• Title/Summary/Keyword: Plate equation

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Application of nonlocal elasticity theory for buckling analysis of nano-scale plates (나노 스케일 판의 좌굴해석을 위한 비국소 탄성 이론의 적용)

  • Lee, Won-Hong;Han, Sung-Cheon;Park, Weon-Tae
    • Journal of the Korea Academia-Industrial cooperation Society
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    • v.13 no.11
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    • pp.5542-5550
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    • 2012
  • Third-order shear deformation theory is reformulated using the nonlocal elasticity of Eringen. The equation of equilibrium of the nonlocal elasticity are derived. This theory has ability to capture the both small scale effects and quadratic variation of shear strain through the plate thickness. Navier's method has been used to solve the governing equations for all edges simply supported boundary conditions. Analytical solutions of buckling of nano-scale plates are presented using this theory to illustrate the effect of nonlocal theory on buckling load of the nano-scale plates. The relations between nonlocal third-order and local theories are discussed by numerical results. Further, effects of (i) length (ii) nonlocal parameter, (iii) aspect ratio and (iv) mode number on nondimensional buckling load are studied. In order to validate the present solutions, the reference solutions are used and discussed. The present results of nano-scale plates using the nonlocal theory can provide a useful benchmark to check the accuracy of related numerical solutions.

A Study on Improvement γ-Reθt Model for Hypersonic Boundary Layer Analysis (극 초음속 경계층 해석을 위한 γ-Reθt모델 개선 연구)

  • Kang, Sunoh;Oh, Sejong;Park, Donghun
    • Journal of the Korean Society for Aeronautical & Space Sciences
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    • v.48 no.5
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    • pp.323-334
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    • 2020
  • Since boundary layer transition has a significant impact on the aero-thermodynamic performance of hypersonic flight vehicles, capability of accurate prediction of transition location is essential for design and performance analysis. In this study, γ-Reθt model is improved to predict transition of hypersonic boundary layers and validated. A coefficient in the production term of the intermittency transport equation that affects the transition onset location is constructed and applied as a function of Mach number, wall temperature, and freestream stagnation temperature based on the similarity numerical solution of compressible boundary layer. To take into account a Mach number dependency of transition onset momentum thickness Reynolds number and transition length, additional correlation equations are determined as function of Mach number and applied to Reθc and Flength correlations of the baseline model. The suggested model is implemented to a commercial CFD code in consideration of practical use. Analysis of hypersonic flat plate and circular cone boundary layers is carried out by using the model for validation purpose. An improvement of prediction capability with respect to variation of Mach number and unit Reynolds number is identified from the comparison with experimental data.

Morphology of La-Co substituted SrM ferrite (La-Co치환량에 따른 스트론튬 페라이트의 미세구조)

  • Jang, Se-Dong
    • Resources Recycling
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    • v.13 no.6
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    • pp.31-36
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    • 2004
  • This experiment was carried out to examine the effects of morphology on properties of La-Co substituted SrM ferrite. The magnetic properties of calcined and sintered materials were varried with the substitutional amount of La and Co elements in Sr-ferrite. In the substituted SrM ferrite, the atomic fraction x of La is directly related to the mole ratio n of iron oxide and the atomic fraction y of Co by equation x=2ny. The Hcj values of the calcined powder were about 270 kA/m and 240 kA/m with x=0.3 and x=0.2, respectively at stoichiometry, n=6.0. Crystallites of the sintered material were grown with a plate shape, and their size decreased with increasing mole ratios. Such a shape was caused by the initial state of crystallite formed after calcination. In case of x=0.3 and n=6.0, Br was 415 mT and Hcj was 355 kA/m, and in x=0.2 and n=6.0, Br was 410 mT and Hcj was 370 kA/m. The squareness in 2nd quarter of BH curve with x=0.2 was smoothly improved to compared with x=0.3.

A Simple Method of Analysis for the Preliminary Design of Structures for Civil Construction made of Particular Composite Laminated Plate (복합적층판으로 구성된 토목건설용 구조물의 예비설계를 위한 간편해석법)

  • 김덕현;원치문
    • Composites Research
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    • v.13 no.2
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    • pp.30-39
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    • 2000
  • It is difficult for civil engineer to apply composite materials of laminated type to structure for civil construction because of complicated theory although those have much merit. A simple method by which one can predict "exact" values of the natural frequency of vibration of laminated plates is presented. Many laminates with particular orientations have negligible values of $B_{16}$ and $B_{26}$ as the number of plies increases. Such laminates, with $D_{16}$ = $D_{26}$ ->0 can be solved by the same equation as for the special orthotropic laminates(1991,1995). If the quasi-isotrpic constants are used, It is possible to simplify analysis procedure since the equations for isotropic plates can be used. Use of some coefficients can produce "exact" values for laminates with such configuration. This coefficient, in fact, represents the effect of the anisotropy of the laminate. D. H. Kim proposed to use a correction factor, he developed, to produce "exact" solution out of the approximate solution obtained by using the quasi-isotropic constants(1995). In this paper, the fiber orienation studied is [$\alpha$/$\beta$/$\beta$/$\gamma$/$\alpha$/$\alpha$/$\beta$]r, with $\alpha$=-$\beta$, and $\gamma$${\gamma}$=$0^{\circ}$ or $90^{\circ}$ and the above-mentioned method is used to obtain the natural frequencies of plates with such orientations, and detailed result is presented for the use of engineers.nted for the use of engineers.

