• Title/Summary/Keyword: Integral equations

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Multi-Scale Contact Analysis Between Net and Numerous Particles (그물망과 대량입자의 멀티 스케일 접촉해석)

  • Jun, Chul Woong;Sohn, Jeong Hyun
    • Transactions of the Korean Society of Mechanical Engineers A
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    • v.38 no.1
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    • pp.17-23
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    • 2014
  • Graphics processing units (GPUs) are ideal for solving problems involving parallel data computations. In this study, the GPU is used for effectively carrying out a multi-body dynamic simulation with particle dynamics. The Hilber-Hushes-Taylor (HHT) implicit integration algorithm is used to solve the integral equations. For detecting collisions among particles, the spatial subdivision algorithm and discrete-element methods (DEM) are employed. The developed program is verified by comparing its results with those of ADAMS. The numerical efficiencies of the serial program using the CPU and the parallel program using the GPU are compared in terms of the number of particles, and it is observed that when the number of particles is greater, more computing time is saved by using the GPU. In the present example, when the number of particles is 1,300, the computational speed of the parallel analysis program is about 5 times faster than that of the serial analysis program.

An analytical study on the heat transfer of the laminar filmwise condensation on a vertical surface (수직평판에서 층류막상 응축열전달에 관한 해석적 고찰)

  • 김형섭
    • Journal of the korean Society of Automotive Engineers
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    • v.2 no.1
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    • pp.21-31
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    • 1980
  • Two phase boundary layer equations of laminar filmwise condensation are solved by an approximate integral method under the following condition; saturated vapour flows vertically downward over a cooled surface of uniform temperature, the condensate film is so thin that the inertia and convection terms are neglected. The following conclusions are drawn under the above assumptions. 1. free convection In case of the linear temperature profile in a liquid film, numerical results for the average coefficients of heat transfer may be expressed as N $u_{m}$=4/3,(G $r_{l}$ /4.H)$^{1}$4/ and in case of the quadratic profile, numerical results may be expressed as N $u_{m}$=2/1.682,(G $r_{l}$ /H)$^{1}$4/. 2. Forced convection When the temperature profile is assumed to be linear in a liquid film, numerical results fir the average heat transfer coefficients may be expressed as N $u_{m}$=(A, R $e_{l}$ /H)$^{1}$2/. This expression is compared with the experimental results hitherto reported; For theoretical Nusselt number (N $u_{m}$)$_{th}$<2*10$^{4}$, the experimental Nusselt number (N $u_{m}$)$_{exp}$ is on the average larger than theoretical Nusselt number (N $u_{m}$)$_{th}$ by 30%. For (N $u_{m}$)$_{th}$>2*10$^{4}$, experimental Nusselt number (N $u_{m}$)$_{exp}$ is about 1.6 times as large as theoretical Nusselt number (N $u_{m}$)$_{th}$. These large deviation may be caused by the presence of turbulence in the liquid film. In case of the quadratic temperature profile in a liquid film, numerical results for the average coefficients of heat transfer may be expressed as N $u_{m}$'=(2,A,Re/H)$^{1}$2/. This formular shows that theoretical Nusselt number (N $u_{m}$)$_{th}$ is larger than experimental Nusselt number (N $u_{m}$)$_{exp}$ by 60%. It is speculated that when the temperature difference between cooled surface and saturated vapour is small, temperature profile in a liquid film is quadratic.quadratic.. quadratic.quadratic..atic..

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Estimation for Primary Tunnel Lining Loads

  • Kim, Hak-Joon
    • Proceedings of the Korean Geotechical Society Conference
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    • 1998.05a
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    • pp.153-204
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    • 1998
  • Prediction of lining loads due to tunnelling is one of the major issues to be addressed in the design of a tunnel. The objective of this study is to investigate rational and realistic design loads on tunnel linings. factors influencing the lining load are summarized and discussed. The instruments for measuring the lining loads are reviewed and discussed because field measurements are often necessary to verify the design methods. Tunnel construction in the City of Edmonton has been very active for storm and sanitary purposes. Since the early 1970's, the city has also been developing an underground Light Rail Transit system. The load measurements obtained from these tunnels are compared with the results from the existing design methods. However, none of the existing methods are totally satisfactory, Therefore, there is some room for improvement in the prediction of lining loads. The convergence-confinement method is reviewed and applied to a case history of a tunnel in Edmonton. The convergence curves are obtained from 2-D finite element analyses using three different material models and theoretical equations. The limitation of the convergence-confinement method is discussed by comparing these curves with the field measurements. Three-dimensional finite element analyses are performed to gain a better understanding of stress and displacement behaviour near the tunnel face. An improved design method is proposed based on the review of existing design methods and the performance of numerical analyses. A specific method or combination of two different methods is suggested for the estimation of lining loads for different conditions of tunnelling. A method to determine the stress reduction factor is described. Typical values of dimensionless load factors nD/H for tunnels in Edmonton are obtained from parametric analyses. Finally, the loads calculated using the proposed method are compared with field measurements collected from various tunnels in terms of soil types and construction methods to verify the method. The proposed method gives a reasonable approximation of the lining loads. The proposed method is recommended as an approximate guideline for the design of tunnels, but the results should be confirmed by field measurements due to the uncertainties of the ground and lining properties and the construction procedures, This is the reason that in-situ monitoring should be an integral part of the design procedure.

