結構最佳化的目的是在尋找材料的適當使用方式，讓結構有最佳的使用效能。在此論文中將整合商用電腦輔助分析軟體的強大的分析能力及遺傳演算法（genetic algorithm）多目標最佳化搜尋能力，以發展一套自動結構最佳化設計程式。商用電腦輔助分析軟體的建構幾何模型及工程分析能力變成為程式的工具，以求解實際的結構設計的問題。在設計過程中利用遺傳演算法去改進設計，以達到結構最佳化的目標。
本論文中，利用整合商用有限元素法軟體ANSYS及自行發展的遺傳演算法程式進行結構形狀最佳化。ANSYS在工程問題上的建模及分析的能力讓設計者得以解決工業應用中實際的最佳化問題，遺傳演算法則能進行全域搜尋最佳解。一些多值域和多目標的測試函式被用來檢驗並程式架構及效能。最後自行開發程式會用二次元與三次元的拓樸結構最佳化問題來進行測試，並且證實這個程式的架構能用於解決不同的實際工程最佳化問題。

Structural optimization aims at finding an appropriate material distribution to achieve the best structural performance. In this study, the analysis capability of commercial CAE program was integrated with the optimization search of genetic algorithms to develop a fully automated structural optimization program. The geometric modeling and analysis capability of commercial CAE program are used as the tool to find the solution of practical problem in structure design. In the design cycle, genetic algorithms will be applied to improve the design and to achieve the target of structural optimization.
In this study, the topology optimization problems of structure were investigated by integration of commercial finite element package ANSYS with the developed genetic algorithms program. The modeling and analysis capability of ANSYS in engineering design will increase the designer’s capability for solving the engineering optimization problem in industry applications and the genetic algorithms can search global optimum solution. Some test functions for multi-modal and multi-objective optimization problems were used to verify the architecture and performance of the program. Finally, the developed program will be tested on problems of topology optimization of two-dimensional and three-dimensional structures. It is shown that the architecture of developed design system is capable to deal with different real engineering optimization problems.

摘要（中文）………………………………………………………….………….…i
Abstract……….…………………………………………………………………….ii
目錄……………………………………………………………………….………….iii
第一章 緒論……………...……………………….…………………..…………….….1
1-1簡介………………………………….……….………………..…..……………..3
1-2研究動機…….…………………...………………………..……………….…...4
第二章遺傳演算法………..………...…………….…………..………………….…...5
2-1簡介…………………………………….…………..………………..……….….5
2-2架構與演算法…………………………….………..………………………….6
2-2.1 適合度函數……………………………….….………………………….6
2-2.2 起始演化基因的產生…………………..……………………………..7
2-2.3 複製機能………………………………..……………………………….8
2-2.3.1 輪盤法…………………………..…………………………………9
2-2-3.2 RSSR……………………………..………………………………….10
2-2-3.3 RSSWOR….……………………..…………………………………...10
2-2-3.4 RSIS……..……………………..…………………………………...11
2-2-3.5 ST…..…………………………..…………………………………...11
2-2.4 交配機能…….…………………….……………………………………12
2-2.4.1 單點交配……………………….……………………..………...12
2-2.4.2 兩點交配……………………….……………………………….13
2-2.4.3 多點交配………………………………………………………..14
2-2.4.4 均勻交配………………………………………………………..15
2-2.5 突變機能……………………………………………………………… .15
2-2.6 Niche Scheme for Genetic Algorithms…………………..….16
2-2.6.1 Crowding Scheme……………………………………………….16
2-2.7 人工選擇…..…………………………………………………………...17
2-3 遺傳演算法模式……….……………………………………………………17
2-3.1 單目標模式……………...……………………………………………..18
2-3.2 多值域模式………………………………………………….…………19
2-3.2.1 多值域函數測試與結果…………...…………………………..21
2-3.3 多目標模式……..……………………..……………………………….27
2-3.3.1 Weighted Sum Approach……………………………………29
2-3.3.2 NSGA法…………………………………………………………..30
2-3.3.3 SPEA法………………..……………………………………...….31
2-3.3.4 多目標方法比較………………………………………………34
2-3.3.5 多目標函數測試與結果……………………………………..36
第三章 整合CAE的結構最佳化設計
3-1簡介……………………………………………………………….……………41
3-2 立體結構元素之有限元素理論介紹……………………………...……41
3-2.1 有限元素分析的程序…………………………………………..……42
3-2.2 有限元素理論分析……………………………………………...……43
3-3 商用有限元素ANSYS軟體架構介紹………………………………...…47
3-4 ANSYS結構分析程序………………………………………………………48
3-5 結合遺傳演算法與結構拓撲設計之介紹……………………….…….49
3-5.1 結構編碼……………………………………………………………….49
3-5.2 基因治療……...……………………………………………….……….50
3-6 結構最佳化程序……………………………………………………………52
3-7 工程應用實例……………………………………………………………….55
3-7.1 SGA設定值………………………………………………………….….56
3-8 驗證的結果與討論……………………………………………….…...……57
第四章 二次元拓樸結構最佳化設計
4-1簡介………………………………………………………………………….…58
4-2 二次元多值域拓樸結構最佳化設計……………………...……………58
4-2.1分析例1………………………………………………………………….58
4-2.1.1 參數設定值……………………………………………………...59
4-2.1.2 結果………………………………………………………..….…..60
4-2.2 分析例二…………………………………………………………….…61
4-2.2.1 參數設定值……………………………………………………...62
4-2.2.2 結果……………………………………………………………….63
4-3 二次元多目標拓樸結構最佳化設計………………………………...…64
4-3.1分析例1…………………………………………………………………64
4-3.1.1 參數設定…………………………………………………………65
4-3.1.2 結果……………………………………………………………….65
4-3.2分析例2………………………………………………………………… 67
4-3.2.1 參數設定…………………………………………………………68
4-3.2.2 結果……………………………………………………………….69
4-4結果與討論……………………………………………………………………70
第五章 三次元拓樸結構最佳化設計…...………………………………………71
5-1簡介………………………………………………………………………..……71
5-2 三次元多值域拓樸結構最佳化設計……………….…………………..71
5-2.1分析例1………………………………………………………..………..72
5-2.1.1 參數設定值………..………………………………………….…72
5-2.1.2 結果…………………………………………………………….…74
5-2.2分析例2………………………………………………………..…….….76
5-2.2.1 參數設定值……………………………………………….…..77
5-2.2.2 結果………………………………………………………….…78
5-3 三次元多目標拓樸結構最佳化設計…………………………………...79
5-3.1分析例1………………………………………………………..………..79
5-3.1.1 參數設定值……………………………………………………...80
5-3.1.2 結果…………………………………………………………….…81
5-3.2分析例2……………………………………………………..………….81
5-3.2.1 參數設定值……………………………………………………...84
5-3.2.2 結果……………………………………………………………….85
5-4 結果與討論…………………………………………………………………86
第六章 結論…...…………………………………………………………………...…87
Reference...…………………………………………………………………...……….88

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