• Title/Summary/Keyword: Analytical calculation

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Analysis of the Existing Analytical Solutions for Isotropic Rectangular Thin Elastic Plates with Three Edges Clamped and the Other Free (등방성 직사각형의 3변 고정 1변 자유 얇은 탄성판에 대한 기존 해석해의 분석)

  • Seo, Seung-Nam
    • KSCE Journal of Civil and Environmental Engineering Research
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    • v.26 no.1A
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    • pp.117-132
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    • 2006
  • The existing analytical solutions for rectangular plates with three edges clamped and the other free are derived based on nondimensional differential equation and their characteristics are analyzed. Since Timoshenko and Woinowsky-Krieger's method (1959) can give solutions for the case limited to the aspect ratio of the plates less than one, this method are proved to be impractical for the bending moment calculation of the plates under consideration. Horii and Moto's method(1968) are modified by adding stabilizing terms to suppress overflow in the matrix computation, from which the series solution with maximum 150 terms can be obtained. By use of the series solution the convergence of computed bending moments is tested. The modified method can be shown to calculate the deflection properties for the plates with wide range of aspect ratios, but the computed x moment at the corner points formed by the free edge and the clamped edges can not satisfy the boundary condition and the cause of problem is discussed in detail.

Dose Calculation of Photon Beam with Wedge Filter for Radiation Therapy Planning System

  • Cheong, Kwang-Ho;Suh, Tae-Suk;Lee, Hyoung-Koo;Choe, Bo-Young
    • Proceedings of the Korean Society of Medical Physics Conference
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    • 2003.09a
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    • pp.41-41
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    • 2003
  • Purpose: Even if the wedge filter is widely used for the radiation therapy to modify the photon beam intensity, the wedged photon beam dose calculation is not so easy. Radiation therapy planning systems (RTPS) have been used the empirical or semi-analytical methods such as attenuation method using wedge filter parameters or wedge filter factor obtained from measurement. However, these methods can cause serious error in penumbra region as well as in edge region. In this study, we propose the dose calculation algorithm for wedged field to minimize the error especially in the outer beam region. Materials and Method: Modified intensity by wedge filter was calculated using tissue-maximum ratio (TMR) and scatter-maximum ratio (SMR) of wedged field. Profiles of wedged and non-wedged direction was also used. The result of new dose calculation was compared with measurement and the result from attenuation method. Results: Proposed algorithm showed the good agreement with measurement in the high dose-gradient region as well as in the inner beam region. The error was decreased comparing to attenuation method. Conclusion: Although necessary beam data for the RTPS commissioning was increased, new algorithm would guarantee the improved dose calculation accuracy for wedged field. In future, this algorithm could be adopted in RTPS.

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History of the Photon Beam Dose Calculation Algorithm in Radiation Treatment Planning System

  • Kim, Dong Wook;Park, Kwangwoo;Kim, Hojin;Kim, Jinsung
    • Progress in Medical Physics
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    • v.31 no.3
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    • pp.54-62
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    • 2020
  • Dose calculation algorithms play an important role in radiation therapy and are even the basis for optimizing treatment plans, an important feature in the development of complex treatment technologies such as intensity-modulated radiation therapy. We reviewed the past and current status of dose calculation algorithms used in the treatment planning system for radiation therapy. The radiation-calculating dose calculation algorithm can be broadly classified into three main groups based on the mechanisms used: (1) factor-based, (2) model-based, and (3) principle-based. Factor-based algorithms are a type of empirical dose calculation that interpolates or extrapolates the dose in some basic measurements. Model-based algorithms, represented by the pencil beam convolution, analytical anisotropic, and collapse cone convolution algorithms, use a simplified physical process by using a convolution equation that convolutes the primary photon energy fluence with a kernel. Model-based algorithms allowing side scattering when beams are transmitted to the heterogeneous media provide more precise dose calculation results than correction-based algorithms. Principle-based algorithms, represented by Monte Carlo dose calculations, simulate all real physical processes involving beam particles during transportation; therefore, dose calculations are accurate but time consuming. For approximately 70 years, through the development of dose calculation algorithms and computing technology, the accuracy of dose calculation seems close to our clinical needs. Next-generation dose calculation algorithms are expected to include biologically equivalent doses or biologically effective doses, and doctors expect to be able to use them to improve the quality of treatment in the near future.