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Development of Longitudinal Dispersion Coefficient Based on Theoretical Equation for Transverse Distribution of Stream-Wise Velocity in Open Channel : Part II. Longitudinal Dispersion Coefficient (개수로에서 흐름방향 유속의 횡분포 이론식에 기반한 종분산계수 개발 : II. 종분산계수)

  • Baek, Kyong Oh
    • Journal of Korea Water Resources Association
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    • v.48 no.4
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    • pp.299-308
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    • 2015
  • The aim of this study is that a theoretical formula for estimating the one-dimensional longitudinal dispersion coefficient is derived based on a transverse distribution equation for the depth averaged stream-wise velocity in open channel. In "Part I. Theoretical equation for stream-wise velocity" which is the former volume of this article, the velocity distribution equation is derived analytically based on the Shiono-Knight Method (SKM). And then incorporating the velocity distribution equation into a triple integral formula which was proposed by Fischer (1968), the one-dimensional longitudinal dispersion coefficient can be derived theoretically in "Part II. Longitudinal dispersion coefficient" which is the latter volume of this article. The proposed equations for the velocity distribution and the longitudinal dispersion coefficient are verified by using observed data set. As a result, the non-dimensional longitudinal dispersion coefficient is inversely proportional to square of the Manning's roughness coefficient and the non-dimensional transverse dispersion coefficient, and is directly proportional to square of the aspect ratio (channel width to depth).

Derivation and Application of Survival Functions for Unthinned Forest Plantation (미간벌(未間伐) 인공림(人工林)에서 잔존림목(殘存林木) 추정(推定) 함수(函數)의 유도(誘導)와 적용(適用))

  • Li, Fengri;Chung, Joosang;Kwon, Soonduk
    • Journal of Korean Society of Forest Science
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    • v.88 no.3
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    • pp.320-326
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    • 1999
  • In this study, 15 survival functions in integral and difference forms for forest plantation were derived based on assumptions for the number of surviving trees and the differential forms of the mortality rate model. Then, performance of the models was evaluated by fitting to remeasurement data of unthinned white pine(Pinus strobes) forest plantation. As a result, three equations associated with a power function of age, $t^{\beta}$, are somewhat more suitable for describing the effect of self-thinning over time. On the other hand, a general survival function for Japanese larch(Larix leptolepts) forest plantation was derived in order to exam the effect of site quality on self-thinning procedures. The results indicate that the $N_{min}$ is negatively correlated with site index and, even though the same initial stand density was assumed, the survival function curves differ in shapes associated with site index values.

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Depth Controller Design for Submerged Body Moving near Free Surface Based on Adaptive Control (적응제어기법을 이용한 수면근처에서 운항하는 몰수체의 심도제어기 설계)

  • Park, Jong-Yong;Kim, Nakwan;Yoon, Hyeon Kyu;Kim, Su Yong;Cho, Hyeonjin
    • Journal of Ocean Engineering and Technology
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    • v.29 no.3
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    • pp.270-282
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    • 2015
  • A submerged body moving near the free surface needs to maintain its attitude and position to accomplish missions. It is necessary to validate the performance of a designed controller before a sea trial. The hydrodynamic coefficients of maneuvering are generally obtained by experiments or computational fluid dynamics, but these coefficients have uncertainty. Environmental loads such as the wave exciting force and suction force act on the submerged body when it moves near the free surface. Thus, a controller for the submerged body should be robust to parameter uncertainty and environmental loads. In this paper, the six-degree-of-freedom equations of motions for the submerged body are constructed. The suction force is calculated using the double Rankine body method. An adaptive control method based on an artificial neural network and proportional-integral-derivative control are used for the depth controller. Simulations are performed under various depth and speed conditions, and the results show the effectiveness of the designed controller.

