• 제목/요약/키워드: Laplace's equation

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The pressure distribution on the rectangular and trapezoidal storage tanks' perimeters due to liquid sloshing phenomenon

  • Saghi, Hassan
    • International Journal of Naval Architecture and Ocean Engineering
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    • 제8권2호
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    • pp.153-168
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    • 2016
  • Sloshing phenomenon is a complicated free surface flow problem that increases the dynamic pressure on the sidewalls and the bottom of the storage tanks. When the storage tanks are partially filled, it is essential to be able to evaluate the fluid dynamic loads on the tank's perimeter. In this paper, a numerical code was developed to determine the pressure distribution on the rectangular and trapezoidal storage tanks' perimeters due to liquid sloshing phenomenon. Assuming the fluid to be inviscid, the Laplace equation and the nonlinear free surface boundary conditions were solved using coupled boundary element - finite element method. The code performance for sloshing modeling was validated using Nakayama and Washizu's results. Finally, this code was used for partially filled rectangular and trapezoidal storage tanks and free surface displacement, pressure distribution and horizontal and vertical forces exerted on the tanks' perimeters due to liquid sloshing phenomenon were estimated and discussed.

Calculation of Topographic Index with Geographic Information System

  • Kim, Sang-Hyun;Ham, Kun-Yeun
    • Korean Journal of Hydrosciences
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    • 제8권
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    • pp.85-95
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    • 1997
  • The multiple flow direction algorithm to calculate the spatial variation of the saturation tendency, I. e. topographic index, is integrated into the Geographic Information System, GRASS. A procedure is suggested to consider the effect of a tile system on calculating the topographic index. A small agricultural subwatershed ($3.4\;\textrm{km}^2$) is used for this study. The impact of a tile system on the groundwater table can be effectively considered by the Laplace's equation to the DEM. The analysis shows that a tile system has a high degree of saturation to compared to the case without tile drainage, and the predicted riparian area is well fitted to the actual watershed condition. A procedure is suggested to consider a tile system's effect on calculating the topographic index.

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Numerical simulation of fully nonlinear sloshing waves in three-dimensional tank under random excitation

  • Xu, Gang;Hamouda, A.M.S.;Khoo, B.C.
    • Ocean Systems Engineering
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    • 제1권4호
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    • pp.355-372
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    • 2011
  • Based on the fully nonlinear velocity potential theory, the liquid sloshing in a three dimensional tank under random excitation is studied. The governing Laplace equation with fully nonlinear boundary conditions on the moving free surface is solved using the indirect desingularized boundary integral equation method (DBIEM). The fourth-order predictor-corrector Adams-Bashforth-Moulton scheme (ABM4) and mixed Eulerian-Lagrangian (MEL) method are used for the time-stepping integration of the free surface boundary conditions. A smoothing scheme, B-spline curve, is applied to both the longitudinal and transverse directions of the tank to eliminate the possible saw-tooth instabilities. When the tank is undergoing one dimensional regular motion of small amplitude, the calculated results are found to be in very good agreement with linear analytical solution. In the simulation, the normal standing waves, travelling waves and bores are observed. The extensive calculation has been made for the tank undergoing specified random oscillation. The nonlinear effect of random sloshing wave is studied and the effect of peak frequency used for the generation of random oscillation is investigated. It is found that, even as the peak value of spectrum for oscillation becomes smaller, the maximum wave elevation on the side wall becomes bigger when the peak frequency is closer to the natural frequency.

Wave propagation in a 3D fully nonlinear NWT based on MTF coupled with DZ method for the downstream boundary

  • Xu, G.;Hamouda, A.M.S.;Khoo, B.C.
    • Ocean Systems Engineering
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    • 제4권2호
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    • pp.83-97
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    • 2014
  • Wave propagation in a three-dimensional (3D) fully nonlinear numerical wave tank (NWT) is studied based on velocity potential theory. The governing Laplace equation with fully nonlinear boundary conditions on the moving free surface is solved using the indirect desingularized boundary integral equation method (DBIEM). The fourth-order predictor-corrector Adams-Bashforth-Moulton scheme (ABM4) and mixed Eulerian-Lagrangian (MEL) method are used for the time-stepping integration of the free surface boundary conditions. A smoothing algorithm, B-spline, is applied to eliminate the possible saw-tooth instabilities. The artificial wave speed employed in MTF (multi-transmitting formula) approach is investigated for fully nonlinear wave problem. The numerical results from incorporating the damping zone (DZ), MTF and MTF coupled DZ (MTF+DZ) methods as radiation condition are compared with analytical solution. An effective MTF+DZ method is finally adopted to simulate the 3D linear wave, second-order wave and irregular wave propagation. It is shown that the MTF+DZ method can be used for simulating fully nonlinear wave propagation very efficiently.

