臺灣博碩士論文加值系統

本研究針對無元素法分析提出平行化的演算法，以無影響節點排除以及網格區域性分割等策略達成系統資源之記憶體的有效使用以及平行分析之運算效能的提升。
分析程式之前後處理程式，為提供使用者方便建立分析模型及檢視分析結果之圖型化介面，好的前後處理程式能加強使用者與分析程式之間的互動，並充分發揮分析程式之功能，有限元素分析之前後處理程式，發展已有一段時間，其模型之建立與分析結果之呈現已有廣為接受的標準模式，然而無元素法為近年來新興研究發展中的數值方法，現有的無元素法分析程式，多仍以編輯文字檔案的方式來處理分析模型之設定與輸出分析結果。故有必要針對無元素分析研究其之圖型化使用者介面，以期為無元素分析提出一套合乎功能需求、有效率且易使用的前後處理模式，並據以開發原型程式驗證其使用性。
本研究針對二維無元素分析，使用JAVA SWING程式語言作為開發，前處理以視窗輸入的方式建立模型，後處理展示出節點的變位，並提出一系列的建模基本模式，有長方形、扇形、梯形、增減節點網格等模式，使用者可基於這些基本模式的搭配使用，有效率地建立廣泛類型的分析模型，例如由長方形模式組合而成L形、H形、T形等，或是使用長方形和梯形模式組成有裂縫的模型，易可用增減節點模式來處理應力集中等問題，可為無元素法建立可供參考的模式。

The Element Free method (EFM) is a developing method. Since most of the EFM programs today still handle the pre- and post- processing using file I/O, a standard practice for developing the Graphical User Interface (GUI) for general EFM analysis is necessary. This research attempt to propose a GUI based model for building analysis models and presenting analysis results for the Element Free method. A pre-processing model is proposed in this paper based on the study of various types of 2D EFM analysis cases. The model consists of three basic building modes, which are rectangle mode, fan mode, and trapezoid mode to create corresponding building blocks for building a model compositely. In addition, the adjusting modes for adding and deleting individual node or cell are also included for the adjustment of a model in detail. By combining the uses of these building and adjusting modes, various types of EFM models are expected to be built conveniently and efficiently. On the other hand, the general algorithms to display model deformation and model stress based on analysis result for post-processing are also proposed in this paper.

目錄
摘要 I
ABSTRACT II
誌謝 III
目錄 IV
圖目錄 VIII
表目錄 XIV
第一章 緒論 1
1.1研究動機 1
1.2研究目的 2
1.3研究方法 3
1.4論文架構 4
第二章 背景說明 5
2.1系統開發相關技術簡介 5
2.1.1無元素法基礎理論 5
2.1.1.1移動式最小平方近似法 5
2.1.1.2權重函數的形式與探討 7
2.1.1.3形狀函數的形式與探討 8
2.1.1.4高斯積分法 9
2.1.1.5邊界條件修正法 10
2.1.2 MPI平行計算環境 10
2.1.3 PC叢集平行計算環境 11
2.2系統開發相關工具簡介 12
2.2.1 OpenGL 12
2.2.2 Java程式語言 12
第三章 文獻回顧 14
3.1無元素法之發展 14
3.2無元素法分析之平行化研究 15
3.3無元素法之前後處理 16
第四章 程式演算法 17
4.1無元素分析演算法 17
4.1.1無元素分析基本演算法 17
4.1.1.1計算總體勁度矩陣演算法 17
4.1.1.2網格積分演算法 20
4.1.2平行化無元素分析演算法 22
4.1.2.1計算總體勁度矩陣平行化演算法 22
4.1.2.2無影響節點排除演算法 24
4.1.2.3網格區域性分割 27
4.2前後處理演算法 30
4.2.1長方形模式演算法 31
4.2.1.1模型邊界設定 31
4.2.1.2節點佈置 31
4.2.1.3網格佈置 34
4.2.1.3積分點佈置 36
4.2.2扇形模式演算法 37
4.2.2.1模型邊界設定 37
4.2.2.2節點佈置 37
4.2.2.3網格佈置 39
4.2.2.4積分點佈置 41
4.2.3梯形模式演算法 43
4.2.3.1模型邊界設定 43
4.2.3.2節點佈置 43
4.2.3.3網格佈置 45
4.2.3.4積分點佈置 48
4.2.4繪圖演算法 50
4.2.4.1模型邊界繪製之演算法 50
4.2.4.2節點繪製之演算法 52
4.2.4.3網格繪製之演算法 52
4.2.4.4積分點繪製之演算法 53
4.2.4.5呈現節點變位演算法 54
4.2.4.6呈現應力分析演算法 55
第五章 前後處理介面程式系統架構與功能探討 57
5.1前言 57
5.2 前後處理圖形化使用者介面程式系統架構 57
5.2.1 GUI類別 58
5.2.1.1 Model Viewer類別 58
5.2.1.2 Model Builder類別 59
5.2.1.3 Model Drawer類別 59
5.2.1.4 Scene Handler類別 59
5.2.2 EFA Model類別 59
5.3主視窗功能 61
5.3.1開啟新檔案 61
5.3.2開啟舊檔案 62
5.3.3儲存檔案 63
5.3.4 Undo/Redo 64
5.3.5 Reset 64
5.3.6 Clear 64
5.3.7 SetRectanglemodel 64
5.3.8 SetCirclemodel 66
5.3.9 SetTrapeziummodel 67
5.3.10 AddNode 68
5.3.11 SetRegularNode 69
5.3.12 SetIrregularNode 70
5.3.13 RemoveNode 71
5.3.14 SetCell 72
5.3.15 RemoveCell 73
5.3.16 SetLoad 74
5.3.17 SetConstraint 75
5.3.18 SetMaterials 76
第六章 前後處理介面使用範例 77
6.1前言 77
6.2單一模型實例 77
6.2.1懸臂梁分析模型 77
6.2.2簡支梁分析模型 87
6.2.3水壩分析模型 93
6.3分析模型建構實例 99
6.3.1 L、H、T形模型 99
6.3.2剛架模型 110
6.3.3含裂縫之模型 123
6.3.4應力集中分析模型 136
6.3.5具圓洞開孔之平板模型 140
第七章 改進平行演算法改進之效能評估 145
7.1前言 145
7.2系統資源使用評估 145
7.3平行效能評估 147
第八章 結論 150
8.1總結 150
8.2未來展望 151
參考文獻 152
附錄一 157
A.1系統成員列表 157
A.1.1 Model類別成員 157
A.1.2 point類別成員 159
A.1.3 node物件 159
A.1.4 gridnode物件 160
A.1.5 cell物件 161
A.1.6 gridcell物件 162
A.1.7 gaussnode物件 163
A.1.8 load物件 164
A.1.9 constraint物件 164
A.1.10 material物件 165

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