二維可變形塊體之向量式運動分析

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姓名

林明廷(Ming-Ting Lin) 查詢紙本館藏

畢業系所

土木工程學系

論文名稱

二維可變形塊體之向量式運動分析
(Vector Form Motion Analysis of 2D Deformation Bodies)

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摘要(中)

本論文應用向量式有限元理論模擬平面固體的幾何非線性行為，並加入頂角與邊之接觸判斷之分析功能，以模擬離散塊體系統之運動行為。
向量式有限元素法是以構件和節點為模擬基礎的物理模式，它將連續體定義成一群質點的組合，利用牛頓運動定律描述質點的運動，因此向量有限元的計算變成一組簡單的向量方程式計算。模擬固體變形運動問題時利用隨動變形座標系統分解剛體位移和變形位移，因此能夠精確的計算多個連續體同時具有大的剛體運動和大的幾何變形行為，也使得固體非線性分析得以簡化，此外，再配合顯式的時間積分公式及對應的向量運動方程式，使向量有限元分析程式不論在計算速度或模擬精度上都有合理的結果。
另外，由於接觸碰撞為工程及物理問題中的重要現象，本論文將
接觸力學分析方法納入向量式有限元之程序中，並透過例題驗證，發
現所開發之數值模擬程序具有極好之精度及能力。

摘要(英)

In this study , the Vector Form Intrinsic Finite Element (VFIFE , V-5) method equipped with the contact detection and analysis algorithm is applied to simulate the large deformation behaviors of structures.
The V-5 method models the analyzed domain to be composed by finite particles and Newton’’s second law is applied to describe each particle’’s motion. Thus, the calculation of the V-5 method becomes solving a set of decoupled vector form equations. In the theory of V-5, a convected reference frame and updated deformation coordinate system are used to separate the rigid body motion and pure deformation of the system. After combining these with explicit time integration scheme,the V-5 method can effectively simulate the dynamic behaviors of multi-bodies system having large deformation.
To study the impact/ contact problems that commonly admitted in engineering and industry applications, the contact detection and contact force calculation algorithms were developed for the solid elements of the V-5 method. Through the numerical analyses of benchmark problems with large rotation, impact, the V-5 method demonstrates its accuracy and efficiency on the analysis of structure with large deformation.

關鍵字(中)

★ 顯示時間積分
★ 向量式有限元素法
★ 接觸
★ 變形座標
★ 可變形塊體
★ 幾何非線性

關鍵字(英)

★ Vector Form Intrinsic Finite Element
★ Contact
★ Explicit Time Intergration
★ Geometrically Nonlinear
★ Deformable Block
★ Deformation Coordinate

論文目次

第一章緒論 1
1.1研究動機與目的 1
1.2 文獻回顧 2
1.3 研究方法與內容 7
第二章向量式有限元之基本理論 8
2.1 簡介 8
2.2 基本假設與離散化 11
2.3 剛體轉動與變形座標系統 13
2.3.1 剛體轉動 13
2.3.2 變形座標 17
2.3.3 變形位移的計算 17
2.4 固體元素節點內力 19
2.4.1三節點常應變元 21
2.4.2 四節點等參元 27
2.5 固體元素節點外力 34
2.5.1三節點常應變元之節點外力 35
2.5.2 四節點等參數元 40
2.6固體元素節點質量 42
2.7 運動方程式 43
2.7.1 含阻尼質點運動方程式的推導(中值差分法) 44
2.7.2 計算程序 46
第三章二維塊體之接觸模擬 49
3.1塊體接觸搜尋 50
3.1.1初步預估可能接觸的塊體組合 50
3.1.2 判斷可能接觸的節點與塊體組合 51
3.1.3 判斷節點與塊體參考邊的接觸組合 52
3.1.4 判斷節點與塊體參考邊的唯一接觸組合 54
3.2 塊體接觸處理 55
3.2.1 點對點接觸 56
3.2.2 點對邊接觸 58
3.3.3 正向接觸力 60
3.3.4 剪向接觸力 64
3.4 計算步驟 69
第四章數值驗證及範例 72
算例4-1 懸臂梁自由端受集中載重作用的變位分析 73
算例4-2 懸臂梁受均佈載重作用之大變位模擬 76
算例4-3 懸臂梁自由端受彎矩作用的大變形模擬 81
算例4-4 接觸判斷機制驗證 84
1.邊與邊的平行接觸 84
2.點與邊的正向接觸 86
3.點與點的接觸 88
算例4-5 二維圓環45°衝擊剛性邊界 89
算例4-6 基礎承載問題之模擬 95
算例4-7 塊體下滑之位移驗證 103
算例4-8 接觸判斷應用 105
1.兩圓環相互撞擊 105
2.齒輪轉動模擬 107
3.沙漏堆積模擬 110
4.飛行柔性桿件撞擊剛性牆 114
5.圓球滾動模擬 115
第五章結論與建議 117
5.1 結論 117
5.2 建議和未來發展 119
參考文獻 121

參考文獻

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指導教授

王仲宇(Chung-Yue Wang)

審核日期

2006-7-20

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