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標題: | 向量式分析求解具高度非線性二維剛架結構問題 Vector Form Analysis of 2-D Frame Structures with High Nonlinearities |
作者: | Wen-Chang Tsai 蔡文昌 |
指導教授: | 李志中(Jyh-Jone Lee) |
關鍵字: | 向量式分析,向量式有限元(VFIFE),材料非線性,接觸非線性, Vector From Analysis,VFIFE,material nonlinearity,contact,fragment, |
出版年 : | 2009 |
學位: | 碩士 |
摘要: | 本論文旨在使用向量式分析求解具高度非線性之二維剛架結構問題。所謂高度非線性意指一個結構,幾何、材料、接觸及斷裂等非線性行為的多重發生。不同於一般用於求解分析力學所導出的微分方程式的計算法,向量式分析直接以點值描述結構的運動並推導控制方程式。在向量式分析中,結構之構形以合理的質點數代替,中間以結構單元連結,質點間的互制力主要以向量式有限元所計算得到,且在結構單元上建立一組變形座標,分解質點的變形與運動;時間則以途徑單元進行區隔,以便於考量更新參考構形或改變束制條件。最後透過時間積分將整個運動過程得出。
材料非線性是採用雙線性彈塑性材料模式,並考慮混合強化法則以及受應變率影響材料下的Cowper-Symonds方程式;接觸演算法包含接觸搜尋和懲罰函數法;斷裂行為則是利用斷裂準則來判斷是否斷裂。本文最後以幾個例題對向量式分析法進行驗證,其中例題分析使用的程式為VFIFE 2D程式。 This study presents the analyses of highly nonlinear planer frame structures using the theory of vector form analysis. Including nonlinear geometry, material, contact/impact and fragment properties, rathen than treating three nonlinear properties such as geometry, material, contact/impact and fragment via analytical mechanics, vector form analysis is developed based on vecter mechanics. The structure is firstly described by a set of particles. The period of analysis are modeled via a set of discrete path element. The interactions among particles are complemented by the generalized forces evaluated by vector form intrinsic finite element (VFIFE). The governing equations, derived via Newton’s law are sloved by finite difference method. It is convenient to update the reference frame and change the constrain conditions. A bilinear elastic-plastic material model with mixed hardening rule and Cowper- Symonds equation for strain rate sensitive material is adopted to account for the material nonlinearity. The contact algorithm includes contact search and penalty function method. The fragment behavior is dealt by fragment criterion.Finally, a few numerical examples are presented to demonstrate the validity of vector form analysis. |
URI: | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/43094 |
全文授權: | 有償授權 |
顯示於系所單位: | 機械工程學系 |
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