• Title/Summary/Keyword: Euler Method

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A New Numerical Method for Solving Differential Equation by Quadratic Approximation (포물선 근사법에 의한 상태방정식의 새로운 수치해석적 접근법에 관한 연구)

  • Lee, Jong-Gi;Kwon, Yong-Jun;Choi, Byoung-Kon;Moon, Young-Hyun
    • Proceedings of the KIEE Conference
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    • 2003.07a
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    • pp.107-109
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    • 2003
  • 전력계통의 과도 안정도 해석의 접근방법에는 SI(Simultaneous Implicit)법과 PE(Partitioned Explicit)법 두 가지방법을 사용해오고 있다. SI법에는 Trapezoidal법 등이 있고, PE법에는 Runge-Kutta법, Euler법등이 사용되고 있다. SI법인 Trapezoidal법은 PE법의 Runge-Kutta법 또는 Euler법에 비해 시간간격을 크게 해서 계산속도를 줄일 수 있다는 장점이 있지만, 정화도면에서는 신뢰한 수 없는 단점이 있다. 이 논문에서는 포물선 사법을 이용하여 Trapezoidal법의 정확도를 개선학 수 있는 방법을 제시하고 명확한 수학적 증명을 통해 타당성을 보여준다. 연속함수와 불연속함수에 대해서 Runge-Kutta법과 Trapezoidal법과 제안한 방법을 적용시켜서 제안한 방법의 정화함을 보여준다.

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A Study on Delay and Modification in Predicting Turbulence Flow in PISG Algorithm (PISO 알고리즘에서 난류예측의 후생성과 보완에 대한 연구)

  • Lee J. W.;Ryou H. S.;Kang K. G.
    • Journal of computational fluids engineering
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    • v.7 no.1
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    • pp.1-9
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    • 2002
  • In this paper, a modification of PISO algorithm based on standard k-ε turbulence model was proposed. The numerical technique used in this research is finite volume method, hybrid scheme for discretizing convection term, Euler implicit scheme for discretizing time term, and non-staggered grid. The basic idea of the modification of PISO algorithm is to perform an additional corrector stage for turbulence kinetic energy and dissipation rate to correct the inconsistence of flow and turbulence. In order to validate this algorithm, simulation of flow around a square cylinder (Re=3000) was performed in two-dimensional case. The results obtained from the proposed scheme show better agreement with those from the experiment than using original PISO algorithm in coherent velocity field.

Free vibration analysis of axially moving beam under non-ideal conditions

  • Bagdatli, Suleyman M.;Uslu, Bilal
    • Structural Engineering and Mechanics
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    • v.54 no.3
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    • pp.597-605
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    • 2015
  • In this study, linear vibrations of an axially moving beam under non-ideal support conditions have been investigated. The main difference of this study from the other studies; the non-ideal clamped support allow minimal rotations and non-ideal simple support carry moment in minimal orders. Axially moving Euler-Bernoulli beam has simple and clamped support conditions that are discussed as combination of ideal and non-ideal boundary with weighting factor (k). Equations of the motion and boundary conditions have been obtained using Hamilton's Principle. Method of Multiple Scales, a perturbation technique, has been employed for solving the linear equations of motion. Linear equations of motion are solved and effects of different parameters on natural frequencies are investigated.

Numerical modelling of nonlinear behaviour of prestressed concrete continuous beams

  • Lou, Tiejiong;Lopes, Sergio M.R.;Lopes, Adelino V.
    • Computers and Concrete
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    • v.15 no.3
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    • pp.373-389
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    • 2015
  • The development of a finite element model for the geometric and material nonlinear analysis of bonded prestressed concrete continuous beams is presented. The nonlinear geometric effect is introduced by the coupling of axial and flexural fields. A layered approach is applied so as to consider different material properties across the depth of a cross section. The proposed method of analysis is formulated based on the Euler-Bernoulli beam theory. According to the total Lagrangian description, the constructed stiffness matrix consists of three components, namely, the material stiffness matrix reflecting the nonlinear material effect, the geometric stiffness matrix reflecting the nonlinear geometric effect and the large displacement stiffness matrix reflecting the large displacement effect. The analysis is capable of predicting the nonlinear behaviour of bonded prestressed concrete continuous beams over the entire loading stage up to failure. Some numerical examples are presented to demonstrate the validity and applicability of the proposed model.

Proper Numerical Scheme to Solve the Flow Past a Circular Cylinder with Time and Grid Size Variations (시간과 격자 크기 변화에 따른 원주후류해석의 경제적 수치기법)

  • Maeng, Joo-Sung;Kim, Yong-Dae;Choi, IL-Kon
    • Transactions of the Korean Society of Mechanical Engineers B
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    • v.24 no.5
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    • pp.652-659
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    • 2000
  • The purpose of this study is to present the most effective numerical scheme to calculate the unsteady flows. In order to calculate the flow quantities of flow past a circular cylinder, Three-time level and five convective schemes are applied to unsteady and convective terms, respectively. The values obtained are compared with those from the existing experimental and numerical studies. At Reynolds numbers up to 160, time intervals can be expanded 10 times of Implicit Euler scheme using Three-time level method, and it is found that QUICK and CUI schemes work much stable than others even if less grid density conditions. The combination of Three-time level and QUICK scheme gives high resolutions for laminar unsteady problems with PC level.