A Study on the Inductance Calculation of SRM using Magnetic Circuit Analysis (자기회로 해석을 통한 SRM의 인덕턴스 산정에 관한 연구)

  • Choi Kyeong-Ho;Kim Dong-Hee;Kim Min-Huei
    • Proceedings of the KIPE Conference
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    • 2004.07a
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    • pp.244-248
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    • 2004
  • This paper present a inductance calculation method of Switched Reluctance Motor (SRM) for torque characteristic analysis using analytical model. Recently, many approaches of inductance calculations are accomplished with Finite Element Analysis (FEM) and curve fitting method using complex nonlinear magnetic circuit model. It this paper, a simple method for inductance calculation is proposed based on the motor design parameters. The simulation result of the proposed method are compared with a FEM analysis for, and a good accuracy is obtained.

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A study on the prediction of wheel wear of railway rolling stock (철도차량 차륜마멸예측에 관한 연구)

  • Kang, Bu-Byoung;Chung, Heung-Chai
    • Proceedings of the KSME Conference
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    • 2003.04a
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    • pp.1270-1276
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    • 2003
  • This paper describes an analytical method for wheel wear prediction. The outputs from vehicle dynamic software are used to calculation the wheel wear. Two calculation examples are shown for a high-speed line and a conventional line. Through the comparison of two cases, we can see the wheel wear characteristics on the conventional line and the high-speed line. The conventional line has many curved tracks that cause severe wheel flange wear. The influences of curve radius on wheel wear are also described considering the operational performance of the high speed trainset. A method of calculation using contact patch work model is presented for determination of the evolution by wear railway wheels.

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Simple equations for the calculation of the temperature within the cross-section of slim floor beams under ISO Fire

  • Zaharia, R.;Franssen, J.M.
    • Steel and Composite Structures
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    • v.13 no.2
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    • pp.171-185
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    • 2012
  • The calculation of fire resistance for a composite structural element comprises the calculation of the temperature within its cross-section and of the load bearing capacity, considering the evolution of the steel and concrete mechanical properties, function of the temperature. The paper proposes a method to calculate the bending capacity under ISO fire, for Slim Floor systems using asymmetric steel beams, with a wider lower flange or a narrow upper flange welded onto a half hot-rolled profile. The temperatures in the cross-section are evaluated by means of empirical formulas determined through a parametrical analysis, performed with the special purpose non-linear finite element program SAFIR. Considering these formulas, the bending capacity may be calculated, using an analytical approach to determine the plastic bending moment, for different fire resistance demands. The results obtained with this simplified method are validated through numerical analysis.

Analysis of Magnetization Currents

  • Miteva, Neda;Slonim, Michael
    • Journal of Electrical Engineering and Technology
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    • v.11 no.6
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    • pp.1610-1613
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    • 2016
  • An analytical method for harmonic estimation of magnetization currents has been developed. The method is based on the results of the waveforms qualitative analysis. The calculation and the experimental results are compared. A good matching is observed.

분포매개정수를 갖는 원자로의 최적제어 1

  • 지창열;김상훈
    • 전기의세계
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    • v.29 no.1
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    • pp.53-57
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    • 1980
  • The analytical treatment for a terminal cost problem of a distributed reactor with a small singular parameter is presented. The inverse of the neutron velocity is regarded as a singular parameter, and the model, adopted for simplicity, is a cylindrically symmetrical reactor. The Helmholtz mode expension is used for the application of the optimal theory for lumped parameter systems to the spatially distributed parameter system. The closed-form solution is explicitely obtained for machine calculation.

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