應用向量式有限元素法於撓性機構的運動分析

Dynamic Analysis of Flexible Mechanisms Using Vector Form Intrinsic Finite Element Method

孫緯翰(Wei-Han Sun)

指導教授 ： 李志中

國立臺灣大學/工學院/機械工程學研究所/碩士(2004年)

https://doi.org/10.6342/NTU.2004.02063

摘要

本文主旨在於應用向量式有限元素法模擬具撓性桿件的機構。此法依照傳統有限元素法的原則，將欲分析的結構物以有限的節點離散化，並將質量假設在節點上，推導符合牛頓第二定律的方程式。為了使分析更加精準，採取剛體位移與變形位移分離的作法，先計算剛體位移，再計算變形位移，並定變形座標算出純變形座標與全域座標的轉角，以提供純變形座標與全域作標間的座標轉換；接著計算出因為純變形而產生的內力，再加上時間積分的疊代過程，就可以簡單而快速的分析出機構的動態行為。最後用向量式有限元素法模擬數個例子，將結果與ABAQUS的模擬結果加以分析比較，以佐證此法在機構分析上的可行性。

關鍵字

向量式有限元素法 ； 撓性機構 ； 變形坐標 ； 顯式時間積分

並列摘要

In this thesis, the dynamic analysis of flexible mechanisms using vector form intrinsic finite element (VFIFE) method is performed. Based on the concept of finite element method, the structure is discretized into finite particles on which the mass is also assumed. In considering the accuracy of the analysis, the calculation of rigid body displacement is separated from the deformation displacement due to flexibility. A deformation coordinate system is introduced to calculate angular relations between the deformation coordinate system and the global coordinate system. Subsequently, the internal force due to deformation is calculated and the equations of motion of each particle are established via the Newton’s second law. Finally, several examples are illustrated to demonstrate the method and the result are compared with those run by the software ABAQUS. It is shown that the validity of the method in the dynamic analysis of flexible mechanisms.

並列關鍵字

deformation coordinates ； VFIFE ； explicit time integration ； flexible mechanism

參考文獻

12.莊清鏘，賴建豪，碩士學位論文，向量式有限元素法於平面構架幾何非線性之應用，2003

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