運動解析應用於三維機構分析

Motion Analysis of Structures for three dimensional mechanisms

陳仲恩(Jon-En Chen)

指導教授 ： 李志中

共同指導教授 ： 吳東岳

國立臺灣大學/工學院/機械工程學研究所/碩士(2007年)

https://doi.org/10.6342/NTU.2007.02522

摘要

本文旨在利用運動解析的觀念，應用於三維機構的運動狀態分析與力學描述。運動解析的觀念可以具體的四點論述：1.仔細考慮分析結構 2.考慮質點路徑 3.估算結構變形與內力 4.時間積分。經過這四個程序的運算，變形結構體或機構的運動狀態，可以透過質點路徑而近似的計算出，每個質點的運動方程式的推導都藉由向量力學或牛頓力學。不同於分析力學使用變分法、能量法求解數值近似值，應力、應變與變形，皆直接透過結構元運動學計算而得。
三維機構問題中，除了結構體的旋轉、平移等特性外，另外需特別考量接頭對於計算上所帶來的影響，不同類型的接頭，拘束條件、邊界條件與物理特性等，都將造成機構在模擬與分析上的困難，在本文裡，利用運動學方式推導球窩接頭(Spherical Joint)以及旋轉接頭(Revolute Joint)的運動方程式，並使用期刊算例驗證其模擬結果。
本文使用運動解析應用於空間剛架理論來考慮幾何非線性，並利用簡單剛架元組成空間機構，與相關期刊比較數值算例與實驗結果來證明理論之正確性與可行性。模擬結果亦相當符合，顯示運動解析在分析三維機構運動、變形的問題上，皆能有效的處理。

關鍵字

向量式有限元 ； 運動解析 ； 撓性機構 ； 三維機構

並列摘要

In this work, we present a study on the analysis of space motion of beams employing a particle method of Motion Analysis of Structures (MAS). The MAS method is based on a vector form of mechanics which discretizes a continuous body into a set of particles described by the Newton’s laws. The interactions among those particles are defined by the element forces formulated by a vector-form intrinsic finite element (VFIFE) so that the elements with large rotation can be successfully handled. A general three dimensional problem has been investigated throughout this work which is more challenging then 2D problems since not only the rotation or displacement but also the types of joints applied to the objects need to be considered. The governing equations describing the motions of both ball and revolute joints are first derived and then the MAS approach is applied in the simulation. Simulation results show the superior performance of the proposed method comparing to other works in the literature.

並列關鍵字

Motion analysis ； Space mechanism ； VFIFE ； Joint

參考文獻

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