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Retention Behaviors of Natural Gas Components on a Single Column by Gas Chromatography (기체 크로마토그래피에 의한 단일 컬럼상에서 천연가스 성분의 머무름 거동)

  • Choi, Yong-Wook;Choe, Kun-Hyung;Lee, Dai-Woon
    • Analytical Science and Technology
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    • v.7 no.3
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    • pp.329-338
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    • 1994
  • The retention behaviors of natural gas components were studied on a single column by gas chromatography. The dead time, $t_0$ was obtained by using extrapolation of homologous series to determine capacity factors. The plots of retention data for homologous series and carbon number at different temperatures were shown to converge into a single point, which point was determined as a dead time. The results of the effect of temperature on the column efficiency for n-butane exhibited the plate number, N incerased with temperature, but the resolution among the fast eluted components decreased. The adsorption enthalpy (${\Delta}H^0{_{ads}}$) for each component on 28% DC 200 stationary phase was determined, and in order to investigate the retention behaviors of natural gas components the regression analysis of log $t_R$, log k' and log ${\alpha}$ vs. van der Waals volume(Vw), molecular connectivity index(X) and hydrophobic fragmental constant(f) were carred out. Good correlation was found between log k' vs. Vw, and log k' vs. f. The correlations between the physical properties of natural gas and the physical parameters were investigated by the linear regression analysis. The relationships between Vw vs. molecular weight and heating value(${\Delta}H_{comb}$), X vs. boiling point, and f vs. molecular weight, boiling point and heating value exhibited the high correlation coefficient more than 0.99. Using the regression equation between the heating value of natural gas and Vw the predicted heating values from $C_6$ to $C_{10}$ showed good agreement with those reported in the literature within 0.2% relative error.

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Analysis on the Shear Behavior of Existing Reinforced Concrete Frame Structures Infilled with L-Type Precast Wall Panel (L형 프리캐스트 콘크리트 벽패널로 채운 기존 철근 콘크리트 골조 구조물의 전단 거동 분석)

  • Yu, Sung-Yong;Ju, Ho-Seong;Ha, Soo-Kyoung
    • Journal of the Korean Society for Advanced Composite Structures
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    • v.6 no.2
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    • pp.105-117
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    • 2015
  • The purpose of this study is to develop a new seismic resistant method by using precast concrete wall panels for existing low-rise, reinforced concrete beam-column buildings such as school buildings. Three quasi-static hysteresis loading tests were experimentally performed on one unreinforced beam-column specimen and two reinforced specimens with L-type precast wall panels. The results were analyzed to find that the specimen with anchored connection experienced shear failure, while the other specimen with steel plate connection principally manifested flexural failure. The ultimate strength of the specimens was determined to be the weaker of the shear strength of top connection and flexural strength at the critical section of precast panel. In this setup of L-type panel specimens, if a push loading is applied to the reinforced concrete column on one side and push the precast concrete panel, a pull loading from upper shear connection is to be applied to the other side of the top shear connection of precast panel. Since the composite flexural behavior of the two members govern the total behavior during the push loading process, the ultimate horizontal resistance of this specimen was not directly influenced by shear strength at the top connection of precast panel. However, the RC column and PC wall panel member mainly exhibited non-composite behavior during the pull loading process. The ultimate horizontal resistance was directly influenced by the shear strength of top connection because the pull loading from the beam applied directly to the upper shear connection. The analytical result for the internal shear resistance at the connection pursuant to the anchor shear design of ACI 318M-11 Appendix-D except for the equation to predict the concrete breakout failure strength at the concrete side, principally agreed with the experimental result based on the elastic analysis of Midas-Zen by using the largest loading from experiment.

Flux Model of One-shaft Rotary Disc UF Module for the Separation of Oil Emulsion (1축 회전판형 UF 모듈의 투과모델 및 Oil Emulsion 분리 특성)

