• Title, Summary, Keyword: time-step analysis method

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Stability and accuracy for the trapezoidal rule of the Newmark time integration method with variable time step sizes (가변시간간격을 갖는 Newmark 시간적분법의 사다리꼴법칙에 대한 안정성과 정확도)

  • Noh, Yong-Su;Chung, Jin-Tae;Bae, Dae-Seong
    • Transactions of the Korean Society of Mechanical Engineers A
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    • v.21 no.10
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    • pp.1712-1717
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    • 1997
  • Stability and accuracy for the trapezoidal rule of the Newmark time integration method are analyzed when variable time step sizes are adopted. A new analytic approach to stability and accuracy analysis is also proposed for time integration methods with variable time step sizes. The trapezoidal rule with variable time step sizes has the "actual" unconditional stability which is the same as that of the method with constant time step sizes. However, the method with variable time step sizes is first-order accurate while the method with constant time step sizes is second-order accurate. accurate.

A novel two sub-stepping implicit time integration algorithm for structural dynamics

  • Yasamani, K.;Mohammadzadeh, S.
    • Earthquakes and Structures
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    • v.13 no.3
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    • pp.279-288
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    • 2017
  • Having the ability to keep on yielding stable solutions in problems involving high potential of instability, composite time integration methods have become very popular among scientists. These methods try to split a time step into multiple sub-steps so that each sub-step can be solved using different time integration methods with different behaviors. This paper proposes a new composite time integration in which a time step is divided into two sub-steps; the first sub-step is solved using the well-known Newmark method and the second sub-step is solved using Simpson's Rule of integration. An unconditional stability region is determined for the constant parameters to be chosen from. Also accuracy analysis is perform on the proposed method and proved that minor period elongation as well as a reasonable amount of numerical dissipation is produced in the responses obtained by the proposed method. Finally, in order to provide a practical assessment of the method, several benchmark problems are solved using the proposed method.

Correction of the Approximation Error in the Time-Stepping Finite Element Method

  • Kim, Byung-Taek;Yu, Byoung-Hun;Choit, Myoung-Hyun;Kim, Ho-Hyun
    • Journal of Electrical Engineering and Technology
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    • v.4 no.2
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    • pp.229-233
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    • 2009
  • This paper proposes a correction method for the error inherently created by time-step approximation in finite element analysis (FEA). For a simple RL and RLC linear circuit, the error in time-step analysis is analytically investigated, and a correction method is proposed for a non-linear system as well as a linear one. Then, for a practical inductor model, linear and non-linear time-step analyses are performed and the calculation results are corrected by the proposed methods. The accuracy of the corrected results is confirmed by comparing the electric input and output powers.

Development of higher performance algorithm for dynamic PIV

  • NISHIO Shigeru
    • 한국가시화정보학회:학술대회논문집
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    • pp.25-32
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    • 2004
  • The new algorithm for higher performance of dynamic PIV has been proposed. Present study considered mathematical basis of PIV analysis for multiple-time-step images and it enables us to analyze the high time-resolution PIV, which is obtained by dynamic PIV system. Conventional single pair image PIV analysis gives us the velocity field data in each time step but it sometimes contains unnecessary information of target flow. Present technique utilize multi-time step correlation information, and it is analyzed.

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APPLICATION OF BACKWARD DIFFERENTIATION FORMULA TO SPATIAL REACTOR KINETICS CALCULATION WITH ADAPTIVE TIME STEP CONTROL

  • Shim, Cheon-Bo;Jung, Yeon-Sang;Yoon, Joo-Il;Joo, Han-Gyu
    • Nuclear Engineering and Technology
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    • v.43 no.6
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    • pp.531-546
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    • 2011
  • The backward differentiation formula (BDF) method is applied to a three-dimensional reactor kinetics calculation for efficient yet accurate transient analysis with adaptive time step control. The coarse mesh finite difference (CMFD) formulation is used for an efficient implementation of the BDF method that does not require excessive memory to store old information from previous time steps. An iterative scheme to update the nodal coupling coefficients through higher order local nodal solutions is established in order to make it possible to store only node average fluxes of the previous five time points. An adaptive time step control method is derived using two order solutions, the fifth and the fourth order BDF solutions, which provide an estimate of the solution error at the current time point. The performance of the BDF- and CMFD-based spatial kinetics calculation and the adaptive time step control scheme is examined with the NEACRP control rod ejection and rod withdrawal benchmark problems. The accuracy is first assessed by comparing the BDF-based results with those of the Crank-Nicholson method with an exponential transform. The effectiveness of the adaptive time step control is then assessed in terms of the possible computing time reduction in producing sufficiently accurate solutions that meet the desired solution fidelity.

