• Title/Summary/Keyword: 연속체방정식

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Free Vibration Analysis of Non-symmetric Thin-Walled Curved Beams with Shear Deformation (전단변형을 고려한 비대칭 박벽 곡선보의 자유진동해석)

  • Kim, Nam-Il;Kim, Moon-Young;Cheol, Min-Byoung
    • Journal of the Earthquake Engineering Society of Korea
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    • v.7 no.4
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    • pp.1-13
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    • 2003
  • For spatial free vibration of non-symmetric thin-walled curved beams with shear deformation, an improved formulation is proposed in the present study. The elastic strain and the kinetic energies are first derived by considering constant curvature and shear deformation effects due to shear forces and restrained warping torsion. Next equilibrium equations and force-deformation relations are obtained using a stationary condition of total potential energy. And the finite element procedures are developed by using isoparametric curved beam element with arbitray thin-walled sections. Particularly not only shear deformation and thickness-curvature effects on vibration behaviors of curved beams but also mode transition and crossover phenomena with change in curvatures of beams are parametrically investigated. In order to illustrate the accuracy and the reliability of this study, various numerical solutions for spatial free vibration are compared with results by available references and ABAQUS's shell element.

An In-silico Simulation Study on Size-dependent Electroelastic Properties of Hexagonal Boron Nitride Nanotubes (인실리코 해석을 통한 단일벽 질화붕소 나노튜브의 크기 변화에 따른 압전탄성 거동 예측연구)

  • Jaewon Lee;Seunghwa Yang
    • Composites Research
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    • v.37 no.2
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    • pp.132-138
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    • 2024
  • In this study, a molecular dynamics simulation study was performed to investigate the size-dependent electroelastic properties of single-walled boron nitride nanotubes(BNNT). To describe the elasticity and polarization of BNNT under mechanical loading, the Tersoff potential model and rigid ion approximation were adopted. For the prediction of piezoelectric constants and Young's modulus of BNNTs, piezoelectric constitutive equations based on the Maxwell's equation were used to calculate the strain-electric displacement and strain-stress relationships. It was found that the piezoelectric constants of BNNTs gradually decreases as the radius of the tubes increases showing a nonnegligible size effect. On the other hand, the elastic constants of the BNNTs showed opposites trends according to the equivalent geometrical assumption of the tubular structures. To establish the structure-property relationships, localized configurational change of the primarily bonded B-N bonded topology was investigated in detail to elucidate the BNNT curvature dependent elasticity.

Soliton Mode-locking and Numerical Analysis of Yb3+-doped Potassium Double Tungstate Lasers in Compact Laser Cavity Geometries (Yb3+ 도핑된 칼륨 이중 텅스테이트 결정을 이용한 소형 공진기에서의 솔리톤 모드 잠금 레이저 구현 및 수치 해석)

  • Deok Woo Kim;Kwang Hoon Ko;Fabian Rotermund
    • Korean Journal of Optics and Photonics
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    • v.35 no.5
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    • pp.241-249
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    • 2024
  • In this study, we demonstrate compact mode-locked laser operations using three different kinds of Yb3+-doped potassium double tungstate laser crystals, Yb:KGdW, Yb:KYW and Yb:KLuW, operating near 1040 nm at a repetition rate of 405 MHz. We utilized a semiconductor saturable absorber mirror as a mode locker, successfully maintaining mode-locked states for several hours without any Q-switching instabilities for all types of laser crystals. Notably, the Yb:KGdW mode-locked laser produces the shortest pulse with a duration of 108 fs, delivering 125 mW of output power. Additionally, we conducted a numerical analysis by solving the Haus master equation, which incorporates the effect of group delay dispersion and self-phase modulation, using the standard split-step Fourier method.

Real-time Fluid Animation using Particle Dynamics Simulation and Pre-integrated Volume Rendering (입자 동역학 시뮬레이션과 선적분 볼륨 렌더링을 이용한 실시간 유체 애니메이션)

  • Lee Jeongjin;Kang Moon Koo;Kim Dongho;Shin Yeong Gil
    • Journal of KIISE:Computer Systems and Theory
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    • v.32 no.1
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    • pp.29-38
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    • 2005
  • The fluid animation procedure consists of physical simulation and visual rendering. In the physical simulation of fluids, the most frequently used practices are the numerical simulation of fluid particles using particle dynamics equations and the continuum analysis of flow via Wavier-Stokes equation. Particle dynamics method is fast in calculation, but the resulting fluid motion is conditionally unrealistic The method using Wavier-Stokes equation, on the contrary, yields lifelike fluid motion when properly conditioned, yet the complexity of calculation restrains this method from being used in real-time applications. Global illumination is generally successful in producing premium-Duality rendered images, but is also excessively slow for real-time applications. In this paper, we propose a rapid fluid animation method incorporating enhanced particle dynamics simulation method and pre-integrated volume rendering technique. The particle dynamics simulation of fluid flow was conducted in real-time using Lennard-Jones model, and the computation efficiency was enhanced such that a small number of particles can represent a significant volume. For real-time rendering, pre-integrated volume rendering method was used so that fewer slices than ever can construct seamless inter-laminar shades. The proposed method could successfully simulate and render the fluid motion in real time at an acceptable speed and visual quality.

