• Title/Summary/Keyword: Galerkin' method

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Antenna Factor Characteristics of EMI Dipole Antennas with Coaxial Cable Balun for Frequencies between 30 and 1,000 MHz (동축 케이블 밸런이 부착된 30~1,000 MHz 대역용 EMI 다이폴 안테나의 안테나 인자 특성)

  • Ju Chang-Hyun;Kim Ki-Chai
    • The Journal of Korean Institute of Electromagnetic Engineering and Science
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    • v.17 no.7 s.110
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    • pp.623-628
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    • 2006
  • This paper presents the characteristics of an antenna factor of two kinds of EMI dipole antennas with a coaxial cable balun used in the frequency range between 30 and 1,000 MHz. The integral equation for unknown current distribution is solved by the Galerkin's method of moments with piecewise sinusoidal functions. An antenna factor for EMI dipole antennas with the coaxial cable balun is derived by using the power loss concepts. We can realize two kinds of EMI dipole antennas with appropriate antenna factors in the frequency range from 30 to 1,000 MHz: 150-cm dipole length($30{\sim}300 MHz$) and 30cm dipole length($300{\sim}1,000 MHz$). To check th ε validity of the theoretical analysis, the complex antenna factor was measured using by reference antenna methods. It is shown that the calculated complex antenna factor is good agreement with experimental results.

Numerical Model of Circulation due to Sudden Variation of Flow Section (흐름 단면(斷面)의 급변화(急變化)에 의한 순환(循環)의 수치모형(數値模型))

  • Suh, Seung Won;Park, Jung Eng;Yoon, Tae Hoon
    • KSCE Journal of Civil and Environmental Engineering Research
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    • v.3 no.4
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    • pp.21-31
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    • 1983
  • Circulation phenamena in open channel with abrupt variation in flow section are studied by solving numerically two dimensional Navier-Stokes equations integrated over depth. Galerkin type finite element method is used as numerical scheme. Numerical results by both implicit and explicit schemes tested in one-demensional rectangular channel agree closely with the known solution. The numerical experiments carded out in the open channel with a pool indicate the expected flow pattern and the center of the circulation coincides with the geometrical center, but the vectors of velocity appear father small, and it remains to be further investigated. Numerically simulated flow profiles along the channel with constrictions such as bridge piers and abutments are shown to be close to hydraulic experimental results. Thus further refined numerical technique is expected to be able to serve as a tool to evaluate the effect of bridge backwater.

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Laminar Convective Heat Transfer in Vertical Square Duct with Variational Symmetric Heat Flux (비균일 대칭성 열Flux인 수직 사각 닥트내의 층류조합대류 열전달 효과)

  • 김시영
    • Journal of the Korean Society of Fisheries and Ocean Technology
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    • v.18 no.1
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    • pp.47-53
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    • 1982
  • An analysis of convection, in a fully developed laminar steady flow through the vertical square duct under the condition of variational symmetric heat flux, is considered. Finite element solution algorithm by Galerkin's method with triangular elements and linear interpolation polynominals for the temperature and velocity profiles are derived for the vertical square duct. The comparison of temperature distribution due to variational symmetric heat flux in the duct were made with available the other data when the condition of peripheral heat flux were uniform and zero. Numerical values for the dimensionless temperatures and Nusselt numbers at selected Rayleigh numbers and pressure gradient parameters were obtained at a few nodal points for the vertical square ducts and effects of corner in the duct were investigated.

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A Finite Element Beam Model Using Shape Functions that Satisfy the Euler Equations (Euler 방정식(方程式)을 만족(滿足)하는 형상함수(形狀凾數)를 이용(利用)한 보 유한요소모(有限要素)모델)

  • Kim, Gyong Chan;Shin, Young Shik;Kim, Sung Wook
    • KSCE Journal of Civil and Environmental Engineering Research
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    • v.6 no.1
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    • pp.61-68
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    • 1986
  • A set of the shape functions which perfectly satisfy the homogeneous Euler Equations has been proposed for deep beam problems. A finite element beam model using the proposed shape functions has been derived by the Galerkin weighted residual method and used to analyze the numerical examples without reduced shear integration, to show the accuracy and efficiency of the proposed shape functions. The result shows that the finite element model using the proposed shape functions gives very accurate solutions for both static and free vibration analyses. The concept of the proposed shape functions is thought to be applied for the finite element analysis of the elasto-static problems.

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Dynamic Analysis of the Multi-Span Beam on Elastic Foundation Part two : Dynamic Response for the Moving Loads (탄성지반 위에 놓여있는 다지지 보의 동적해석 제2보 : 움직이는 하중에 대한 동적응답)

  • K.J. Choi;Y.C. Kim
    • Journal of the Society of Naval Architects of Korea
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    • v.28 no.1
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    • pp.92-98
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    • 1991
  • The structures such as railway bridges can be modelled as the multi-span beam on the elastic foundation. These structures are usually subject to the moving load, which has a great effect on dynamic stresses and can cause severe motions, especially at high velocities. In this paper, the dynamic responses of the multi-span beam on the elastic foundation were obtained by using the Galerkin's method and the numerical time integration technique. As trial functions, the same orthogonal polynomial functions obtained in part 1, were used. From the numerical results, it was found that the one term expansion of the assumed solution usually leads to the accurate solutions. However, in the case that the stiffness of the transnational spring is very high or the rotational spring is placed where the slope of the first mode is zero, the higher modes must be included to obtain the accurate solutions.

