向量式DKT薄殼元推導與板殼結構運動分析

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陳詩宏(Shih-Hung Chen) 查詢紙本館藏

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論文名稱

向量式DKT薄殼元推導與板殼結構運動分析
(Development of the Vector Form DKT thin Shell Element and Motion Analyses if shell Structures)

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摘要(中)

本文以向量式有限元(Vector Form Intrinsic Finite Element，VFIFE，V-5)以及運動解析作為板殼結構分析之基本理論，發展板殼結構的VFIFE-DKT元素。引用運動解析理論中的概念：點值描述，途徑單元和移動基礎架構，將板殼結構的非線性運動行為，轉為可用材料力學微變形分析概念處理的小變形問題，並在元素層面引入DKT板元與CST薄膜元的分析概念，完成VFIFE-DKT元素的推導。基於運動解析的發展理念，本文著重於板殼結構運動行為的驗證與探討，在動力分析部份，本文提出兩種轉動慣量的計算方式，並以穩定的變形座標選定法則計算板殼結構的小變位振動與自由運動及動力挫屈等問題，其結果皆與文獻結果一致。在靜力問題部份則是提出一套VFIFE板殼元標準的靜力分析程序，算例結果顯示此程序穩定並具有良好的收斂性。而為了驗證板殼轉動慣量的準確性，本文亦完成一薄殼結構大變位實驗之量測與比對，結果顯示本文VFIFE-DKT元素與轉動慣量計算與所得分析實驗結果近似。最終則是依運動解析的理念，提出一個板殼元簡易的開裂分析程序，確保結構系統破壞後能夠成為獨立的運動體，且系統總能在開裂過程不會有額外的損失。

摘要(英)

In order to simulate the large displacement of a thin shell structure, a novel shell element based on the vector form intrinsic finite element (VFIFE) method is presented. The motion of the shell structure is characterized by the motions of finite particles. Each particle is subjected to the external forces and internal forces. The motion of each particle satisfies the Law of Mechanics. In addition, three key processes of the VFIFE method such as the point value description, path element and convected material frame are adopted. A fictitious reversed rigid body motion is used to separate the rigid body motion and the deformations of the VFI-DKT element within each path element. The internal forces of the element determined in the deformation coordinate system satisfy the equilibrium equations. Through the numerical analyses of the benchmark structures undergo extremely-large displacements and rotation during motion, this novel shell element of the VFIFE method demonstrates its outstanding accuracy and efficiency.

關鍵字(中)

★ 薄殼元
★ 大變位分析
★ 向量式有限元(VFIFE)
★ 運動分析
★ 變形座標

關鍵字(英)

★ shell element
★ large displacement analysis
★ vector form intrinsic finite element (VFIFE)
★ motion analyses
★ deformation coordinates

論文目次

中文摘要 i
英文摘要 ii
誌謝 iii
目錄 iv
圖目錄 vii
表目錄 xiv
符號說明 xv
第一章緒論 1
1-1 研究方向 2
1-2 研究方法及步驟 2
第二章文獻回顧 5
2.1板殼元素之發展 5
2.2向量式有限元之研究與發展現況 9
2.2.1 VFIFE理論改善之研究 10
2.2.2增加VFIFE元素之研究 11
2.2.3工程問題模擬應用之研究 12
2.4文獻回顧整理與研究方法 14
第三章運動解析 17
3.1質點運動控制方程式 17
3.2途徑單元與點值描述 19
3.3剛體運動估算 21
3.4逆向轉動和變形座標 24
第四章向量式有限板殼元 28
4.1向量式DKT有限板殼元(VFIFE-DKT)之推導 28
4.2 VFIFE-DKT板殼元之質量矩陣 37
4.2.1質點式轉動慣量矩陣 38
4.2.2三角平板式轉動慣量矩陣 39
4.3運動方程式 45
4.4板殼元外力計算 49
4.5 VFIFE-DKT元靜力分析模式 54
4.6 VFIFE-DKT元素斷裂分析 58
4.7變形座標之定義程序 63
第五章數值算例 68
5.1 VFIFE-DKT之動力分析結果驗證 68
5.1.1 半圓形球殼之小變位振動分析 68
5.1.2扭曲梁之小變位振動分析 70
5.1.3懸臂矩形方板端點受拉之大變形分析 72
5.1.4單點支承之長方形板受重力作用之大轉動分析 74
5.1.5矩形板空間自由運動分析 76
5.1.6 半圓柱型頂板受集中力作用後之動力失穩行為分析 80
5.2 VFIFE-DKT之大變位靜力分析結果驗證 83
5.2.1 VFIFE-DKT元之靜力分析程序驗證。 83
5.2.2圓環狀薄板結構之大變位靜力分析 94
5.2.3圓柱形球殼之受徑向拉力後挫曲之靜力分析 98
5.2.4 18度開孔之半圓形球殼之大變位與大轉動靜力分析 102
5.3 VFIFE-DKT板殼元之應用 111
5.3.1圓環型薄板受集中力後之大變位行為實驗與分析比較 112
5.3.2 T字形薄殼結構自由運動分析與肋板挫屈補強 122
5.3.3圓環形薄殼結構開裂運動分析 126
第六章結論與建議 129
6.1結論 129
6.2建議 130
參考文獻 132
附錄 140
A. 空間轉動位移的計算 140
B. DKT元形狀函數 145
C. 轉動慣量積分 148
D. ABAQUS程式使用說明 152

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指導教授

王仲宇(Chung-Yue Wang)

審核日期

2013-7-30

推文