a solar drying system, quality loss, airflow requirements, temperature rise of drying air, fan power and energy requirements should be throughly studied. The factors affecting solar drying systems are airflow rate, initial moisture content, the amount of heat added to drying air, fan operation method and the weather conditions. The major objectives of this study were to analyze the effects of the performance factors and determine design parameters such as airflow requirements, optimum bed depth, optimum temperature rise of drying air, fan operation method and collector size. Three hourly observations based on the 4-year weather data in Chuncheon area were used to simulate rough rice drying. The results can be summarized as follows: 1. The results of the statistical analysis indicated that the experimental and predicted values of the temperature rise of the air passing through the collector agreed well. 2. Equilibrium moisture content was affected a little by airflow rate, but affected mainly by the amount of heat added, to drying air. Equilibrium moisture content ranged from 12.2 to 13.2 percent wet basis for the continuous fan operation, from 10.4 to 11.7 percent wet basis for the intermittent fan operation respectively, in range of 1. 6 to 5. 9 degrees Centigrade average temperature rise of drying air. 3. Average moisture content when top layer was dried to 15 percent wet basis ranged from 13.1 to 13.9 percent wet basis for the continuous fan operation, from 11.9 to 13.4 percent wet basis for the intermittent fan operation respectively, in the range of 1.6 to 5.9 degrees Centigrade average temperature rise of drying air and 18 to 24 percent wet basis initial moisture content. The results indicated that grain was overdried with the intermittent fan operation in any range of temperature rise of drying air. Therefore, the continuous fan operation is usually more effective than the intermittent fan operation considering the overdrying. 4. For the continuous fan operation, the average temperature rise of drying air may be limited to 2.2 to 3. 3 degrees Centigrade considering safe storage moisture level of 13.5 to 14 perceut wet basis. 5. Required drying time decrease ranged from 40 to 50 percent each time the airflow rate was doubled and from 3.9 to 4.3 percent approximately for each one degrees Centigrade in average temperature rise of drying air regardless of the fan operation methods. Therefore, the average temperature rise of drying air had a little effect on required drying time. 6. Required drying time increase ranged from 18 to 30 percent approximately for each 2 percent increase in initial moisture content regardless of the fan operation methods, in the range of 18 to 24 percent moisture. 7. The intermittent fan operation showed about 36 to 42 percent decrease in required drying time as compared with the continuous fan operation. 8. Drymatter loss decrease ranged from 34 to 46 percent each time the airflow rate was doubled and from 2 to 3 percent approximately for each one degrees Centigrade in average temperature rise of drying air, regardless of the fan operation methods. Therefore, the average temperature rise of drying air had a little effect on drymatter loss. 9. Drymatter loss increase ranged from 50 to 78 percent approximately for each 2 percent increase in initial moisture content, in the range of 18 to 24 percent moisture. 10. The intermittent fan operation: showed about 40 to 50 percent increase in drymatter loss as compared with the continuous fan operation and the increasing rate was higher at high level of initial moisture and average temperature rise. 11. Year-to-year weather conditions had a little effect on required drying time and drymatter loss. 12. The equations for estimating time required to dry top layer to 16 and 1536 wet basis and drymatter loss were derived as functions of the performance factors. by the least square method. 13. Minimum airflow rates based on 0.5 percent drymatter loss were estimated. Minimum airflow rates for the intermittent fan operation were approximately 1.5 to 1.8 times as much as compared with the continuous fan operation, but a few differences among year-to-year. 14. Required fan horsepower and energy for the intermittent fan operation were 3. 7 and 1. 5 times respectively as much as compared with the continuous fan operation. 15. The continuous fan operation may be more effective than the intermittent fan operation considering overdrying, fan horsepower requirements, and energy use. 16. A method for estimating the required collection area of flat-plate solar collector using average temperature rise and airflow rate was presented.

