• Title/Summary/Keyword: 뉴턴-랩슨 반복법

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A Study on the Acceleration of the Solution Convergence for the Rigid Plastic FEM (강소성 유한요소해석에서 해의 수렴 가속화에 관한 연구)

  • 최영
    • Proceedings of the Korean Society of Precision Engineering Conference
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    • 2004.10a
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    • pp.347-350
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    • 2004
  • In this paper, the acceleration is studied for the rigid-plastic FEM of metal forming simulation. In the FEM, the direct iteration and Newton-Raphson iteration are applied to obtain the initial solution and accurate solution respectively. In general, the acceleration scheme for the direct iteration is not used. In this paper, an Aitken accelerator is applied to the direct iteration. In the modified Newton-Raphson iteration, the step length or the deceleration coefficient is used for the fast and robust convergence. The step length can be determined by using the accelerator. The numerical experiments have been performed for the comparisons. The faster convergence is obtained with the acceleration in the direct and Newton-Raphson iterations.

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Local Nonlinear Static Analysis via Static Condensation (강성응축기법을 이용한 국부 비선형 정적 해석)

  • Shin, Han-Seop;Oh, Min-Han;Boo, Seung-Hwan
    • Journal of the Korean Society of Marine Environment & Safety
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    • v.27 no.1
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    • pp.193-200
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    • 2021
  • In this study, an analysis technique using static condensation is proposed for an efficient local nonlinear static analysis. The static condensation method is a model reduction method based on the degrees of freedom, and the analysis model is divided into a target part and a condensed part to be omitted. In this study, the nonlinear and linear parts were designated to the target and the omitted parts, respectively, and both the stiffness matrix and load vector corresponding to the linear part were condensed into the nonlinear part. After model condensation, the reduced model comprising the stiffness matrix and the load vector for the nonlinear part is constructed, and only this reduced model was updated through the Newton-Raphson iteration for an efficient nonlinear analysis. Finally, the efficiency and reliability of the proposed analysis technique were presented by applying it to various numerical examples.