Growth of Plant and Changes in Phosphorus Availability in Phosphorus Accumulated Soils (인 축적 토양에서 작물의 생장과 토양 유효인 함량의 경시적 변화)

  • Kim, Sheng-Ai;Yoo, Sun-Ho
    • Korean Journal of Soil Science and Fertilizer
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    • v.32 no.3
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    • pp.261-267
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    • 1999
  • Pot experiments were conducted to evaluate the phosphorus (P) availability with cropping in soils where P were highly accumulated. Bray 1-P contents of the used three soils were 584, 695 and $1043P\;mg\;kg^{-1}$, respectively. Corn ${\rightarrow}$ Chinese cabbage ${\rightarrow}$ Chinese cabbage ${\rightarrow}$ corn were sequentially grown from 1996 to 1998. P fertilizer was applied at three levels of 0 (P0), recommended application rate (P1), and double of recommended application rate (P2). At the end of each crop growth, available P content was determined by methods of Bray 1-P, Olsen-P and Lancaster-P. The growth of crops were not significantly affected by the rates of P applications. The relative yields of PO treatment were more than 88% of P1 treatment. The recoveries of added phosphorus were relatively low due to the high content of available phosphorus in soils. Although available phosphorus contents decreased through cropping, the concentration of soil available phosphorus was maintained high level even after the final cropping. In the case of P0 treatment in the three soils, the residual concentration was in the range of $410{\sim}610mg\;kg^{-1}$ for Bray 1-P, $284{\sim}410mg\;kg^{-1}$ for Olsen-P and $368{\sim}524mg\;kg^{-1}$ for Lancaster-P. The amount of soil available phosphorus decreased during the experiments was linearly regressed with high significance to the amount of P taken up by crops. The regressions of soil 1 as follow, Bray 1-P : y=149.7x=102.7, Lancaster-P : y=209.2x-140.2, Olsen-P: y=60.8x=19.9. The decrease rate of available phosphorus in the P0 treatment with cropping was described by an equation of first-order chemical reaction. The equation of soil1 was as follow: Bray 1-P: In(C)= -0.12N + 6.96 r=-0.991, Lancaster-P: In(C)= -0.14N = 6.88 r= -0.938, Olsen-P: In(C)= -0.07N = 6.37 r= -0.959. The rate constants seemed to be affected by ply, sand and silt content, and exchangeable $Ca^{2+}$ concentration. The times of cropping needed to reduce the content of available P to half of the initial or to the index level could be predicted by using that equation.

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A Study on the Critical Point and Bifurcation According to Load Mode of Dome-Typed Space Frame Structures (돔형 스페이스 프레임 구조물의 하중모드에 따른 분기점 특성에 관한 연구)

  • Shon, Su-Deok;Kim, Seung-Deog;Lee, Seung-Jae;Kim, Jong-Sik
    • Journal of Korean Association for Spatial Structures
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    • v.11 no.1
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    • pp.121-130
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    • 2011
  • Space frame structures have the advantage of constructing a large space structures without column and it may be considered as a shell structure. Nevertheless, with the characteristics of thin and long term of spacing, the unstable problem of space structure could not be set up clearly, and there is a huge difference between theory and experiment. Therefore, in this work, the tangential stiffness matrix of space frame structures is studied to solve the instability problem, and the nonlinear incremental analysis of the structures considering rise-span ratio(${\mu}$) and the ratio of load($R_L$) is performed for searching unstable points. Basing on the results of the example, global buckling can be happened by low rise-span ratio(${\mu}$), nodal buckling can be occurred by high rise-span ratio(${\mu}$). And in case of multi node space structure applying the ratio of load($R_L$), the nodal buckling phenomenon occur at low the ratio of load($R_L$), the global buckling occur a1 high the ratio of load($R_L$). In case of the global buckling, the load of bifurcation is about from 50% to 70% of perfect one's snap-through load.

Free Vibration Analysis of a Degenerated Timoshenko Beam Including the Effect of Shear Deformation and Rotatory Inertia (전단변형(剪斷變形)과 회전관성(回轉慣性)을 고려(考慮)한 Timoshenko 보의 자유진동(自由振動) 해석(解析))

  • Byun, Dong Kyun;Shin, Young Shik;Jang, Jong Tak
    • KSCE Journal of Civil and Environmental Engineering Research
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    • v.3 no.4
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    • pp.109-122
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    • 1983
  • An accurate thick beam element (TB4) which includes the effects of the shear deformation and rotatory inertia has been degenerated from the three dimensional continuum by employing the Timoshenko beam assumptions. The proposed TB4 element has four nodes and two degrees of freedom at each node, totally eight degrees of freedom. The transverse deflection W and plane rotation ${\theta}$ with the cubic interpolation functions are selected as nodal variables. The element characteristics are formulated by discretizing the beam equations of motion, using the Galerkin weighted residual method, and are numerically integrated by the reduced shear integration technique, using the three-point Gauss quadrature with the various shear coefficients. Several numerical examples are analyzed to demonstrate the accuracy and the monotonic convergence behavior of the proposed TB4 beam element. The result indicates that the TB4 element shows the more excellent performance and the monotonic convergence behavior than the other existing Timoshenko beam type elements for the whole range of the beam aspect ratios, in both static and free vibration analyses.

