FINITE ELEMENT METHOD FOR NONLINEAR SLOSHING ANALYSIS OF PERFECT FLUIDS : Analysis of two-dimensional rectangular containers

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  • YAMAMOTO Kenji
    Dept. of Architecture & Architectural Eng., Faculty of Engineering, Kagoshima Univ.
  • MINAKAWA Youichi
    Dept. of Architecture & Architectural Eng., Faculty of Engineering, Kagoshima Uuiv.

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Other Title
  • 完全流体における非線形スロッシングの有限要素解析法 : 二次元矩形容器の解析
  • カンゼン リュウタイ ニ オケル ヒセンケイ スロッシング ノ ユウゲン ヨウソ カイセキホウ 2ジゲン クケイ ヨウキ ノ カイセキ

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Abstract

This paper proposes a finite element method for nonlinear sloshing analysis of perfect fluids. In this paper, the discrete governing equations of free surface flows are derived based on the variational principle. The energy functional is denoted by the volume integration of the Bernoulli's pressure equation, and by descritizing this functional previously, i.e. by applying the Ritz method, the governing equations are easily obtained. Furthermore, we introduce the scheme that the governing equations contain the movement rules of the fluid element nodes in which the elements automatically change shape along with the free surface deformation. Also, the several time-marching schemes for the governing equations are examined. On one of their schemes, we find that the sloshing behaviors are expressed as the dynamic equation of a nonlinear spring-mass-damper system, where the mass depends on the displacement of the spring. The results are compared with the ealier works on the numerical examples, and the effectiveness of the proposed method is confirmed.

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