모드III 탄성 균열문제 해석에 대한 연구 (Elastic Analysis of the Mode III Crack Problem)

  • 김윤영;윤민수
    • 대한기계학회논문집
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    • 제19권4호
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    • pp.941-949
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    • 1995
  • An efficient method based on analytic solutions is applied to solve anti-plane Mode III crack problems. The analytic technique developed earlier by the present authors for Laplace's equation in a simply-connected region is now extended to general Mode III crack problems. Unlike typical numerical methods which require fine meshing near crack tips, the present method divides the cracked bodies, typically non-convex or multiply-connected, into only a few super elements. In each super element, an element stiffness matrix, relating the series coefficients of the traction and displacement, is first formed. Then an assembly algorithm similar to that used in the finite elements, is first formed. Then an assembly algorithm similar to that used in the finite elements, is developed. A big advantage of the present method is that only the boundary conditions are to be satisfied in the solution procedure due to the use of analytic solutions. Several numerical results demonstrate the efficiency and accuracy of the present method.

선형 격자 형성 방정식을 이용한 직교 격자 형성에 관한 연구 (Orthogonal Grid Generation Using Linear Grid Generating Equations)

  • 이상욱;권장혁;권오준
    • 한국전산유체공학회:학술대회논문집
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    • 한국전산유체공학회 2000년도 춘계 학술대회논문집
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    • pp.99-106
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    • 2000
  • A method of two and three dimensional orthogonal grid generation with control of spacing by using the covariant Laplace equation is Presented. An important feature of the methodology is its ability to control effectively the grid spacing especially near the boundaries still maintaining good orthogonality in whole field. The method is based on the concept of decomposition of the global transformation into consecutive transformation of an approximate conformal mapping and au auxiliary orthogonal mapping to have linear and uncoupled equations. Control of cell spacing is based on the concept of reference arc length, and orthogonal correction is performed in the auxiliary domain. It is concluded that the methodology can successfully generate well controlled orthogonal grids around bodies of 2 and 3 dimensional configurations.

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초소형 밀폐형 이상 써모싸이폰 기포의 거동에 관한 해석적인 연구 (Analytical Study on the Behavior of the Bubble in the Micro Two-Phase Closed Thermosyphon)

  • 이윤표;이영수;이영
    • 설비공학논문집
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    • 제5권2호
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    • pp.85-93
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    • 1993
  • The rise of a large gas bubble or slug in a Micro Two-Phase Closed Thermosyphon with a thin wire insert has been analiged by the potential flow theory. The effect of the interfacial surface tension is explicitly accounted by application of the Kelvin-Laplace equation and solved for the bubble shape. The solution is expressed in terms of the Stokes stream function which consists of an infinite series of Bessel functions. The conditions of the bubble movement in a Micro Two-Phase Closed Thermosyphon were theoretically ascertained.

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Frequency Response Analysis of Cylindrical Shells Conveying Fluid Using Finite Element Method

  • Seo Young-Soo;Jeong Weui-Bong;Yoo Wan-Suk;Jeong Ho-Kyeong
    • Journal of Mechanical Science and Technology
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    • 제19권2호
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    • pp.625-633
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    • 2005
  • A finite element vibration analysis of thin-walled cylindrical shells conveying fluid with uniform velocity is presented. The dynamic behavior of thin-walled shell is based on the Sanders' theory and the fluid in cylindrical shell is considered as inviscid and incompressible so that it satisfies the Laplace's equation. A beam-like shell element is used to reduce the number of degrees-of-freedom by restricting to the circumferential modes of cylindrical shell. An estimation of frequency response function of the pipe considering of the coupled effects of the internal fluid is presented. A dynamic coupling condition of the interface between the fluid and the structure is used. The effective thickness of fluid according to circumferential modes is also discussed. The influence of fluid velocity on the frequency response function is illustrated and discussed. The results by this method are compared with published results and those by commercial tools.

End-point positioning of one-link flexible arm under translational motion

  • Lee, Seong-Cheol;Chonan, Seiji;Inooka, Hikaru
    • 제어로봇시스템학회:학술대회논문집
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    • 제어로봇시스템학회 1990년도 한국자동제어학술회의논문집(국제학술편); KOEX, Seoul; 26-27 Oct. 1990
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    • pp.890-895
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    • 1990
  • A theoretical and experimental study of a single link flexible arm a tip mass is presented for the translational end-point positioning. The problem of shifting the end-point from its initial position to the commanded position by the amount of W $_{d}$ is considered for the open loop control such that the base follows up the given path function. The theoretical results are obtained by applying the method of the Laplace transform to the governing equation, and the solution is calculated by the method of numerical inversion. Experimental results are obtained and compared with the theoretical ones.s.

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Dynamic analysis of gradient elastic flexural beams

  • Papargyri-Beskou, S.;Polyzos, D.;Beskos, D.E.
    • Structural Engineering and Mechanics
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    • 제15권6호
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    • pp.705-716
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    • 2003
  • Gradient elastic flexural beams are dynamically analysed by analytic means. The governing equation of flexural beam motion is obtained by combining the Bernoulli-Euler beam theory and the simple gradient elasticity theory due to Aifantis. All possible boundary conditions (classical and non-classical or gradient type) are obtained with the aid of a variational statement. A wave propagation analysis reveals the existence of wave dispersion in gradient elastic beams. Free vibrations of gradient elastic beams are analysed and natural frequencies and modal shapes are obtained. Forced vibrations of these beams are also analysed with the aid of the Laplace transform with respect to time and their response to loads with any time variation is obtained. Numerical examples are presented for both free and forced vibrations of a simply supported and a cantilever beam, respectively, in order to assess the gradient effect on the natural frequencies, modal shapes and beam response.