本論文結合線性規劃法與改良式灰狼演算法於結構拓樸最佳化之研究。本研究使用ANSYS當作分析結構的工具，以複合材料分配法作為拓樸設計方法並使用線性規劃法及改良式灰狼演算法獲得最佳之材料分布。線性規劃法的優點是可以利用靈敏度分析提供搜尋方向，因此在求解的速度上較快，但存在著易落入區域最佳解的問題，而灰狼演算法是以隨機搜尋的方式，因此可降低落入區域最佳解的機率，但在大量變數的情況下難以收斂，因此本研究將改良灰狼演算法期望減少收斂時間。本研究利用線性規劃法找出初始設計外形，再以混合法將模糊元素及不連續之結構做限制，以求得更清晰之外形，最後再以B-spline函數重新定義邊界不平滑元素之上下限以修整拓樸外形輪廓，並應用改良式灰狼演算法來滿足總體積之限制，本研究在三階段拓樸設計後能得到較合理的拓樸設計外形。
    	本研究以六個不同範例來執行拓樸最化設計，結果顯示在大量的變數下仍能得到明確的幾何外形，以利於工業中的加工製造。

A methodology of topology optimization design by Linear Programming and Improved Grey Wolf Algorithms was used in this study. The finite element analysis software ANSYS was used for structural analysis. The advantage of the linear programming method is that it can use sensitivity analysis to provide the search direction effectively, but the disadvantage of Linear Programming is that the final result is easily falling into local optimum. The gray wolf algorithm is a random search method, so it can reduce the probability of falling into the local optimum area. In the case of large number of variables, the convergence of the gray wolf algorithm is slow. The proposed improved gray wolf algorithm is developed to improve the convergence speed in this study. The optimal topology design was obtained by the concept of material distribution borrowed from density method with Linear Programming and Improved Grey Wolf Algorithms. In this paper, the first stage optimum structure was obtained by Linear Programming. The second stage optimum design structure was determined by eliminating the unnecessary and discontinuity element. The final stage optimum design of structure was obtained by using B-spline function to smooth the design shape and using Improved Grey Wolf Algorithm to satisfy the limit of the total volume. The reasonable topology design shape can be obtained after the three-stage topology procedures. 
     There are six different structures were discussed in this study. The results show that a clear geometric shape can be obtained, which is beneficial to manufacturing in the industry.

目錄
目錄	iii
圖目錄	v
第一章 緒論	1
1.1研究動機	1
1.2文獻回顧	3
1.3本文架構	10
第二章 拓樸最佳化	11
2.1均質法	11
2.2生物成長法	12
2.3密度函數法	12
2.3.1材料分配法	13
2.3.2複合材料分配法	14
第三章 最佳化方法	15
3.1線性規劃法	15
3.1.1靈敏度分析	16
3.2灰狼演算法	19
3.2.1灰狼演算法執行流程	22
3.2.2改良式灰狼演算法	24
3.2.3函數測試分析	27
第四章 最佳化設計	28
4.1最佳化概念	28
4.2適應值	29
4.3 B-spline函數	30
4.3.1 B-spline函數於拓樸最佳化之應用	31
4.4三階段拓樸最佳化	32
4.5程式執行流程	33
第五章 數值分析	35
5.1範例一 : 自由端垂直受力之懸臂薄板	35
5.2範例二 : 單附載之兩端固定薄板	40
5.3範例三 : 多附載之兩端固定薄板	45
5.4範例四 : UAV側板結構	50
5.5範例五 : UAV機翼結構	55
5.6範例六 : UAV機頭側板結構	61
第六章 結論	67
參考文獻	68

圖目錄
圖1 均質法之細胞結構	12
圖2 灰狼演算法	21
圖3 灰狼演算法執行流程	23
圖4 線性遞減	25
圖5 指數遞減	25
圖6 迭代時的權重關係	26
圖7 B-spline曲線	31
圖8 拓樸執行流程	34
圖9 範例一垂直受力之懸臂薄板設計範圍	36
圖10 範例一第一階段之外形	37
圖11 範例一第二階段之外形	38
圖12 範例一最佳之外形	39
圖13 範例二單負載之兩端固定薄板設計範圍	41
圖14 範例二第一階段之外形	42
圖15 範例二第二階段之外形	43
圖16 範例二最佳之外形	44
圖17 多負載之兩端固定薄板設計範圍	46
圖18 範例三第一階段之外形	47
圖19 範例三第二階段之外形	48
圖20 範例三最佳之外形	49
圖21 範例四UAV側板結構之原始設計圖	51
圖22 範例四UAV側板結構設計範圍	51
圖23 範例四第一階段之外形	52
圖24 範例四第二階段之外形	53
圖25 範例四最佳之外形	54
圖26 範例五UAV機翼原始設計圖	56
圖27 範例六UAV機翼設計範圍	56
圖28 範例五第一階段之外形	57
圖29 範例五第二階段之外形	58
圖30 範例五最佳之外形	59
圖31 UAV機翼最佳設計	60
圖32 範例六UAV機頭側板原始設計圖	62
圖33 範例六UAV機頭側板設計範圍	62
圖34 範例六第一階段之外形	63
圖35 範例六第二階段之外形	64
圖36 範例六最佳之外形	65
圖37 UAV機頭側板最佳設計	66

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