臺灣博碩士論文加值系統

本研究之目的為整合移動漸近線法與模糊理論於結構多目標拓樸最佳化設計。研究中使用ANSYS作為結構分析的工具，並利用複合材料分配法和移動漸近線法求得最佳結構拓樸外形。本文應用模糊理論中歸屬函數以及交集決策的概念，將多目標最佳化的問題轉換為單目標最佳化問題，最後求得結構多目標拓樸最佳化問題的Pareto最佳解。本研究使用三階段最佳化設計的技巧來進行結構拓樸最佳化。第一階段利用對偶法得到初始拓樸圖形。第二階段使用混合法，移除不必要元素，並保留必要元素，使拓樸圖形更為清晰。第三階段再應用B-Spline函數修正不平滑的拓樸邊界外形。
本論文將執行四個不同的範例求解結構多目標拓樸最佳化設計的問題，並探討各階段拓樸外形的差異。範例中顯示經過三階段拓樸最佳化後，可以得到較清晰且平滑之結構外形。

An integrated method of moving asymptotes and fuzzy theory for multi-objective topology optimization is developed in this study. The finite element analysis software ANSYS is used for structural analysis. By using the method of material distribution with method of moving asymptotes, the optimum topology design of structure is obtained. In this paper, the multi-objective optimization problem transfer to single optimization problem by utilizing the concept of the fuzzy theory, which is using membership function and intersection set of decision-making. After implementing the concept above, the Pareto solution of the multi-objective topology optimization problem can be obtained. Three stages of topology design were employed in this study. In first stage, a dual method is used to obtain the initial topology design. To eliminate unnecessary element and retain necessary element by element growth-removal combined method (EGRCM) in second stage. The B-Spline curve is used to smooth the design shape in the final stage.
Four different multi-objective problems are demonstrated in this paper. The topology optimization result will be discussed in each stage. After using three stages topology design, the results shows that the optimum shapes of structures are more clear and smooth.

目錄
中文摘要...................................................I
英文摘要..................................................II
目錄...................................... ..............IV
圖目錄...................................................VI
第1章 緒論.................................................1
1.1研究動機................................................1
1.2文獻回顧................................................2
1.3研究方法................................................5
第2章 結構拓樸最佳化.......................................7
2.1拓樸設計................................................7
2.2多階段拓樸最佳化.......................................10
2.3靈敏度分析.............................................15
第3章 多目標拓樸最佳化....................................19
3.1最佳化問題................................. ...........19
3.2Pareto最佳解解.........................................19
3.3模糊理論...............................................21
第4章 最佳化設計..........................................25
4.1移動漸近線法...........................................25
4.2最佳化問題.............................................31
4.3對偶法.................................................32
4.4程式執行流程................................. .........34
第5章 數值分析............................................37
5.1範例一：中心受單一負載之四端固定薄板...................37
5.2範例二：多種負載之兩邊固定薄板.........................44
5.3範例三：腳踏車車架結構......................... .......51
5.4範例四：自由端中心垂直受力之懸臂薄板...................58
第6章 結論................................................65
參考文獻..................................................66

圖目錄

圖一 單位細胞矩形孔洞.................................................................8
圖二 B-spline曲線.................................................................12
圖三 多階段拓樸最佳化設計流程.................................................14
圖四 多目標最小化問題示意圖.....................................................20
圖五 階段拓樸最佳化程式執行流程.............................................36
圖六 範例一 中心受單一負載之四端固定薄板............................38
圖七 範例一 最小順從度之拓樸最佳化.......................................39
圖八 範例一 最大特徵值之拓樸最佳化.......................................40
圖九 範例一 第一階段多目標拓樸最佳化....................................41
圖十 範例一 第二階段多目標拓樸最佳化....................................42
圖十一 範例一 第三階段多目標拓樸最佳化...............................43
圖十二 範例二 多種負載之兩邊固定薄板....................................45
圖十三 範例二 受集中力F2之拓樸最佳化................................46
圖十四 範例二 受集中力F1之拓樸最佳化................................47
圖十五 範例二 第一階段多目標拓樸最佳化................................48
圖十六 範例二 第二階段多目標拓樸最佳化................................49
圖十七 範例二 第三階段多目標拓樸最佳化................................50
圖十八 範例三 腳踏車車架結構..........................................52
圖十九 範例三 最小順從度之拓樸最佳化....................................53
圖二十 範例三 最大特徵值之拓樸最佳化....................................54
圖二十一 範例三 第一階段多目標拓樸最佳化...........................55
圖二十二 範例三 第二階段多目標拓樸最佳化............................56
圖二十三 範例三 第三階段多目標拓樸最佳化............................57
圖二十四 範例四 自由端中心垂直受力之懸臂薄板....................59
圖二十五 範例四 最小順從度之拓樸最佳化................................60
圖二十六 範例四 最大特徵值之拓樸最佳化................................61
圖二十七 範例四 第一階段多目標拓樸最佳化............................62
圖二十八 範例四 第二階段多目標拓樸最佳化............................63
圖二十九 範例四 第三階段多目標拓樸最佳化............................64

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