本文使用有限元素法、最佳化設計與拓樸設計的理念，以模組整合方式，結合結構分析軟體，最佳化工具與拓樸法則於一最佳化設計系統中，以達到易於使用的目標，建構拓樸最佳化設計整合系統。在進行完第一階段拓樸最佳化設計後，使用混合法來同時保留及移除必要與非必要元素，接著再進行第二階段拓樸最佳化設計，最後使用Bezier函數之概念定義設計參數上下限來平滑結構外形，經過這三階段拓樸最佳化設計後，可改善原始最佳化設計不合理之現象，以達到更具實用性之拓樸最佳化設計。本研究採用線性規劃法來執行結構之最佳化設計，結果顯示在最佳化的過程中可以迅速有效的得到最佳值。
在本文中以不同結構範例來驗證吾人所採用的方法在拓樸設計上之效益。在數值分析中可發現本文所採用之多階段拓樸最佳化設計所得之結構外形比只經由一次拓樸最佳化設計之結構外形少了許多模糊元素，在外形上也更為明確。期望本研究應用到工業界實際的結構設計問題時，可提供製造上之便利性。

A system including finite element analysis, optimization method and topological design was developed in this study. This system provides a user-friendly environment for engineers to execute the multi-stage topology optimization easily. After carries on the first stage to topological optimization design, we use the element growth-removal combined method (EGRCM) simultaneously to grow and remove the essential element and the non-essential element on the second stage. The third stage, new design move limits were obtained by Bezier curve concept to smooth the design shape. After three stages topological optimum design, the primitive optimum design can be improved to more practical topological optimum design. The topological optimum design was obtained by Linear Programming efficiently in this study.
Different numerical example was developed to demonstrate the ability of multi-stage topological optimization. After three stages, the results of the optimum design was better then the results of first stage. We hope the results of this study can provide the convenience of manufacturing to the Industry of structural design.

目錄

中文摘要………………………………………………………I
英文摘要……………………………………………………III
目錄…………………………………………………………V
圖目錄………………………………………………………VII

第一章 緒論…………………………………………………1
1-1	研究動機與目的……………………………1
1-2	文獻回顧………………………………………4
1-3	本文架構………………………………………7
第二章 拓樸最佳化理論……………………………………8
2-1	理論說明………………………………………8
2-2	多階段拓樸最佳化設計………………………11
2-3	靈敏度分析……………………………………18
第三章 最佳化設計…………………………………………20
3-1	線性規劃法……………………………………20
3-2	Bezier函數……………………………………22
第四章 數值分析……………………………………………25
4-1	範例一：垂直受力懸臂樑……………………25
4-2	範例二：水平受力懸臂樑……………………30
4-3	範例三：單負荷兩端固定樑…………………35
4-4	範例四：多負荷兩端固定樑…………………40
4-5	範例五：懸臂中空樑…………………………45
4-6	範例六：腳踏車車架結構……………………50
第五章 結論…………………………………………………55

參考文獻……………………………………………………57


                     圖 目 錄

圖1.1	 結構最佳化設計的分類……………………………… 2
圖2.1	 單位細胞結構………………………………………… 9
圖2.2	 系統整合圖……………………………………………12
圖2.3	 元素等級顏色表示圖…………………………………14
圖2.4	 多階段拓樸最佳化設計流程圖………………………16
圖2.5	 階段拓樸最佳化設計流程圖…………………………17
圖3.1	 Bezier曲線……………………………………………23
圖4.1	 範例一垂直受力懸臂薄板設計範圍…………………26
圖4.2	 範例一第一階段拓樸型態分布圖……………………27
圖4.3	 範例一第二階段拓樸型態分布圖……………………28
圖4.4	 範例一最佳結構外形圖………………………………29
圖4.5	 範例一水平受力懸臂薄板設計範圍…………………31
圖4.6	 範例二第一階段拓樸型態分布圖……………………32
圖4.7	 範例二第二階段拓樸型態分布圖……………………33
圖4.8	 範例二最佳結構外形圖………………………………34
圖4.9	 範例三單負荷兩端固定薄板設計範圍………………36
圖4.10	 範例三第一階段拓樸型態分布圖…………………37
圖4.11	 範例三第二階段拓樸型態分布圖…………………38
圖4.12	 範例三最佳結構外形圖……………………………39
圖4.13	 範例四多負荷兩端固定薄板設計範圍……………41
圖4.14	 範例四第一階段拓樸型態分布圖…………………42
圖4.15	 範例四第二階段拓樸型態分布圖…………………43
圖4.16	 範例四最佳結構外形圖……………………………44
圖4.17	 範例五懸臂中空薄板設計範圍……………………46
圖4.18	 範例五第一階段拓樸型態分布圖…………………47
圖4.19	 範例五第二階段拓樸型態分布圖…………………48
圖4.20	 範例五最佳結構外形圖……………………………49
圖4.21	 範例六腳踏車車架結構設計範圍…………………51
圖4.22	 範例六第一階段拓樸型態分布圖…………………52
圖4.23	 範例六第二階段拓樸型態分布圖…………………53
圖4.24	 範例六最佳結構外形圖……………………………54

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