Free vibration of FGM plates with porosity by a shear deformation theory with four variables

  • Yousfi, Mahfoud;Atmane, Hassen Ait;Meradjah, Mustapha;Tounsi, Abdelouahed;Bennai, Riadh
    • Structural Engineering and Mechanics
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    • v.66 no.3
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    • pp.353-368
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    • 2018
  • In this work, a high order hyperbolic shear deformation theory with four variables is presented to study the vibratory behavior of functionally graduated plates. The field of displacement of the theory used in this work is introduced indeterminate integral variables. In addition, the effect of porosity is studied. It is assumed that the material characteristics of the porous FGM plate, varies continuously in the direction of thickness as a function of the power law model in terms of volume fractions of constituents taken into account the homogeneous distribution of porosity. The equations of motion are obtained using the principle of virtual work. An analytical solution of the Navier type for free vibration analysis is obtained for a FGM plate for simply supported boundary conditions. A comparison of the results obtained with those of the literature is made to verify the accuracy and efficiency of the present theory. It can be concluded from his results that the current theory is not only accurate but also simple for the presentation of the response of free vibration and the effect of porosity on the latter.

Bending behaviour of FGM plates via a simple quasi-3D and 2D shear deformation theories

  • Youcef, Ali;Bourada, Mohamed;Draiche, Kada;Boucham, Belhadj;Bourada, Fouad;Addou, Farouk Yahia
    • Coupled systems mechanics
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    • v.9 no.3
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    • pp.237-264
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    • 2020
  • This article investigates the static behaviour of functionally graded (FG) plates sometimes declared as advanced composite plates by using a simple and accurate quasi-3D and 2D hyperbolic higher-order shear deformation theories. The properties of functionally graded materials (FGMs) are assumed to vary continuously through the thickness direction according to exponential law distribution (E-FGM). The kinematics of the present theories is modeled with an undetermined integral component and satisfies the free transverse shear stress conditions on the top and bottom surfaces of the plate; therefore, it does not require the shear correction factor. The fundamental governing differential equations and boundary conditions of exponentially graded plates are derived by employing the static version of principle of virtual work. Analytical solutions for bending of EG plates subjected to sinusoidal distributed load are obtained for simply supported boundary conditions using Navier'is solution procedure developed in the double Fourier trigonometric series. The results for the displacements and stresses of geometrically different EG plates are presented and compared with 3D exact solution and with other quasi-3D and 2D higher-order shear deformation theories to verify the accuracy of the present theory.

Maximum Coupling Through a Narrow Slit in a Short-Ended Parallel-plate Waveguide with a Nearby Conducting Strip (단락종단된 평행평판 도파관의 좁은 슬릿을 통한 근접 도체스트립과의 최대 결합)

  • Lee, Jong-Ik;Jo, Yeong-Gi
    • Journal of the Institute of Electronics Engineers of Korea TC
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    • v.37 no.12
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    • pp.15-21
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    • 2000
  • In this study, the electromagnetic coupling through a narrow slit in the upper wall of a short-ended parallel-plate waveguide(PPW) covered by a dielectric slab with a nearby conducting strip on the slab Is considered for the case that the TEM wave is incident in the PPW. Coupled integral equations whose unknowns are the slit electric field and the induced electric current over the strip are derived and solved numerically by use of the method of moments. From results, it has been observed that most of the incident power can be coupled exterior to the guide by appropriately setting the strip width and position, though the slit is very narrow. In addition, the differences between the radiation phenomena, observed in the cases that the conducting strip and the upper Plate of the PPW form a cavity and that strip behaves like a parasitic element, are discussed.

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Highly Linear Wideband LNA Design Using Inductive Shunt Feedback

  • Jeong, Nam Hwi;Cho, Choon Sik;Min, Seungwook
    • JSTS:Journal of Semiconductor Technology and Science
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    • v.14 no.1
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    • pp.100-108
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    • 2014
  • Low noise amplifier (LNA) is an integral component of RF receiver and frequently required to operate at wide frequency bands for various wireless system applications. For wideband operation, important performance metrics such as voltage gain, return loss, noise figure and linearity have been carefully investigated and characterized for the proposed LNA. An inductive shunt feedback configuration is successfully employed in the input stage of the proposed LNA which incorporates cascaded networks with a peaking inductor in the buffer stage. Design equations for obtaining low and high impedance-matching frequencies are easily derived, leading to a relatively simple method for circuit implementation. Careful theoretical analysis explains that input impedance can be described in the form of second-order frequency response, where poles and zeros are characterized and utilized for realizing the wideband response. Linearity is significantly improved because the inductor located between the gate and the drain decreases the third-order harmonics at the output. Fabricated in $0.18{\mu}m$ CMOS process, the chip area of this wideband LNA is $0.202mm^2$, including pads. Measurement results illustrate that the input return loss shows less than -7 dB, voltage gain greater than 8 dB, and a little high noise figure around 6-8 dB over 1.5 - 13 GHz. In addition, good linearity (IIP3) of 2.5 dBm is achieved at 8 GHz and 14 mA of current is consumed from a 1.8 V supply.