等向性多孔彈曼德爾問題解法應用於關節軟骨的暫態行為;Isotropic poroelastic Mandel’s problem solutions for application to transient behavior of articular cartilage

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题名:	等向性多孔彈曼德爾問題解法應用於關節軟骨的暫態行為;Isotropic poroelastic Mandel’s problem solutions for application to transient behavior of articular cartilage
作者:	李允玓;Li, Yun-Di
贡献者:	機械工程學系
关键词:	曼德爾;多孔彈;暫態;Mandel;poroelastic;transient
日期:	2021-01-28
上传时间:	2021-03-18 17:51:01 (UTC+8)
出版者:	國立中央大學
摘要:	本研究的目的是分析受固定壓縮力後滑液孔隙壓力和軟骨位移的動態行為，因為軟骨的可滲透和兩相特性，所以我們利用多孔彈性理論來建立模型。本研究我們使用有限元素法將多孔彈性方程式離散後再代入Mandel’s problem的問題定義來模擬軟骨受固定壓縮力後的行為，由於目前為止沒有文獻關於Mandel’s problem動態多孔彈的解析解可以驗證，因此我們從準靜態方面進行FreeFEM++模擬的數值解與推導出的解析解來比較，此外也藉由COMSOL Multiphysics與FreeFEM++驗證軟骨模型的數值解，驗證完準靜態數值解後，再加入慣性項來計算軟骨受固定壓縮力後的動態解，最後再與準靜態解進行比較，進而探討孔隙壓力和軟骨位移暫態的變化，此動態解顯現激振開始時的暫態行為，在未來能應用於振動或應力波的情況。;The purpose of this study is to analyze the dynamic behavior of synovial fluid pore pressure and cartilage displacement under a constant compressive force. Because of the permeability and biphasic characteristics of cartilage, the poroelastic theory was used to build the model. In this study, the poroelastic equations are discretized by finite element method. After that, the discretized equations are substituted into the definition of Mandel′s problem to simulate the cartilage behavior under a constant compressive force. To our best knowledge, the dynamic poroelastic analytical solution of Mandel′s problem has not been derived in any literature. The numerical solution calculated by FreeFEM++ is compared with the analytical solution for the quasi-static state. In addition, the numerical static solution of FreeFEM++ is validated against that of COMSOL Multiphysics. After verification of the numerical quasi-static solution, an inertia term is added to calculate the dynamic solution of the cartilage under a constant compressive force. Finally, the dynamic solution is compared with the quasi-static solution to discuss the transient variations of pore pressure and cartilage displacement. The dynamic solution shows the transient behavior at the beginning of the excitation. In the future, it will be applied to vibration or stress waves.
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