• Title/Summary/Keyword: Lagrangian method

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Finite Element Analysis of Thermoforming Process for Axisymmetric System (축대칭형계 열성형공정의 수치모사연구)

  • 이재욱
    • The Korean Journal of Rheology
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    • v.8 no.3_4
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    • pp.215-225
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    • 1996
  • 평판형의 열가소성 수지를 유리전이온도 이상으로 가열한 다음 압력을 가함으로써 원하는 형상의 제품을 성형하는 열성형공정은 대상 수지가 큰 변형을 일으킬 뿐만 아니라 비선형적 거동을 보이게 된다. 따라서 수지의 변형거동 예측과 최적성형조건의 설정에 많은 어려움과 시행착오를 거치게 되는 바, 열성형 공정의 최적화를 위한 연구의 일환으로 원형 평판위 수지를 대상으로 수지의 부풀림 거동과 이에 따른 두께 분포를 예측할수 있는유한요 소법의 수치모사 알고리듬을 개발하고자 하였다. Piola-Kirchhoff 응력 텐서와 Green 변형 텐서 및 lagrangian 변형 텐서를 사용하여 평판상의 응력-변형에 대한 비선형의 에너지 수 지식을 수립하고 Newton-Raphson 반복수렴법을 이용하여 근사적으로 해석하였으며 수지의 유변학적 구성방정식으로는 neo-Hookean 모델, Mooney-Rivlin 모델 및 Ogden 모델등의 초탄성 모델을 사용하여 그결과를 비교하였다. 수치모사에는 두께가 매우 얇기 때문에 두께 방향의 응력변화를 무시할수 있는 membrane 가정을 도입한 2차원적 해석과 두께 방향의 응력 변화를 고려하는 3차원적 해석을 모두 수행하고 그 차이를 비교하였으며 3차원적 해석 의 경우에는 penalty법을 이용하여 비 압축성을 만족하였다. 일차적으로 내압을 받는 두꺼 운 원통계에 대한 수치모사 해석을 수행하고 완전해와 비교함으로써 개발된 수치모사 알고 리듬의 열성형 공정에의 적용 타당성을 검증하였으며 이를 이용하여 원형 평판의 자유부풀 림거동을 예측한 결과 Treloar 등의 실험결과와 잘 부합함을 확인하였다. 또 간단한 형상의 금형이 있는 경우와 반지름 방향으로의 온도변화에 따른 수지의 변형거동을 해석함으로써 실제 열성형 공정에서 요구되고 있는 성형품의 두께 분포를 균일하게 하기 위한 방안을 제 시하였다.

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EUNHA: A NEW COSMOLOGICAL HYDRODYNAMIC SIMULATION CODE

  • Shin, Jihye;Kim, Juhan;Kim, Sungsoo S.;Park, Changbom
    • Journal of The Korean Astronomical Society
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    • v.47 no.3
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    • pp.87-98
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    • 2014
  • We develop a parallel cosmological hydrodynamic simulation code designed for the study of formation and evolution of cosmological structures. The gravitational force is calculated using the TreePM method and the hydrodynamics is implemented based on the smoothed particle hydrodynamics. The initial displacement and velocity of simulation particles are calculated according to second-order Lagrangian perturbation theory using the power spectra of dark matter and baryonic matter. The initial background temperature is given by Recfast and the temperature uctuations at the initial particle position are assigned according to the adiabatic model. We use a time-limiter scheme over the individual time steps to capture shock-fronts and to ease the time-step tension between the shock and preshock particles. We also include the astrophysical gas processes of radiative heating/cooling, star formation, metal enrichment, and supernova feedback. We test the code in several standard cases such as one-dimensional Riemann problems, Kelvin-Helmholtz, and Sedov blast wave instability. Star formation on the galactic disk is investigated to check whether the Schmidt-Kennicutt relation is properly recovered. We also study global star formation history at different simulation resolutions and compare them with observations.

Fast Algorithm for Constructing Wavelet Packet Bases Yielding the Maximum Coding Gain (최대 부호화 이득을 내는 웨이블릿 기저를 구축하기 위한 고속 알고리즘)

  • Kim, Won-Ha
    • Journal of the Institute of Electronics Engineers of Korea CI
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    • v.38 no.2
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    • pp.16-26
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    • 2001
  • This paper develops the fast dynamic programming technique to construct the subband structure yielding the maximum coding gain for given filter bases and a given limit of implementation complexity. We first derive the unified coding gain which can be applied to non-orthogonal filter basis as well as orthogonal filter basis and to arbitrary subband decompositions. Then, we verify that the unified coding gains in real systems are monotonically increasing function for the implementation complexities which are proportional to the number of subbands. By using this phenomenon, the implementation complexity and the coding gain are treated in the same way as the rate and distortion function. This makes it possible to use the Lagrangian multiplier method for finding the optimal subband decomposition producing the maximum coding gain [or a given limit of implementation complexity.

