• Title/Summary/Keyword: Kirchhoff Method

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3-Dimensional Finite Element Analysis of Thermoforming Processes (열성형공정의 3차원 유한요소해석)

  • G.J. Nam;D.S. Son;Lee, J.W.
    • The Korean Journal of Rheology
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    • v.11 no.1
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    • pp.18-27
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    • 1999
  • Predicting the deformation behaviors of sheets in thermoforming processes has been a daunting challenge due to the strong nonlinearities arising from very large deformations, mold-polymer contact condition and hyperelasticity constitutive equations. Nonlinear numerical analysis is always required to face this challenge especially for realistic processing conditions. In this study a 3-D algorithm and the membrane approximation are developed for thermoforming processes. The constitutive equation is expressed in terms of the 2nd Piola-Kirchhoff stress tensor and the Cauchy-Green deformation tensor. The 2-term Mooney-Rivlin model is used for the material model equation. The algorithm is established by the finite element formulation employing the total Lagrangian coordinate. The deformation behavior and the stress distribution results of 3-D algorithm with various point boundary conditions are compared to those of the membrane approximation algorithm. Also, the slip boundary condition and the no-slip boundary condition are applied for the systems that have molds. Finally, the effect of sheet temperatures on the final thickness distribution is investigated for the ABS material.

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Numerical Investigation on Radiation Characteristics of Noise Propagating through Asymmetry Aero-Intake (비대칭 공기흡입구를 통해 전파하는 소음의 방사특성에 관한 수치적 연구)

  • Park, Yong-Hwan;Kim, Min-Woo;Lee, Kyu-Ho;Lee, Soo-Gab
    • Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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    • 2007.11a
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    • pp.1476-1481
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    • 2007
  • Numerical investigation on radiation characteristics of discrete frequency noise from asymmetry aero-intakes was carried out. The near-field predictions were obtained by solving the linearized Euler equations with computational aeroacoustic techniques consisting of high order finite difference scheme, non-reflecting boundary conditions, oversetgrid techniques. For the prediction of far-field directivity pattern, the Kirchhoff integral method was applied. By comparing the directivities of noise radiating from the scarf and the scoop aero-intakes with that from an axisymmetric aero-intake, it is shown that noise reduction at downward peak radiation angle can be achieved. The scattering of the radiating acoustic wave by background mean flow shifts the peak lobe radiation angle toward ground and increases the amplitude of the acoustic pressure compared with the cases without mean flow effect.

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Energy Flow Finite Element Analysis(EFFEA) of Coplanar Coupled Mindlin Plates (동일 평면상에서 연성된 Mindlin 판 구조물의 에너지흐름유한요소해석)

  • Park, Young-Ho
    • Journal of the Society of Naval Architects of Korea
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    • v.53 no.4
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    • pp.307-314
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    • 2016
  • Energy flow analysis(EFA) is a representative method that can predict the statistical energetics of structures at high frequencies. Generally, as the frequency increases, the shear distortion and rotatory inertia effects in the out-of-plane motion of beams or plates become important. Therefore, to predict the out-of-plane energetics of coupled structures in the high frequency range, the energy flow analyses of Timoshenko beam and Mindlin plate are required. Unlike the energy flow model of Kirchhoff plate, the energy flow model of Mindlin plate is composed of three kinds of energy governing equations(out-of-plane shear wave, bending dominant flexural wave, and shear dominant flexural wave). This paper performed the energy flow finite element analysis(EFFEA) of coplanar coupled Mindlin plates. For EFFEA of coplanar coupled Mindlin plates, the energy flow finite element formulation of out-of-plane energetics in the Mindlin plate was performed. The general EFFEA program was implemented by MATLAB® language. For the verification of EFFEA of Mindlin plate, the various numerical applications were done successfully.

