• Title/Summary/Keyword: 이차방정식과 이차함수

Search Result 27, Processing Time 0.036 seconds

Constitutive Equation for Concrete using Anisotropic Continuum Damage Model (이방성 손상모델을 이용한 콘크리트 구성방정식의 도출)

  • Lee, Ki Seong;Byun, Keun Joo
    • KSCE Journal of Civil and Environmental Engineering Research
    • /
    • v.14 no.4
    • /
    • pp.751-759
    • /
    • 1994
  • Concrete contains numerous microcracks initially. The growth and propagation of microcracks cause failure of concrete. These processings are termed as "damage". The concepts of the continuum damage mechanics are presented and the damage evolution law and constitutive equation are derived by using the Helmholz free energy and the dissipation potential by means of the thermodynamic principles. The constitutive equation includes the effects of elasticity, damage and plasticity of concrete. The proposed model successfully predicts the nonlinear behavior of concrete subject to monotonic uniaxial and biaxial loadings.

  • PDF

Comparison of Numerical Methods on Heat Transfer in a Rod with Second Order-Boundary Value Problem (이차 경계문제를 가지는 봉의 열전달에 대한 수치해석적 비교)

  • Kim, M.J.;Chea, G.H.
    • Journal of Power System Engineering
    • /
    • v.14 no.5
    • /
    • pp.5-9
    • /
    • 2010
  • 본 연구는 수정 오일러 법칙을 이용한 봉의 열전달문제를 엄밀해와 수치해를 수치해석적 해법을 이용해 비교한 것이다. 경계조건으로는 열전도 및 대류가 동시에 존재하는 경우의 모델을 가정하여 계산하였고, 봉의 길이가 원주방향에 비해 상당히 길다고 가정하여 1차원으로 지배방정식을 정리하여 2차 상미분방정식을 유도하여 계산을 수행하였다. 계산을 수행한 결과 적절한 초기 추측값인 ${\beta}$값을 정의하면 오일러의 방정식으로도 충분히 만족할만한 결과를 얻을 수 있다는 것을 알았고, 지수함수 형태의 유도 상관식이 엄밀해와 ${\pm}1%$ 범위 내에서 일치한다는 결과를 얻었다.

STUDY ON FLUX FUNCTIONS FOR THE EULER EQUATIONS (Euler 방정식의 Flux Function 특성 비교 연구)

  • Chae, E.J.;Lee, S.
    • 한국전산유체공학회:학술대회논문집
    • /
    • 2006.10a
    • /
    • pp.36-40
    • /
    • 2006
  • A comparative study on flux functions for the 2-dimensional Euler equations has been conducted. Explicit 4-stage Runge-Kutta method is used to integrate the equations. Flux functions used in the study are Steger-Warming's, van Leer's. Godunov's, Osher's(physical order and natural order), Roe's, HILE, AUSM, AUSM+ and AUSMPW+. The performance of MUSCL limiters and MLP limiters in conjunction with flux functions are compared extensively for steady and unsteady problems.

  • PDF

Spring-back Evaluation of Automotive Sheets Based on Combined Isotropic-Kinematic Hardening Rule (혼합 등방-이동 경화규칙에 기초한 자동차용 알루미늄합금 및 Dual-Phase 강 판재의 스프링백 예측)

  • ;;;Chongmin kim;Michael L. Wenner
    • Transactions of Materials Processing
    • /
    • v.13 no.1
    • /
    • pp.15-20
    • /
    • 2004
  • In order to evaluate spring-back behavior in automotive sheet forming processes, a panel shape idealized as a double S-rail has been investigated. After spring-back has been predicted for double S-rails using the finite element analysis, results has been compared with experimental measurements for three automotive sheets. To account for hardening behavior such as the Bauschinger and transient effects in addition to anisotropic behavior, the combined isotropic-kinematic hardening law based on the Chaboche type model and a recently developed non-quadratic anisotropic yield function have been utilized, respectively.