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Numerical Evaluation of charged Liquid Particle′s Behavior in Fluid Flow and Electric Field and The Electric Effect on the Particle Dispersion (유동과 전기장 내에서의 액체입자의 거동과 전기장이 입자의 산란에 미치는 영향에 관한 수치적 연구)

  • Kim, Hyeong-Min
    • Transactions of the Korean Society of Mechanical Engineers B
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    • v.26 no.4
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    • pp.570-577
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    • 2002
  • Charged liquid particle's behavior in electric and flow field was simulated to define the effect of electric field on the contact area and its dispersion. For the simulation of flow and electric field finite volume method was applied. To find out the particle's moving path in that field lagrangian equation of motion was solved by Runge-Kutta methods. We assumed that the particle was charged 10% of Rayleigh limit while the particle passing through the electrode and the particle does not have an effect on the electric field. In case of 30[Kv] of voltage charging the particles injected from the central 60% of the nozzle injection area adhere to the grounded moving plate and no dispersion occurred. Increasing the charged voltage to 40[Kv], it brought about the same phenomena as that of 30[Kv] charging except the dispersion. Voltage increasing from 30[Kv] to 40 [Kv] caused higher Coulomb force acts on the particle and it made the particle dispersion.

Numerical Study of Particle Motion and Particle Beam Formation Through a Critical Orifice (임계 오리피스를 통과한 입자의 운동특성과 입자 빔에 관한 수치적 연구)

  • Ahn, Jin-Hong;Ahn, Kang-Ho
    • Transactions of the Korean Society of Mechanical Engineers B
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    • v.23 no.10
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    • pp.1240-1247
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    • 1999
  • Particle motion through a disk type critical orifice placed in a 3.0cm diameter chamber has been studied numerically. In the simulation, the velocity field is solved using Pantankar's SIMPLER algorithm for the compressible flow and convergence of the computation is confirmed if the mass source at each control volume is smaller than $10^{-7}$. The particle motion in the flow field is solved in Lagrangian method. The particle trajectories showed that the particles injected away from the center line are expanded rapidly. At lower pressures, this expansion phenomena are more dominant. At lower pressures, the clear difference in particle and air speed is showed all the way down to the exit plan. It was found that particles with Stokes number of ca.2.5 tend to focus close to the center line very well except the particles travelling near the wall. However, particles with Stokes number greater than ca.2.5 show a tendency to cross the center line.

Vibration Control of a Tracked Vehicle with ER Suspension Units (II);Modeling and Control of a Tracked Vehicle (ER 현수장치를 갖는 궤도 차량의 진동제어 (II);궤도차량의 모델링 및 제어)

  • Park, Dong-Won;Choe, Seung-Bok;Gang, Yun-Su;Seo, Mun-Seok;Sin, Min-Jae;Choe, Gyo-Jun
    • Transactions of the Korean Society of Mechanical Engineers A
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    • v.23 no.11 s.170
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    • pp.1960-1969
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    • 1999
  • This paper presents dynamic modeling and controller design of a tracked vehicle installed with the double rod type ERSU(electro-rheological suspension unit). A 16 degree-of-freedom model for the tracked vehicle is established by Lagrangian method followed by the formulation of a new sky-ground hook controller. This controller takes account for both the ride quality and the steering stability. The weighting parameter between the two performance requirements is adopted to adjust required performance characteristics with respect to the operation conditions such as road excitation. The parameter is appropriately determined by employing a fuzzy algorithm associated with the vehicle motion. Computer simulations are undertaken in order to demonstrate the effectiveness of the proposed control system. Acceleration values at the driver's seat are analyzed under bump road profile, while frequency responses of vertical acceleration are investigated under random road excitation.

Multiscale modeling of elasto-viscoplastic polycrystals subjected to finite deformations

  • Matous, Karel;Maniatty, Antoinette M.
    • Interaction and multiscale mechanics
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    • v.2 no.4
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    • pp.375-396
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    • 2009
  • In the present work, the elasto-viscoplastic behavior, interactions between grains, and the texture evolution in polycrystalline materials subjected to finite deformations are modeled using a multiscale analysis procedure within a finite element framework. Computational homogenization is used to relate the grain (meso) scale to the macroscale. Specifically, a polycrystal is modeled by a material representative volume element (RVE) consisting of an aggregate of grains, and a periodic distribution of such unit cells is considered to describe material behavior locally on the macroscale. The elastic behavior is defined by a hyperelastic potential, and the viscoplastic response is modeled by a simple power law complemented by a work hardening equation. The finite element framework is based on a Lagrangian formulation, where a kinematic split of the deformation gradient into volume preserving and volumetric parts together with a three-field form of the Hu-Washizu variational principle is adopted to create a stable finite element method. Examples involving simple deformations of an aluminum alloy are modeled to predict inhomogeneous fields on the grain scale, and the macroscopic effective stress-strain curve and texture evolution are compared to those obtained using both upper and lower bound models.