Vibration Analysis of Rotating Disk-Spindle System Using Finite Element Method and Substructure Synthesis (유한 요소법과 부분 구조 합성법을 이용한 회전 디스크-스핀들 계의 진동 해석)

  • Jeong, Myeong-Su;Jang, Geon-Hui
    • Transactions of the Korean Society of Mechanical Engineers A
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    • v.24 no.9 s.180
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    • pp.2201-2210
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    • 2000
  • Vibration of a rotating disk-spindle system is analyzed by using Hamilton's principle, FEM and substructure synthesis. A rotating disk undergoes the rigid body motion and the elastic deformation. It s equation of motion is derived by Kirchhoff plate theory and von Karman nonlinear strain. A rotating shaft is described by Rayleigh beam theory considering the axial rigid body motion. The stationay shaft supporting the rotating disk-spindle-bearing system is modeled by Euler beam theory, and the stiffness of ball bearing is determined by A.B.Jones' theory. FEM is used to solve the derived governing equations, and substructure synthesis is introduced to assemble each structure of the rotating disk-spindle system. The developed theory is applied to the spindle system of a 35' computer hard disk drive with 3 disks to verify the simulation results. The simulation results agree very well with the experimental ones. The proposed theory may be effectively expanded to the complex structure of a disk-spindle system.

Study on the High Voltage Pulse Profile Characteristics of a Turbulently Heated Theta Pinch (난류가열 쎄타핀치의 고전압 펄스 발생에 관한 연구)

  • 강형보;정운관;육종철
    • The Transactions of the Korean Institute of Electrical Engineers
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    • v.33 no.11
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    • pp.456-463
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    • 1984
  • The fast-rising high-voltage pulse generation circuit system of a theta pinch is both theoretically and experimentally investigated. The idealized model of this circuit system is a hybrid circuit system composed of three parts: a lumped circuit part being consisted of a capacitor bank and a spark switch connected in series, another lumped circuit part being consisted of the Blumlein transmission line, whose end load is the pinch coil. the voltage difference between two ends of the pinch coil is formulated by analyzing this hybrid circuit system by means of the law of the signal propagation in the transmission line and Kirchhoff's laws. The expedient numerical method for computer calculation is developed to generate the pulse profile of the voltage difference across the pinch coil. The period of the experimentally measured main pulse is a fourth of the theoretical one neglecting the resistance of the pinch coil. We attribute this discrepancy to the modelling in the theoretical calculation that hte resistance and inductance of the spark switch and capacitor bank are assumed to be constant through discharge. Therefore, we can see that the rise time of the imploding magnetic-field pulse is mainly dependent on the spark switch and capacitor bank.

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A Fault Detection and Location Algorithm Using a Time Constant for DC Railway Systems (시정수를 이용한 직류철도급전계통에서의 고장판단 및 고장점표정 알고리즘)

  • 양언필;강상희;권영진
    • The Transactions of the Korean Institute of Electrical Engineers A
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    • v.52 no.10
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    • pp.563-570
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    • 2003
  • When a fault occurs on railway feeders it is very important to detect the fault to protect trains and facilities. Because a DC railway system has low feeder voltage, The fault current can be smaller than the current of load starting. So it is important to discriminate between the small fault current and the load starting current. The load starting current increases step by step but the fault current increases at one time. So the type of $\Delta$I/ relay(50F) was developed using the different characteristics between the load starting current and the fault current. The load starting current increases step by step so the time constant of each step is much smaller than that of the fault current. First, to detect faults in DC railway systems, an algorithm using the time constant calculated by the method of least squares is presented in this paper. If a fault occurs on DC railway systems it is necessary to find a fault location to repair the faulted system as soon as possible. The second aim of the paper is to calculate the accurate fault location using Kirchhoff's voltage law.