  • 김제우;노수홍
    • Membrane Journal
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    • v.6 no.2
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    • pp.86-95
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    • 1996
  • Rotary disc ultrafiltration module(RDM) was developed for the separation of oil e$$\mu$sions. This module was devised to reduce the gel polarization phenomenon by decoupling the operation pressure and the surface velocity of solution in ultrafiltration(UF) processes. The rotary disc membrane consists of 3mm-thick ABS plate covered with UF membrane (UOP, U.S.A.). When the angular velocity($\omega$) was increased, the pure water flux was slightly decreased due to pressure drop caused by centrifugal force and slip flow at the surface of membrane. The pressure drop was proportional to the square of linear velocity(${\omega}r$). When the angular velocity was changed from 52.36rad/s to 2.62rad/s, the flux decline for 5% cutting oil in one-shaft RDM at $25^{\circ}C$ and 0.1MPa was 30.16%. In the lower concentrations, angular velocity tends to give less effect on the flux. Flux(J; $kg/m^{2} \cdot s$) in a rotating disc module is mainly a function of the bulk concentration($C_{B}$; %), the linear velocity(${\omega}r$; m/s) and the effective transmembrane pressure($\Delta P_{T}$ ; Pa). Using a modified resistance-in-series model, the flux data of cutting oil experiments were fitted to give the following equation.

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The Forced Motion Analyses by Using Two Dimensional 6-Node and Three Dimensional 16-Node Isoparametric Elements with Modification of Gauss Sampling Point (6절점 2차원 및 16절점 3차원 등매개변수 요소의 가우스 적분점 수정을 이용한 강제진동 해석)

  • 김정운;권영두
    • Computational Structural Engineering
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    • v.8 no.4
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    • pp.87-97
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    • 1995
  • For the same configuration of two-dimensional finite element models, 6-node element exhibits stiffer bending stiffness than 8-node element. This is true in the relation between 16-node element and 20-node element for three-dimensional model. This stiffening phenomenon comes from the elimination of several mid nodes from full-node elements. Therefore, this may be called 'relative stiffness stiffening phenomenon'. It seems that there are a couple of ways to correct the stiffening effect, however, we could find only one effective method-the method of modification of Gauss sampling points-which passes the patch test and does not alter other kinds of stiffness, such as extensional stiffness. The quantity of modification is a function of Poisson's ratios of the constituent materials. We could obtain two modification equations, one for plane stress case and the other for plane strain case. This method can be extended to 3-dimensional solid elements. Except the exact plane strain cases, most 3-dimensional plates could be modeled successfully with 16-node element modified by the equation for the plane stress case. The effectiveness of the modification method is checked by applying it to several examples with excellent improvements. In numerical examples, beams with various boundary conditions are subjected to static and time-dependent loads. Free and forced motion analyses of beams and plates are also tested. The beam and plate may be composed of isotropic multilayers as well as a single layer.

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Development of a force measurement device for curling sweeping with load cells (로드셀을 이용한 컬링 스위핑 힘 측정 장치 개발)

  • Lee, Sangcheol;Kim, Taewhan;Kil, Sekee;Choi, Sanghyup
    • Journal of the Korea Convergence Society
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    • v.8 no.11
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    • pp.49-56
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    • 2017
  • Curling sweeping is one of important motion to control the position of the curling stone, and sweeping speed and applied force to the broom pad are major research subjects. In this study, a device was developed to measure the force applied to the curling broom pad in curling sweeping motion, and two load cells were mounted between the broom pad and pad holder. Analog signals generated from the load cells were sampled about 300 times per second using a micro controller, and then converted to 10-bit digital signals. Calibration of the load cell and set up of regression equations to convert the measured electrical signals into mass (force) was done by three M1 class weights, and the developed system was designed as wearable device to minimize increasing of total weight of the broom. Same force was applied to the developed system and a force plate that was using as a reference force measurement system in field of sports, and the difference between the measured values were showed about $0.909{\pm}1.375N$(mean and standard deviation). The developed system could be applied other kinds of study which required force measurement function similar to sweeping motion.

The Effect of Impact Velocity on Droplet-wall Collision Heat Transfer Above the Leidenfrost Point Temperature (Leidenfrost 지점 온도 이상에서 액적-벽면 충돌 열전달에 대한 충돌 속도의 영향)

  • Park, Jun-seok;Kim, Hyungdae;Bae, Sung-won;Kim, Kyung Doo
    • Transactions of the Korean Society of Mechanical Engineers B
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    • v.39 no.7
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    • pp.567-578
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    • 2015
  • Single droplet-wall collision heat transfer characteristics on a heated plate above Leidenfrost temperature were experimentally investigated considering the effects of impact velocity. The collision characteristics of the droplet impinged on the heated wall and the changes in temperature distribution were simultaneously measured using synchronized high-speed video and infrared cameras. The surface heat flux distribution was obtained by solving the three-dimensional transient heat conduction equation for the heated substrate using the measured surface temperature data as the boundary condition for the collision surface. As the normal impact velocity increased, heat transfer effectiveness increased because of an increase in the maximum spreading diameter and a decrease in the vapor film thickness between the droplet and heated wall. For We < 30, droplets stably rebounded from a heated wall without breakup. However, the droplets broke up into small droplets for We > 30. The tendency of the heat transfer to increase with increasing impact velocity was degraded by the transition from the rebounding region to the breakup region; this was resulted from the reduction in the effective heat transfer area enlargement due to the breakup phenomenon.