Optimal Design of a 6-DOF Parallel Mechanism using a Genetic Algorithm (유전 알고리즘을 이용한 6자유도 병렬기구의 최적화 설계)

  • Hwang, Youn-Kwon;Yoon, Jung-Won
    • Journal of Institute of Control, Robotics and Systems
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    • v.13 no.6
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    • pp.560-567
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    • 2007
  • The objective of this research is to optimize the designing parameters of the parallel manipulator with large orientation workspace at the boundary position of the constant orientation workspace (COW). The method uses a simple genetic algorithm(SGA) while considering three different kinematic performance indices: COW and the global conditioning index(GCI) to evaluate the mechanism's dexterity for translational motion of an end-effector, and orientation workspace of two angle of Euler angles to obtain the large rotation angle of an end-effector at the boundary position of COW. Total fifteen cases divided according to the combination of the sphere radius of COW and rotation angle of orientation workspace are studied, and to decide the best model in the total optimized cases, the fuzzy inference system is used for each case's results. An optimized model is selected as a best model, which shows better kinematic performances compared to the basis of the pre-existing model.

A Study on the Nozzle-Rotor Interactions of Partial Admission Supersonic Turbines

  • Seong, Young-sik;Han, Seong-hoon;Kim, Kui-soon;Park, Chang-kyu
    • Proceedings of the Korean Society of Propulsion Engineers Conference
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    • 2004.03a
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    • pp.391-397
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    • 2004
  • The performance characteristics of partial admission supersonic turbines are analyzed by using the commercial CFD program FLUENT6.0. The governing equations were discretized with Euler implicit method in time and 2nd-order upwind scheme of FVM in space. The k-$\varepsilon$ turbulence model was utilized to describe the turbulent flow field. In order to investigate the nozzle--rotor interactions and the effect of partial admission, the flows in supersonic turbine rotor cascades with a nozzle are computed. Extensive computations of partial admission supersonic turbines provide the shock structures and flow patterns in the nozzle and rotor. It is clearly shown that the nozzle flow is highly affected by the shocks or expansion waves propagated from the rotor leading edge. And the rotor flow is also affected by the shocks or wakes originated from the nozzle.

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Mixing algorithm for attitude computation of underwater vehicle using fuzzy theory (퍼지 이론을 이용한 수중 운동체의 자세계산 혼합 알고리즘)

  • 김영한;이장규;한형석
    • The Transactions of the Korean Institute of Electrical Engineers
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    • v.45 no.2
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    • pp.265-272
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    • 1996
  • In this paper, attitude computation algorithm for a strap down ARS(Attitude Reference System)of an underwater vehicle has been studied. Attitude errors o the ARS using low-level gyroscopes tend to increase with time due to gyroscope errors. To cope with this problem, a mixing algorithm of accelerometer aided attitude computation has been developed. The algorithm can successfully bound the error increase for cruising motion, but it gives instantaneously large errors when a vehicle maneuvers. To improve the performance in case of vehicle's maneuver, a new attitude computation mixing algorithm complying state of vehicle and to manage the adjustment of the gains which are invariant in the existing algorithm. In addition, a gain scheduling method is applied to fuzzy inference composition process for real-time computation. Monte Carlo simulation results show that the proposed algorithm provides better performance than the existing algorithm.

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Analysis of Electromechanical - Coupled Field of the Spindle Motor in Computer Hard Disk Drives (컴퓨터 하드 디스크 드라이브용 스핀들 모터의 기전 연성계 해석)

  • Chang, Jung-Hwan;Jang, Gun-Hee;,
    • The Transactions of the Korean Institute of Electrical Engineers B
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    • v.49 no.11
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    • pp.742-748
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    • 2000
  • This paper presents a numerical method to analyze the electromechanical-coupled field in the spindle motor of a computer hard drive and investigates dynamic response due to the electromechanical excitation, i.e. unbalanced magnetic force and centrifugal force for the rotational asymmetric motor. Magnetic field is calculated from Maxwells equation and voltage equation by introducing nonlinear time-dependent finite element analysis. Mechanical motion of rotor is calculated by solving Newton-Euler equation. Electromechanical excitation and dynamic response are characterized by analyzing the free response of a rotating rotor and Fourier analysis of the excitation force and resulting vibration of a rotor. It shows that centrifugal force produces the unbalanced magnetic force even in the rotational symmetric motor. It also shows that resonance produces quite considerable vibration even when the high excitation frequency with small amplitude matches with the natural frequency of the spindle motor.

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The Flow Analysis of Past Flow a Circular Cylinder By Direct Numerical Simulation (DNS에 의한 원주후류에 대한 유동해석)

  • ;Mamoru TANAHASHI;Toshio MIYAUCHI
    • Proceedings of the Korean Society of Marine Engineers Conference
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    • 2001.05a
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    • pp.52-57
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    • 2001
  • Laminar two-dimensional time-dependent flow past a circular cylinder is numerically investigated using direct numerical simulation for the low Reynolds number (Re=164∼280). The higher-order finite difference scheme is employed for the spatial distributions along with the second order Adams-Bashforth and the first order backward-Euler time integration. The convection term is applied by the 7th order up wind scheme and the pressure and viscosity terms are applied by the 4th order central difference. The grid system makes use of the regular grid system and it is generated by an equation. The calculated results of drag coefficients, lift coefficients, pressure distributions, and vorticity contours and other information are compared with experimental and numerical ones. These results obtained by the present DNS show good agreement with the previous studies.

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