Elastic Stability of Perforated Concrete Shear Wall (개구부를 갖는 콘크리트 전단벽의 탄성안정)

  • 김준희;김순철
    • Computational Structural Engineering
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    • v.11 no.1
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    • pp.251-259
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    • 1998
  • Concrete shear wall with opening is modeled as a rectangular thin plate. The stability analysis results are presented by the buckling coefficient, k, for two different boundary conditions. The other parameters whose variation have been considered are the ratio of the bending induced force to gravity force, a, the ratio of the horizontal shear force to the gravity force ratio, A and the change of location and the size of perforated part. To obtain the results by finite element method, an example plate has been divided into 27*9 square elements. Four node rectangular c.deg. continuous finite elements having three degrees of freedom per each node is adopted. It is generally concluded that the buckling coefficients decrease as the size of hole increases, and the location of hole moves to free edge of the wall.

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Electromagnetic Wave Scattering from a Perfectly Conducting Random Rough Surface with Considering the Edge Effect (가장자리 효과가 고려된 임의의 기복을 가진 완전도체 표면에서의 전자파 산란)

  • 최동묵;김채영
    • The Journal of Korean Institute of Communications and Information Sciences
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    • v.27 no.3B
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    • pp.244-250
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    • 2002
  • In this paper, rile scattered field from a random rough perfectly conducting surface by method of moment(MoM) was computed. A one-dimensional random rough surface predetermined statistical properties was generated by a digital computer. The number of surface realization for the computed field and the width of surface realization are set to be 100, 80 λ, respectively. To eliminate the scattering from the ends of the surface, the Gaussian taper function is used. Using Monte Carlo technique, we calculated hi-static scattering and back scattering coefficient. In order to verify the result by MoM we compare the MoM results with those of Kirchhoff approximations, which show good agreement between them.

Estimation of a circulating current of a three-phase Y-Y-$\Delta$ transformer (3권선 변압기 순환전류 추정 알고리즘)

  • Kang, Yong-Cheol;Lee, Mi-Sun;Lee, Byung-Eun;Jang, Sung-Il;Kim, Yong-Gyun
    • Proceedings of the KIEE Conference
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    • 2007.07a
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    • pp.559-560
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    • 2007
  • In the case of the transformers including the delta winding such as a three-phase Y-Y-$\Delta$ transformer, a delta winding current flows in the delta windings. The delta winding current of a three-phase Y-Y-$\Delta$ transformer is decomposed into a non-circulating current and a circulating current. The former can be estimated directly from the line currents, but the latter can not. This paper proposes an estimation method for a circulating current of a Y-Y-$\Delta$ Transformer. A first order differential equation for the circulating current is derived by applying the Kirchhoff's voltage law on the loop of the delta side. The circulating current can be estimated by solving the differential equation. Various test results indicate the algorithm can estimate the circulating current accurately even under over-excitation and magnetic inrush.

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Millimeter-wave diffraction-loss model based on over-rooftop propagation measurements

  • Kim, Kyung-Won;Kim, Myung-Don;Lee, Juyul;Park, Jae-Joon;Yoon, Young Keun;Chong, Young Jun
    • ETRI Journal
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    • v.42 no.6
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    • pp.827-836
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    • 2020
  • Measuring the diffraction loss for high frequencies, long distances, and large diffraction angles is difficult because of the high path loss. Securing a well-controlled environment to avoid reflected waves also makes long-range diffraction measurements challenging. Thus, the prediction of diffraction loss at millimeter-wave frequency bands relies on theoretical models, such as the knife-edge diffraction (KED) and geometrical theory of diffraction (GTD) models; however, these models produce different diffraction losses even under the same environment. Our observations revealed that the KED model underestimated the diffraction loss in a large Fresnel-Kirchhoff diffraction parameter environment. We collected power-delay profiles when millimeter waves propagated over a building rooftop at millimeter-wave frequency bands and calculated the diffraction losses from the measurements while eliminating the multipath effects. Comparisons between the measurements and the KED and GTD diffraction-loss models are shown. Based on the measurements, an approximation model is also proposed that provides a simple method for calculating the diffraction loss using geometrical parameters.