移動漸近線法的原理是將一個函數利用倒數近似法加上中介變數轉換為近似原問題的函數。因移動漸近線法可以處理各種設計參數並因應各式目標函數與限制條件，本研究應用移動漸近線法之特性得到函數之近似式並利用對偶法對最佳化問題求解。對偶法為將原本的最小化問題以與之有關的最大化對偶函數取代。也就是將原設計問題轉換為凸性且為可分離的子問題，這有助於結構最佳化問題能夠快速地求解。因此本研究應用移動漸近線法得到結構行為之近似函數，再採用對偶法執行結構之最佳化設計。
　　數值分析中將對各種結構作分析，分別以結構輕量化設計或提高結構之第一自然振動頻率為目的。本研究以ANSYS有限元素分析軟體中的APDL語法與FORTRAN程式結合成一系統程式，並使用有限差分法計算靈敏度以獲得執行移動漸近線法所需之數據。範例中證明移動漸近線法於結構之最佳化設計上可以得到比其他文獻更好的結果。

Method of Moving Asymptotes (MMA) is used by reciprocal approximate and moving asymptotes to approximate a original function. Because MMA can deal with various kinds of design parameters and handle all kinds of objective and constraint functions, this study applies the characteristics of MMA to obtain the approximation function and then uses dual method to solve the problem. Dual method is that the original minimization problem is replaced by maximization of dual function relating to it. That is, the dual method was used to solve design problem by a subproblem, which is convex and separable. Therefore, this study applies MMA to get the approximate function of structural behavior, and then adopts dual method to obtain the optimum design of structures.
　　Optimum design of different structures will be analyzed in Numerical examples. A systematic program which combined APDL with FORTRAN to calculate sensitivity and necessary data for MMA was developed in this study. Optimum design of structures by MMA can obtain better results than other references was proved in this study.

中文摘要................................................I
英文摘要..............................................III
目錄...................................................IV
圖目錄.................................................VI
表目錄................................................VII
第一章　緒論............................................1
1.1 研究動機............................................1
1.2 文獻回顧............................................2
1.3 本文架構............................................4
第二章　移動漸近線法理論................................5
第三章　設計最佳化.....................................10
3.1 對偶法.............................................10
3.2 靈敏度分析.........................................12
第四章　數值分析與討論.................................14
4.1 範例一：懸臂壓電單層金屬薄板結構之輕量化設計.......16
4.2 範例二：懸臂壓電雙層複材薄板結構之輕量化設計.......20
4.3 範例三：壓電複合梯形斜板結構之自然頻率最大化設計...23
4.4 範例四：懸臂壓電多層複材薄板結構之輕量化設計.......26
4.5 範例五：十桿件桁架結構最佳化設計...................29
4.6 範例六：直昇機尾桁結構最佳化設計...................31
第五章　結論...........................................33
參考文獻...............................................34
附錄一.................................................61
附錄二.................................................64

圖目錄
圖一 執行流程………………………………………………………37
圖二 範例一 懸臂壓電單層金屬薄板結構外型圖………………38
圖三 範例一 懸臂壓電單層金屬薄板結構之收斂歷程圖………39
圖四 範例二 懸臂壓電雙層複材薄板結構外型圖………………40
圖五 範例二 懸臂壓電雙層複材薄板結構之收斂歷程圖………41
圖六 範例三 壓電複合梯形斜板結構外型圖……………………42
圖七 範例三 壓電複合梯形斜板結構之收斂歷程圖……………43
圖八 範例四 懸臂壓電多層複材薄板結構外型圖………………44
圖九 範例四 懸臂壓電多層複材薄板結構之收斂歷程圖………45
圖十 範例五 十桿件桁架結構外型圖……………………………46
圖十一 範例 五十桿件桁架結構之收斂歷程圖…………………47
圖十二 範例 六直昇機尾桁結構外型圖…………………………48
圖十三 範例 六直昇機尾桁結構之收斂歷程圖…………………49
VII
表目錄
表一 範例一之迭代過程……………………………………………50
表二 範例一初始值與最佳值之比較………………………………51
表三 範例二之迭代過程……………………………………………52
表四 範例二初始值與最佳值之比較………………………………53
表五 範例三之迭代過程……………………………………………54
表六 範例三初始值與最佳值之比較………………………………55
表七 範例四之迭代過程……………………………………………56
表八 範例四初始值與最佳值之比較………………………………57
表九 範例五初始值與最佳值之比較………………………………58
表十 直昇機尾桁之桿件分類………………………………………59
表十一 範例六初始值與最佳值之比較……………………………60

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