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Development of Numerical Method for Large Deformation of Soil Using Particle Method (입자법을 이용한 토사의 대변형 해석법 개발)

  • Park, Sung-Sik;Lee, Do-Hyun;Kwon, Min-Ho
    • Journal of the Korean Geotechnical Society
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    • v.29 no.12
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    • pp.35-44
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    • 2013
  • In this study, a particle method without using grid was applied for analysing large deformation problems in soil flows instead of using ordinary finite element or finite difference methods. In the particle method, a continuum equation was discretized by various particle interaction models corresponding to differential operators such as gradient, divergence, and Laplacian. Soil behavior changes from solid to liquid state with increasing water content or external load. The Mohr-Coulomb failure criterion was incorporated into the particle method to analyze such three-dimensional soil behavior. The yielding and hardening behavior of soil before failure was analyzed by treating soil as a viscous liquid. First of all, a sand column test without confining pressure and strength was carried out and then a self-standing clay column test with cohesion was carried out. Large deformation from such column tests due to soil yielding or failure was used for verifying the developed particle method. The developed particle method was able to simulate the three-dimensional plastic deformation of soils due to yielding before failure and calculate the variation of normal and shear stresses both in sand and clay columns.

Optimization of MOF-801 Synthesis Using Sequential Design of Experiments (순차적 실험계획법을 이용한 MOF-801 합성공정 최적화)

  • Lee, Min Hyung;Yoo, Kye Sang
    • Applied Chemistry for Engineering
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    • v.32 no.6
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    • pp.621-626
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    • 2021
  • A sequential design of experiments was used to optimize MOF-801 synthesis process. For the initial screening, a general 2k factorial design was selected followed by the central composition design, one of the response surface methods. A 23 factorial design based on the molar ratio of fumaric acid, dimethylformamide (DMF), and formic acid was performed to select the more suitable response variable for the design of experimental method among the crystallinity and BET specific surface area of MOF-801. After performing 8 synthesis experiments designed by MINITAB 19 software, the characteristic analysis was performed using XRD analysis and nitrogen adsorption method. The crystallinity with R2 = 0.999 was found to be more suitable for the experimental method than that of BET specific surface area. Based on analysis of variance (ANOVA), it was confirmed that the molar ratio of fumaric acid and formic acid was a major factor in determining the crystallinity of MOF-801. Through the response optimization and contour plot of two factors, the optimal molar ratio of ZrOCl2·8H2O : fumaric acid : DMF : formic acid was 1 : 1 : 39 : 35. In order to optimize the synthesis process, the central composition design on synthesis time and temperature was performed under the identical molar ratio of precursors. The results derived through the designed 9 synthesis experiments were calculated using the quadratic model equation. Thus, the maximum crystallinity of MOF-801 predicted under the synthesis time and temperature of 7.8 h and 123 ℃, respectively.

Geotechnical Hybrid Simulation System for the Quantitative Prediction of the Residual Deformation in the Liquefiable Sand During and After Earthquake Motion (액상화 가능 지반의 진동 도중 및 후의 잔류 변형에 대한 정량적 예측을 위한 하이브리드 시뮬레이션 시스템)

  • Kwon, Young Cheul
    • KSCE Journal of Civil and Environmental Engineering Research
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    • v.26 no.1C
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    • pp.43-52
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    • 2006
  • Despite several constitutive models have been proposed and applied, it is still difficult to choose a suitable model and to estimate adequate analysis parameters. Furthermore, a cyclic shear behavior under the volume change caused by the seepage is more complex. None of the constitutive model is available at present in the expression of the cyclic behavior of soil under an additional volume change condition by seepage. Therefore, a new geotechnical hybrid simulation system which can control the pore water immigration was developed. The system enables a quantitative evaluation of the residual deformation such as lateral spreading and settlement caused by the liquefaction. The seismic responses in a one-dimensional slightly inclined multilayered soil system are taken into consideration, and the soils are governed by both equation of motion and the continuity equation. Furthermore, the estimation and the selection of the soil parameter for the representation of the strong nonlinearity of the material are not required, because soil behaviors under the earthquake motions are directly introduced instead of a numerical soil constitutive model. This paper presents the concept and specifications of the system. By applying the system to an example problem, the permeability effect on the seismic response during cyclic shear is studied. The importance of the volume change characteristics of sandy soil during and after cyclic shear is shown in conclusion.