Real-time Oil Spill Dispersion Modelling (실시간 유출유 확산모델링)

  • 정연철
    • Journal of the Korean Society of Marine Environment & Safety
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    • v.5 no.1
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    • pp.9-18
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    • 1999
  • To predict the oil spill dispersion phenomena in the ocean, the oil spill response model, which can be used for strategic purpose on the oil spill site, based on Lagrangian particle-tracking method was formulated and applied to the neighboring area with Pusan port where the oil spill incident occurred when the tanker ship No.1 Youil struck on a small rock near the Namhyungjeto on September 21, 1995. The real-time tidal currents to be required as input data of the oil spill model were obtained by the two-dimensional hydrodynamic model and the tide prediction model. Evaluation of tidal currents using observation data was successful. For wind data, other input data of oil spill model, observed data on the spot were used. To verify the oil spill model, the oil spill modelling results were compared with the field data obtained from the spill site. Compared the modelling results with the observation data, there exist some discrepancies but the general pattern of modelling results was similar to that of field observation. The modelling results on 7 days after spill occurred showed that the 40% of spilled oil is in floating, 36% in evaporated, 23% at shore, and 1% in out of boundary, respectively. According to the evaluation of weighting curves of effective components to the dispersion of oil, the winds make a 37% of contribution to the dispersion of oil, turbulent diffusion 39.5%, and tidal currents 23.5%, respectively. Provided the more accurate wind data are supported, more favorable results might be obtained.

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Strain-based seismic failure evaluation of coupled dam-reservoir-foundation system

  • Hariri-Ardebili, M.A.;Mirzabozorg, H.;Ghasemi, A.
    • Coupled systems mechanics
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    • v.2 no.1
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    • pp.85-110
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    • 2013
  • Generally, mass concrete structural behavior is governed by the strain components. However, relevant guidelines in dam engineering evaluate the structural behavior of concrete dams using stress-based criteria. In the present study, strain-based criteria are proposed for the first time in a professional manner and their applicability in seismic failure evaluation of an arch dam are investigated. Numerical model of the dam is provided using NSAD-DRI finite element code and the foundation is modeled to be massed using infinite elements at its far-end boundaries. The coupled dam-reservoir-foundation system is solved in Lagrangian-Eulerian domain using Newmark-${\beta}$ time integration method. Seismic performance of the dam is investigated using parameters such as the demand-capacity ratio, the cumulative inelastic duration and the extension of the overstressed/overstrained areas. Real crack profile of the dam based on the damage mechanics approach is compared with those obtained from stress-based and strain-based approaches. It is found that using stress-based criteria leads to conservative results for arch action while seismic safety evaluation using the proposed strain-based criteria leads to conservative cantilever action.

Resource Allocation based on Hybrid Sharing Mode for Heterogeneous Services of Cognitive Radio OFDM Systems

  • Lei, Qun;Chen, Yueyun
    • KSII Transactions on Internet and Information Systems (TIIS)
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    • v.9 no.1
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    • pp.149-168
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    • 2015
  • In cognitive radio networks (CRNs), hybrid overlay and underlay sharing transmission mode is an effective technique for improving the efficiency of radio spectrum. Unlike existing works in the literature, where only one secondary user (SU) uses overlay and underlay modes, the different transmission modes should be allocated to different SUs, according to their different quality of services (QoS), to achieve the maximal efficiency of radio spectrum. However, hybrid sharing mode allocation for heterogeneous services is still a challenge in CRNs. In this paper, we propose a new resource allocation method for hybrid sharing transmission mode of overlay and underlay (HySOU), to achieve more potential resources for SUs to access the spectrum without interfering with the primary users. We formulate the HySOU resource allocation as a mixed-integer programming problem to optimize the total system throughput, satisfying heterogeneous QoS. To decrease the algorithm complexity, we divide the problem into two sub-problems: subchannel allocation and power allocation. Cutset is used to achieve the optimal subchannel allocation, and the optimal power allocation is obtained by Lagrangian dual function decomposition and subgradient algorithm. Simulation results show that the proposed algorithm further improves spectrum utilization with a simultaneous fairness guarantee, and the achieved HySOU diversity gain is a satisfactory improvement.