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태양에너지를 이용한 곡물건조시스템의 시뮬레이션에 관한 연구 (Simulation of Drying Grain with Solar-Heated Air)

  • 금동혁
    • Journal of Biosystems Engineering
    • /
    • 제4권2호
    • /
    • pp.64-64
    • /
    • 1979
  • Low-temperature drying systems have been extensively used for drying cereal grain such as shelled corn and wheat. Since the 1973 energy crisis, many researches have been conducted to apply solar energy as supplemental heat to natural air drying systems. However, little research on rough rice drying has been done in this area, especially very little in Korea. In designing a solar drying system, quality loss, airflow requirements, temperature rise of drying air, fan power and energy requirements should be throughly studied. The factors affecting solar drying systems are airflow rate, initial moisture content, the amount of heat added to drying air, fan operation method and the weather conditions. The major objectives of this study were to analyze the effects of the performance factors and determine design parameters such as airflow requirements, optimum bed depth, optimum temperature rise of drying air, fan operation method and collector size. Three hourly observations based on the 4-year weather data in Chuncheon area were used to simulate rough rice drying. The results can be summarized as follows: 1. The results of the statistical analysis indicated that the experimental and predicted values of the temperature rise of the air passing through the collector agreed well.2. Equilibrium moisture content was affected a little by airflow rate, but affected mainly by the amount of heat added, to drying air. Equilibrium moisture content ranged from 12.2 to 13.2 percent wet basis for the continuous fan operation, from 10.4 to 11.7 percent wet basis for the intermittent fan operation respectively, in range of 1. 6 to 5. 9 degrees Centigrade average temperature rise of drying air.3. Average moisture content when top layer was dried to 15 percent wet basis ranged from 13.1 to 13.9 percent wet basis for the continuous fan operation, from 11.9 to 13.4 percent wet basis for the intermittent fan operation respectively, in the range of 1.6 to 5.9 degrees Centigrade average temperature rise of drying air and 18 to 24 percent wet basis initial moisture content. The results indicated that grain was overdried with the intermittent fan operation in any range of temperature rise of drying air. Therefore, the continuous fan operation is usually more effective than the intermittent fan operation considering the overdrying.4. For the continuous fan operation, the average temperature rise of drying air may be limited to 2.2 to 3. 3 degrees Centigrade considering safe storage moisture level of 13.5 to 14 perceut wet basis.5. Required drying time decrease ranged from 40 to 50 percent each time the airflow rate was doubled and from 3.9 to 4.3 percent approximately for each one degrees Centigrade in average temperature rise of drying air regardless of the fan operation methods. Therefore, the average temperature rise of drying air had a little effect on required drying time.6. Required drying time increase ranged from 18 to 30 percent approximately for each 2 percent increase in initial moisture content regardless of the fan operation methods, in the range of 18 to 24 percent moisture.7. The intermittent fan operation showed about 36 to 42 percent decrease in required drying time as compared with the continuous fan operation.8. Drymatter loss decrease ranged from 34 to 46 percent each time the airflow rate was doubled and from 2 to 3 percent approximately for each one degrees Centigrade in average temperature rise of drying air, regardless of the fan operation methods. Therefore, the average temperature rise of drying air had a little effect on drymatter loss. 9. Drymatter loss increase ranged from 50 to 78 percent approximately for each 2 percent increase in initial moisture content, in the range of 18 to 24 percent moisture. 10. The intermittent fan operation: showed about 40 to 50 percent increase in drymatter loss as compared with the continuous fan operation and the increasing rate was higher at high level of initial moisture and average temperature rise.11. Year-to-year weather conditions had a little effect on required drying time and drymatter loss.12. The equations for estimating time required to dry top layer to 16 and 1536 wet basis and drymatter loss were derived as functions of the performance factors. by the least square method.13. Minimum airflow rates based on 0.5 percent drymatter loss were estimated.Minimum airflow rates for the intermittent fan operation were approximately 1.5 to 1.8 times as much as compared with the continuous fan operation, but a few differences among year-to-year.14. Required fan horsepower and energy for the intermittent fan operation were3. 7 and 1. 5 times respectively as much as compared with the continuous fan operation.15. The continuous fan operation may be more effective than the intermittent fan operation considering overdrying, fan horsepower requirements, and energy use.16. A method for estimating the required collection area of flat-plate solar collector using average temperature rise and airflow rate was presented.