Zienkiewicz動態多孔彈性力學模型之穩定性探討

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题名:	Zienkiewicz動態多孔彈性力學模型之穩定性探討
作者:	李子立;Li, Tsu-Li
贡献者:	機械工程學系
关键词:	穩定性;穩定區;多孔彈性;stability;stable region;poroelasticity
日期:	2021-10-08
上传时间:	2021-12-07 13:43:52 (UTC+8)
出版者:	國立中央大學
摘要:	Zienkiewicz等人基於了Biot提出之多孔彈性動力學模型重新推導並額外考慮了一固體位移慣性項和流體加速度項，為了滿足位移–壓力型多孔彈性力學，Zienkiewicz等人在實際物理機制允許的情況下將流體加速度項省略了，以至於後來鮮少人能針對Zienkiewicz等人提出之多孔彈性動力學模型進行額外的分析及模擬，吾人通過馮諾依曼穩定性分析針對該多孔彈性力學模型分析之，並發現該模型存在無條件不穩定的區域，雖然該多孔彈性力學模型並不穩定，吾人仍可找出兩個條件收斂的穩定性條件，而且這兩條穩定性條件也分別對應了統御方程式中的質量方程式與動量方程式。另一方面，吾人於馮諾依曼穩定性分析中考慮不同變數(如：位移、孔壓)擁有不同之波數，相較於前人提出之馮諾依曼穩定性分析，此不同波數的假設更能全面的了解變數對穩定性的影響，甚至能得到假設相同波數的穩定性分析無法得到的結果。;Zienkiewicz et al. consider an additional inertial term of displacement and acceleration term of fluid in the poroelastodynamics model established by Biot. To satisfy the displacement-pressure formula. They consider neglecting acceleration terms of fluid with some physical condition. After they received his study, there were rarely researches also studying on theirs. Because of that, this study forces on his poroelastodynamic model using von Neumann stability analysis. However, this study points out that their poroelastodynamic model is unconditionally instability, finding out unconditionally instability region. Although this model is unstable, this paper finds the other two conditionally stable conditions, wave-like and diffusion-like conditions. On the other hand, this study assumes the different wavenumbers for each unknown, e.g. u (displacement) and p (pore pressure). This assumption is not the same as previous studies, but it can analyse this model more generally. In addition, utilizing this assumption can get more results than assuming the same wavenumbers for each unknown.
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