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Analysis of the Effect of Solar Radiation on Internal Temperature Distribution in Concrete Mat Foundation (태양 복사열이 콘크리트 매트기초의 내부 온도분포에 미치는 영향에 관한 해석적 연구)

  • Song, Chung Hyun;Lee, Chang Joo
    • Journal of the Korea Institute of Building Construction
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    • v.17 no.1
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    • pp.63-72
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    • 2017
  • This research investigated the effect of solar radiation on the temperature distribution in concrete mat foundation. Zhang and Huang Model was utilized to estimate solar radiation heat at a given date and time. A one-dimensional finite element formula was derived with the fundamental laws of heat transfer and Galerkin method. Based on the formula, a one dimensional finite element analysis code was developed using MATLAB. Hydration heat analysis of mat foundation were conducted using the developed code. It was found that the solar radiation reduced the maximum temperature difference in mat foundation, and this temperature difference reduction was more prominent in case of summer season cast, a higher initial concrete temperature, and a thicker mat foundation depth. The research recommended that the solar radiation should be considered in hydration heat analysis of concrete mat foundation so as not to overestimate the maximum temperature difference in mat foundation.

Analysis of the Electromagnetic Scattering of Resistive Strip Grating with Uniform Resistivity on a Grounded Dielectric Layer - H-Polarization Case - (접지된 유전체 위의 저항율이 일정한 저항띠 격자구조에 대한 전자파 산란 해석 - H-분극인 경우 -)

  • Tchoi Young-Sun;Yang Seung-In
    • The Journal of Korean Institute of Communications and Information Sciences
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    • v.31 no.3A
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    • pp.321-327
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    • 2006
  • In this paper, when a H-polarized plane wave is incident on the grating consisting of uniform resistive strips, electromagnetic scattering is analyzed using the moment of methods (MoM). The current density of each resistive strip on a grounded dielectric plane is fixed by zero at both edges. To satisfy the condition at both ends of each resistive strip, the induced surface current density is expanded in a series of cosine and sine functions. The scattered electromagnetic fields are expanded in a series of floquet mode functions. The boundary conditions are applied to obtain the unknown current coefficients. According to the variation of the involving parameters such as strip width and spacing and angle of the incident field, numerical simulations are performed by applying the Fourier-Galerkin moment method. The numerical results of the normalized reflected power for resistive strips case for zero and several resistivities are obtained.

Numerical Analysis of Reflection Characteristics of Perforated Breakwater with a Resonant Channel (공진수로 내장형 유공방파제의 반사특성에 관한 수치해석 연구)

  • Kim, Jeong-Seok;Seo, Ji-Hye;Lee, Joong-Woo;Park, Woo-Sun
    • Journal of Navigation and Port Research
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    • v.38 no.5
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    • pp.503-509
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    • 2014
  • In this study, a new concept perforated breakwater is proposed, which is having resonant channels. In the channel, perforated plate is installed for dissipating wave energy induced by flow separations. The breakwater has two advantages compared with conventional perforated breakwater having wave chamber with slotted walls. One is easy to control the target wave condition for dissipating wave energy, and the other is having the high structural safety because the structural members are not exposed to impact waves, directly. To evaluate wave reflection characteristics of the proposed breakwater, numerical experiment was carried out by using Galerkin's finite element model based on the linear potential theory. The results indicated that considerable energy dissipation occurs near the resonant period of channel, and wave reflection characteristics are affected by channel shape, location and opening ratio.

A radial point interpolation method for 1D contaminant transport modelling through landfill liners

  • Praveen Kumar, R.;Dodagoudar, G.R.
    • Geomechanics and Engineering
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    • v.2 no.2
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    • pp.141-156
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    • 2010
  • In the framework of meshfree methods, a new methodology is developed based on radial point interpolation method (RPIM). This methodology is applied to a one-dimensional contaminant transport modelling in the saturated porous media. The one-dimensional form of advection-dispersion equation involving reactive contaminant is considered in the analysis. The Galerkin weak form of the governing equation is formulated using 1D meshfree shape functions constructed using thin plate spline radial basis functions. MATLAB code is developed to obtain the numerical solution. Numerical examples representing various phenomena, which occur during migration of contaminants, are presented to illustrate the applicability of the proposed method and the results are compared with those obtained from the analytical and finite element solutions. The proposed RPIM has generated results with no oscillations and they are insensitive to Peclet constraints. In order to test the practical applicability and performance of the RPIM, three case studies of contaminant transport through the landfill liners are presented. A good agreement is obtained between the results of the RPIM and the field investigation data.

A multiple scales method solution for the free and forced nonlinear transverse vibrations of rectangular plates

  • Shooshtari, A.;Khadem, S.E.
    • Structural Engineering and Mechanics
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    • v.24 no.5
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    • pp.543-560
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    • 2006
  • In this paper, first, the equations of motion for a rectangular isotropic plate have been derived. This derivation is based on the Von Karmann theory and the effects of shear deformation have been considered. Introducing an Airy stress function, the equations of motion have been transformed to a nonlinear coupled equation. Using Galerkin method, this equation has been separated into position and time functions. By means of the dimensional analysis, it is shown that the orders of magnitude for nonlinear terms are small with respect to linear terms. The Multiple Scales Method has been applied to the equation of motion in the forced vibration and free vibration cases and closed-form relations for the nonlinear natural frequencies, displacement and frequency response of the plate have been derived. The obtained results in comparison with numerical methods are in good agreements. Using the obtained relation, the effects of initial displacement, thickness and dimensions of the plate on the nonlinear natural frequencies and displacements have been investigated. These results are valid for a special range of the ratio of thickness to dimensions of the plate, which is a characteristic of the Multiple Scales Method. In the forced vibration case, the frequency response equation for the primary resonance condition is calculated and the effects of various parameters on the frequency response of system have been studied.