向量式剛架有限元於二維結構之大變位與接觸行為分析

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吳思穎(Szu-Ying Wu) 查詢紙本館藏

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土木工程學系

論文名稱

向量式剛架有限元於二維結構之大變位與接觸行為分析
(Large Deformation and Contact Analysis of 2D Frame Structure by the Vector Form Intrinsic Finite Element Method)

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摘要(中)

本論文應用向量式有限元理論模擬平面構架的幾何非線性行為，並加入構件與構件之接觸判斷之分析功能。
向量式有限元素法是以構件和接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。模擬結構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，也使得結構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不錯的結果。
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，並透過標準題驗證，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 frame 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 frame elements of the V-5 method. Through the numerical analyses of benchmark problems with large rotation, impact, self-contact characters, the V-5 method demonstrates its accuracy and efficiency on the analysis of frame structure with large deformation.

關鍵字(中)

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

關鍵字(英)

★ Vector Form Intrinsic Finite Element
★ Geometrically nonlinear
★ Explicit time integration
★ Co-rotation approach
★ Contact

論文目次

中文摘要………………………………………………………………….I
英文摘要………………………………………………………………….II
致謝……………………………………………………………………….III
目錄……………………………………………………………………….IV
圖目錄…………………………………………………………………….VII
表目錄…………………………………………………………………….XI
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………………………………………………………5
第二章向量式剛架有限元素之基本理論……………………………….6
2.1 簡介……………………………………………………………………6
2.2 基本假設與離散化……………………………………………………8
2.3 變形座標系統 (Deformation coordinate system)………………10
2.4 剛架元節點內力、外力與質量………………………………………12
2.4.1剛架元節點內力…………………………………………………….13
2.4.2剛架元節點作用力………………………………………………….17
2.4.3剛架元節點質量…………………………………………………….18
2.5運動方程式…………………………………………………………….19
2.5.1含阻尼質點運動方程式的推導(中值差分法)…………………….19
2.5.2具栓性連結的處理方式…………………………………………….21
2.5.3 計算程序……………………………………………………………22
第三章二維離散體之接觸碰撞分析…………………………………….25
3.1 接觸判斷方法簡介……………………………………………………25
3.2 接觸判斷方式…………………………………………………………29
3.2.1 剛架元與剛性無限域接觸判斷……………………………………30
3.2.2 剛架元與剛性有限域接觸判斷……………………………………34
3.2.3 兩可變形剛架之接觸判斷…………………………………………37
3.2.4 點對點接觸判斷……………………………………………………47
3.3 接觸力…………………………………………………………………49
3.3.1 正向接觸力…………………………………………………………49
3.3.2 接觸剪力之計算……………………………………………………56
3.4 步驟……………………………………………………………………58
第四章數值驗證………………………………………………………….62
算例4-1 二維剛架後挫屈分析………………………………………….63
算例4-2 懸臂梁受均步載重 ………..…………………………………65
算例4-3 端點施以旋轉角之柔性機器手臂 ……………………………67
算例4-4 端點施以彎矩力之柔性機器手臂 ……………………………71
算例4-5 柔性機械手臂………………………………………………….73
算例4-6 飛行柔性桿 ……………………………………………………76
算例4-7 飛行空心管線 …………………………………………………78
算例4-8 多體系統飛行構件 ……………………………………………81
算例4-9 閉合方鍊……………………………………………………….82
算例4-10 巴特單擺(Bathe’s pendulum)考慮重力效應 …………….84
算例4-11 巴特單擺(Bathe’s pendulum)不考慮重力效應 ………….87
算例4-12 接觸判斷機制驗證…………………………………………….89
算例4-13 二維圓環衝擊剛性邊界 …………………………………….97
算例4-14 二維圓環正向衝擊V型剛性邊界 …………………………….99
算例 4-15接觸判斷應用………………………………………………….102
第五章結論與建議……………………………………………………….109
5.1結論…………………………………………………………………….109
5.2建議和未來發展……………………………………………………….110
參考文獻……………………………………………………………………112

參考文獻

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指導教授

王仲宇(Chung Yue Wang)

審核日期

2005-1-20

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