Structure Borne Noise Analysis of a Flexible Body in Multibody System (다물체계내 유연체의 구조기인 소음해석)

  • 김효식
    • Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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    • pp.130-135
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    • 2003
  • This paper presents the method for structure borne noise analysis of a flexible body in multibody system. The proposed method is the superposition method using flexible muitibody dynamic analysis and finite element one. This method is executed in 3 steps. In the la step, time dependent quantities such as dynamic loads, modal coordinates ana gross body motion of the flexible body are calculated efficiently through flexible multibody dynamic analysis. And frequency response functions are computed using Fourier transforms of those time dependent quantities. In the 2$\^$nd/ step, acoustic pressure coefficients are obtained through structure-acoustic coupling analysis by finite element analysis. In the final step, frequency responses of acoustic pressure at the acoustic nodes are recovered through linear superposition of frequency response functions with acoustic pressure coefficients. The accuracy of the proposed method is verified in the numerical example of a simple car model.

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Study on the error correction for the time-step FSA in electric machine (전기기기에 대한 시간차분해석의 오차보정에 관한연구)

  • Yu, Byoung-Hun;Kim, Byung-Taek
    • Proceedings of the KIEE Conference
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    • pp.26-28
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    • 2008
  • This paper proposes a method correcting the error which is created inherently by time-step approximation in FEA. For a simple RL linear circuit, the error in time-step analysis is analytically investigated and the correction method is proposed. Then for a practical inductor model, non-linear time-step analysis is performed and the calculation result is corrected by the proposed method. The accuracy of the corrected result is confirmed by comparing the electric input and output power.

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Time-dependent analysis of reinforced concrete structures using the layered finite element method

  • Bradford, M.A.;Gilbert, R.I.;Sun, S.C.H.
    • Structural Engineering and Mechanics
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    • v.8 no.6
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    • pp.561-578
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    • 1999
  • The response of a reinforced concrete structure to loading is both immediate and time-dependent. Under a sustained load, the deflections caused by creep and shrinkage may be several times their instantaneous values. The paper describes a general finite element procedure, based on the so-called layered model, to analyse reinforced concrete members, and shows in particular how the simple Step by Step Method may be incorporated into this procedure. By invoking the Modified Newton Raphson Method as a solution procedure, the accuracy of the finite element method is verified against independent test results, and then applied to a variety of problems in order to demonstrate its efficacy. The method forms a general method for analysing highly indeterminate concrete structures in the time domain.

Finite element method for porous media using equal order element (동차선형요소를 사용한 다공질 매체의 커플링 유한요소해석)

  • Park, Tae-Hyo;Tak, Moon-Ho
    • Proceedings of the Computational Structural Engineering Institute Conference
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    • pp.20-25
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    • 2008
  • The finite element analysis for porous media is severe job because constituents have different physical peoperties, and element's continuity and stability should be considered. Thus, we propose the new mixed finite element method in order to overcome the problems. In this method, multi time step, remeshing step, and sub iteration step are introduced. The multi time step and remeshing step make it possible to satisfy a stability and an accuracy during sub iteration in which global time is determined. Finally, the proposed method is compared with the ABAQUS(2007) software and exact solution(Schiffman 1967) through two dimensional consolidation model.

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Effects of Space Increment and Time Step to the Accuracy of the Implicit Finite Difference Method in a Two-Dimensional Transient Heat Conduction Problem (이차원과도열전도에 대한 음함수형 유한차분법의 정도에 미치는 공간증분 및 시간간격의 영향)

  • CHO Kwon-Ok;LEE Yong-Sung;OH Hoo-Kyu
    • Korean Journal of Fisheries and Aquatic Sciences
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    • v.18 no.1
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    • pp.15-22
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    • 1985
  • The study on computation time, accuracy, and convergency characteristic of the implicit finite difference method is presented with the variation of the space increment and time step in a two-dimensional transient heat conduction problem with a dirichlet boundary condition. Numerical analysis were conducted by the model having the conditions of the solution domain from 0 to 3m, thermal diffusivity of 1.26 $m^2/h$, initial condition of 272 K, and boundary condition of 255.4 K. The results obtained are summarized as follows : 1) The degree of influence with respect to the accuracy of the time step and space increment in the alternating-direction implicit method and Crank-Nicholson implicit method were relatively small, but in case of the fully implicit method showed opposite tendency. 2) To prescribe near the zero for the space increment and tine step in a two dimensional transient problem were good in a accuracy aspect but unreasonable in a computational time aspect. 3) The reasonable condition of the space increment and the time step considering accuracy and computation time could be generalized with the Fourier modulus increment, F, ana dimensionless space increment, X, irrespective of the solution domain.

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