A Case Study on Students' Mathematical Concepts of Algebra, Connections and Attitudes toward Mathematics in a CAS Environment (CAS 그래핑 계산기를 활용한 수학 수업에 관한 사례 연구)

  • Park, Hui-Jeong;Kim, Kyung-Mi;Whang, Woo-Hyung
    • Communications of Mathematical Education
    • /
    • v.25 no.2
    • /
    • pp.403-430
    • /
    • 2011
  • The purpose of the study was to investigate how the use of graphing calculators influence on forming students' mathematical concept of algebra, students' mathematical connection, and attitude toward mathematics. First, graphing calculators give instant feedback to students as they make students compare their written answers with the results, which helps students learn equations and linear inequalities for themselves. In respect of quadratic inequalities they help students to correct wrong concepts and understand fundamental concepts, and with regard to functions students can draw graphs more easily using graphing calculators, which means that the difficulty of drawing graphs can not be hindrance to student's learning functions. Moreover students could understand functions intuitively by using graphing calculators and explored math problems volunteerly. As a result, students were able to perceive faster the concepts of functions that they considered difficult and remain the concepts in their mind for a long time. Second, most of students could not think of connection among equations, equalities and functions. However, they could understand the connection among equations, equalities and functions more easily. Additionally students could focus on changing the real life into the algebraic expression by modeling without the fear of calculating, which made students relieve the burden of calculating and realize the usefulness of mathematics through the experience of solving the real-life problems. Third, we identified the change of six students' attitude through preliminary and an ex post facto attitude test. Five of six students came to have positive attitude toward mathematics, but only one student came to have negative attitude. However, all of the students showed positive attitude toward using graphing calculators in math class. That's because they could have more interest in mathematics by the strengthened and visualization of graphing calculators which helped them understand difficult algebraic concepts, which gave them a sense of achievement. Also, students could relieve the burden of calculating and have confidence. In a conclusion, using graphing calculators in algebra and function class has many advantages : formulating mathematics concepts, mathematical connection, and enhancing positive attitude toward mathematics. Therefore we need more research of the effect of using calculators, practical classroom materials, instruction models and assessment tools for graphing calculators. Lastly We need to make the classroom environment more adequate for using graphing calculators in math classes.

Wave Energy Absorption Efficiency of Pneumatic Chamber of OWC Wave Energy Converter (진동수주형 파력발전장치 공기실의 파력에너지 흡수효율)

  • Hong, Key-Yong;Shin, Seung-Ho;Hong, Do-Chun
    • Journal of the Korean Society for Marine Environment & Energy
    • /
    • v.10 no.3
    • /
    • pp.173-180
    • /
    • 2007
  • Oscillating wave amplitude in a bottom-mounted OWC chamber designed for wave energy converter is investigated by applying characteristic wave conditions in Korean coastal water. The effects of shape parameters of OWC chamber in a view of wave energy absorbing capability are analyzed. Both experimental and numerical approaches are adopted and their results are compared to optimize the shape parameters which can result in a maximum power production under given wave distribution. The experiment was carried out in a wave flume under 2-D assumption of OWC chamber. The numerical scheme employed a hybrid Green integral equation which adopts the Rankine Green function inside chamber to take account of fluctuating air pressure, while it uses the Kelvin Green function in outer domain. Air duct diameter, chamber width, and submerged depths of front skirt and back wall of chamber changes the magnitude and peak frequency of wave absorption significantly.

  • PDF

Analysis on Forward/Backward Current Distribution and Off-current for Doping Concentration of Double Gate MOSFET (DGMOSFET의 도핑분포에 따른 상 · 하단 전류분포 및 차단전류 분석)

  • Jung, Hakkee
    • Journal of the Korea Institute of Information and Communication Engineering
    • /
    • v.17 no.10
    • /
    • pp.2403-2408
    • /
    • 2013
  • This paper has analyzed the change of forward and backward current for channel doping concentration to analyze off-current of double gate(DG) MOSFET. The Gaussian function as channel doping distribution has been used to compare with experimental ones, and the two dimensional analytical potential distribution model derived from Poisson's equation has been used to analyze the off-current. The off-current has been analyzed for the change of projected range and standard projected range of Gaussian function with device parameters such as channel length, channel thickness, gate oxide thickness and channel doping concentration. As a result, this research shows the off-current has greatly influenced on forward and backward current for device parameters, especially for the shape of Gaussian function for channel doping concentration.

