臺灣博碩士論文加值系統

本文應用更新式推演法(Updated Lagrange)U.L.法與剛體運動法則作為基礎，從而建立具有大變形及大轉角特性之薄殼幾何非線性理論的無網格數值分析架構。在方程式推導過程中利用位置向量求得薄殼變形前後的切平面座標，並應用剛體旋轉，將控制點建立在切平面上，藉此簡化方程式的推導，同時提升數值分析效率。
在分析幾何非線性的問題上，將採用弧長控制法進行迭代，以驗證本文提出的非線性理論及數值分析架構的正確性和合理性。而迭代過程又可分為預測及修正兩階段: (1)預測階段─忽略增量位移的高次項，應用更新式推演法，求得簡易形式的薄殼線性化增量位移表示式；(2)修正階段─採用更新式推演法並應用剛體運動法則建立薄殼幾何非線性微分方程式，並利用迭代收斂至正確解。
本文在無網格法的使用上，將應用移動最小二乘法及廣義有限差分法建立微分方程式與求解物理量，另外在無網格法的佈點上，也將引入虛擬節點來解決邊界已知條件數與未知條件數不相等的問題，最後將以例題驗證本文方法的可行性，並同時探討薄殼的慣性矩問題。

Based on the Update Lagrange Method and rigid body motion rule, a meshless numerical analysis framework of the geometrical nonlinear theory will be established for thin-shells with large deformations and large rotations. In the equation derivation process, position vectors are used to obtain the tangent plane coordinates before and after the deformation of the thin shell, and the rigid body rotation is applied to ignore the contribution of the higher-order term of the incremental displacement, simplifying the derivation of the equation and improving the efficiency of numerical analysis.
In the analysis of geometric nonlinearity, the arc length control method will be used to iterate to verify the correctness and rationality of the nonlinear theory and numerical analysis framework proposed in the present. The iterative process can be divided into two stages of prediction and correction: (1) In the prediction stage, ignoring the higher-order terms of incremental displacement, and obtain a simple form of linearized incremental displacement expression of thin shells by applying Update Lagrange Method. (2) In the correction stage, using Update Lagrange Method and rigid body motion to establish the law of shell geometry nonlinear differential equations, and iterative convergence to the correct solution..
In the present, the meshless method will use the Moving Least Squares Differential Method and the Generalized Finite Difference Method to establish differential equations and solve physical quantities. In addition, on the layout of the meshless method, virtual nodes will also be introduced to solve known conditions and unknowns with the problem of unequal conditions. Finally, verify the feasibility of the method in the present with examples and discuss the inertia of thin shells.

誌謝....I
中文摘要....II
Abstract....III
目錄....IV
圖目錄....VI
表目錄....VIII
縮寫、符號表....IX
第一章 導論....1
1-1 文獻回顧....1
1-2 研究目的及方法....2
1-3 論文架構與內容....2
第二章 薄殼幾何非線性理論推導....4
2-1 前言....4
2-2 薄殼中曲面幾何性質....4
2-3 應變表示式....6
2-4 第一類及第二類截面力(彎矩)....8
2-5 力平衡方程式....10
2-6 組成律及等效剪力....11
2-7 預測階段-線性化增量位移表示式....14
第三章 無網格數值分析方法概述....17
3-1 前言....17
3-2 無網格分析方法介紹....17
3-3 移動最小二乘法介紹....17
3-4 虛擬佈點....20
第四章 非線性數值方法討論....21
4-1 前言....21
4-2 弧長法....21
4-3 切平面座標建立....25
4-3-1 切平面座標....25
4-3-2 旋轉矩陣....27
4-4 內力計算程序....29
第五章 實例分析....30
5-1 前言....30
5-2 線性分析....30
5-3 實例分析-線性分析....32
5-3-1 薄板承受軸向應力....32
5-3-2 薄板承受z方向剪應力....35
5-3-3 薄板承受軸向應力和側向拉應力....37
5-3-4 薄殼承受軸向應力....39
5-3-5 薄殼承受彎矩....42
5-4 非線性分析....49
5-4-1 預測階段....49
5-4-2 修正階段....52
5-5 實例分析-非線性分析....54
5-5-1 薄板承受軸向壓應力和z方向剪力微小擾動(t=0.5mm)....54
5-5-2 薄板承受軸向壓應力和z方向剪力微小擾動(t=1mm)....55
5-5-3 薄殼承受軸向壓應力和彎矩微小擾動(t=0.5mm)....56
5-5-4 薄殼承受軸向壓應力和彎矩微小擾動(t=0.7mm)....57
第六章 結論與建議....58
6-1 結論....58
6-2 建議....58
參考文獻....59
附錄A....A-1

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