• Title/Summary/Keyword: the Galerkin method

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Horizontal 2-D Finite Element Model for Analysis of Mixing Transport of Heat Pollutant (열오염 혼합 거동 해석을 위한 수평 2차원 유한요소모형)

  • Seo, Il Won;Choi, Hwang Jeong;Song, Chang Geun
    • KSCE Journal of Civil and Environmental Engineering Research
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    • v.31 no.6B
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    • pp.507-514
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    • 2011
  • A numerical model has been developed by employing a finite element method to simulate the depth-averaged 2-D dispersion of the heat pollutant, which is an important pollutant material in natural streams. Among the finite element methods, the Streamline Upwind/Petrov Galerkin (SUPG) method was applied. Also both linear and quadratic elements can be applied so that irregular river boundaries can be easily represented. To show the movement of heat pollutants, the reaction term describing heat transfer was represented as an equation in which sink/source term is proportional to the difference between the equilibrium temperature and water surface temperature. The equation was expressed so that the water surface temperature changes according to the temperature transfer coefficient and the equilibrium temperature. For the calibration of the model developed, analytic and numerical results from a case of rectangular channel with full width continuous injection have been compared in a steady state. The comparisons showed that the numerical results were in good agreement with analytical solutions. The application site was selected from the downstream of Paldang dam to Jamsil submerged weir, and overall length of this site is about 22.5 km. The change of water temperature caused by the discharge from the Guri sewage treatment plant has been simulated, and results were similar to the observed data. Overall it is concluded that the developed model can represent the water temperature changes due to heat transport accurately. But the verification using observed data will further enhance the validity of the model.

Elastic Wave Propagation in Nuclear Power Plant Containment Building Walls Considering Liner Plate and Concrete Cavity (라이너 플레이트 및 콘크리트 공동을 고려한 원전 격납건물 벽체의 탄성파 전파 해석)

  • Kim, Eunyoung;Kim, Boyoung;Kang, Jun Won;Lee, Hongpyo
    • Journal of the Computational Structural Engineering Institute of Korea
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    • v.34 no.3
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    • pp.167-174
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    • 2021
  • Recent investigation into the integrity of nuclear containment buildings has highlighted the importance of developing an elaborate diagnostic method to evaluate the distribution and size of cavities inside concrete walls. As part of developing such a method, this paper presents a finite element approach to modeling elastic waves propagating in the containment building walls of a nuclear power plant. We introduce a perfectly matched layer (PML) wave-absorbing boundary to limit the large-scale nuclear containment wall to the region of interest. The formulation results in a semi-discrete form with symmetric damping and stiffness matrices. The transient elastic wave equations for a mixed unsplit-field PML were solved for displacement and stresses in the time domain. Numerical results show that the sensitivity of displacement, velocity, acceleration, and stresses is large depending on the size and location of the cavity. The dynamic response of the wall slightly differs depending on the existence of the containment liner plate. The results of this study can be applied to a full-waveform inversion approach for characterizing cavities inside a containment wall.

A Study of Meshless Method Programming (무요소법 프로그래밍에 관한 연구)

  • 김학수;배동명
    • Journal of the Korean Society of Fisheries and Ocean Technology
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    • v.38 no.2
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    • pp.110-118
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    • 2002
  • The element free Galerkin method has been suggested by Belyschko, etc. it is applied for linear elastic analysis of solid problems and its convergence characteristics and stability are shown according to the weight function, influence domain and scattered points. The various numerical examples are performed to check the efficiency of 1D EFG and 2D EFG program by changing factors. As a result it have the best results when it used the cubic spline weight function and the scaling parameter d$_{max}$=2. These programs were developed by mixed language programming method using Visual Basic and the C language. so it is fast and efficient. and visually shown the result.t.

Development of a Software to Evaluate the CPES(Cable Penetration Fire Stop) System in Nuclear Power Plane I (원자력발전소 케이블관통부 충전시스템 평가용 소프트웨어 개발 I)

  • 윤종필;권성필;조재규;윤인섭
    • Fire Science and Engineering
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    • v.18 no.1
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    • pp.24-30
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    • 2004
  • In this work the dynamic heat transfer occurring in a cable penetration fire stop system built in the firewall of nuclear power plants is three-dimensionally investigated to develop a test-simulator that can be used to verify effectiveness of the sealants. Here was carried out an experiment to observe the heat transfer in the cable penetration fire stop system made of DOW CORNING products. The dynamic heat transfer occurring in the fire stop system is formulated in a parabolic partial differential equation subjected to a set of initial and boundary conditions. And it was modeled, simulated, and analyzed. The simulation results were illustrated in three-dimensional graphics and were compared with experimental data. Through the simulations, it was shown clearly that the temperature distribution was influenced very much by the number, position, and temperature of the cable streams. It also was found that the dynamic heat transfer through the cable streams was one of the most dominant factors, and the feature of heat conduction could be understood as an unsteady-state process. It is certain that these numerical results are useful for making a performance-based design for the cable penetration fire stop system.

An accurate analytical model for the buckling analysis of FG-CNT reinforced composite beams resting on an elastic foundation with arbitrary boundary conditions

  • Aicha Remil;Mohamed-Ouejdi Belarbi;Aicha Bessaim;Mohammed Sid Ahmed Houari;Ahmed Bouamoud;Ahmed Amine Daikh;Abderrahmane Mouffoki;Abdelouahed Tounsi;Amin Hamdi;Mohamed A. Eltaher
    • Computers and Concrete
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    • v.31 no.3
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    • pp.267-276
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    • 2023
  • The main purpose of the current research is to develop an efficient two variables trigonometric shear deformation beam theory to investigate the buckling behavior of symmetric and non-symmetric functionally graded carbon nanotubes reinforced composite (FG-CNTRC) beam resting on an elastic foundation with various boundary conditions. The proposed theory obviates the use to shear correction factors as it satisfies the parabolic variation of through-thickness shear stress distribution. The composite beam is made of a polymeric matrix reinforced by aligned and distributed single-walled carbon nanotubes (SWCNTs) with different patterns of reinforcement. The material properties of the FG-CNTRC beam are estimated by using the rule of mixture. The governing equilibrium equations are solved by using new analytical solutions based on the Galerkin method. The robustness and accuracy of the proposed analytical model are demonstrated by comparing its results with those available by other researchers in the existing literature. Moreover, a comprehensive parametric study is presented and discussed in detail to show the effects of CNTs volume fraction, distribution patterns of CNTs, boundary conditions, length-to-thickness ratio, and spring constant factors on the buckling response of FG-CNTRC beam. Some new referential results are reported for the first time, which will serve as a benchmark for future research.