A Study on the Selective Use of Higher Order Elements (고차 요소의 선택적 사용에 대한 연구)

  • Kim, Jin-Whan
    • Journal of Ocean Engineering and Technology
    • /
    • v.13 no.4 s.35
    • /
    • pp.1-9
    • /
    • 1999
  • 일차원 및 이차원의 단순한 문제에 대하여 계층 요소를 사용한 혼합 차수 유한 요소해의 정확성 및 수렴성을 조사하였다. 이러한 작업은 임의의 차수를 가진 블록들을 조합하여 요소를 구성함으로서 이루어질 수 있다. 블록간의 연결성이 유지될 수 있는 블록의 구성과 요소 생성에 대하여는 코드개발과 관련하여 설명하고 있으며, 서로 다른 차수를 가진 인접 블록간의 해의 연속성에 대하여는 계층 요소의 구성과 관련하여 서술되었다. 수치적 결과는 블록의 차수를 잘 선택함으로서 유한 요소해의 수렴성과 정확성을 증가시킬 수 있음을 보여주고 있으며, 고차 요소 영역을 너무 많이 할당하여 선형 요소의 영역이 너무 적을 경우에는 경계 조건에 따라 오차가 내부로 전파됨을 보여준다. 또한 세분화된 요소에 대한 고차 보간의 경우, 해의 수렴성이 저해될 수 있음이 발견되었다.

  • PDF

Thickness Optimization for Spar Cap of Composite Tidal Current Turbine Blade using SQP Method (SQP법을 사용한 복합재 조류력 발전용 블레이드의 스파 캡에 대한 두께 최적화)

  • Cha, Myung-Chan;Kim, Sang-Woo;Jeong, Min-Soo;Lee, In;Yoo, Seung-Jae;Park, Cheon-Jin
    • Composites Research
    • /
    • v.26 no.4
    • /
    • pp.207-212
    • /
    • 2013
  • In this study, the thickness optimization for uni-directional (UD) glass fiber reinforced polymer (GFRP) laminates of the spar cap of composite tidal blades was performed under the tip deflection constrains. The spar cap was composed of GFRP composites and carbon fiber reinforced polymer (CFRP) composites. The stress distributions in the blade as well as its material costs for the optimized results were additionally investigated. The optimized thickness was obtained by interacting a sequential quadratic programming (SQP) algorithm and an ABAQUS software to calculate an objective function. It was confirmed that the thickness of UD GFRP increased with a decrease of the restrained tip deflection when a thickness of UD CFRP laminates was constrained to 9 mm. The weight of the optimized spar-cap increased up to 96.2% while the maximum longitudinal tensile stress decreased up to 24.6%. The thickness of UD GFRP laminates increased with a decrease of the thickness of UD CFRP laminates when the tip deflection was constrained to 126.83 mm. The weight increased up to 40.1%, but the material cost decreased up to 16.97%. Finally, the relationships among the weight, internal tensile stress, and material costs were presented based on the optimized thicknesses of the spar cap.

A Study on Estimation of Energy required for Fin Unfolding (공력면 전개에 필요한 전개 에너지의 추산에 관한 연구)

  • Jung, Suk-Young
    • Journal of the Korean Society for Aeronautical & Space Sciences
    • /
    • v.37 no.3
    • /
    • pp.283-292
    • /
    • 2009
  • Considering an integral equation governing the motion of unfolding fin, an algebraic equation was acquired to get estimated minimum deployment energy required for the successful fin unfolding under the given wind condition. To complete the integration of moment, some approximations had to be introduced particularly to frictional moment and aerodynamic damping for which deployment angular speed of the unfolding fin was modelled as a function of deployment angle only with assumed profile using expected maximum angular speed. Technique for the estimation of the minimum required deployment energy was finalized by introducing the ideal deployment angular speed representing work done by the fin unfolding device alone during fin unfolding and was confirmed by comparing results from simulation with various aerodynamic conditions and profiles of the hinge torque.