臺灣博碩士論文加值系統

本文研究限制條件的處理對於結構最佳化設計之遺傳演算法的影響。首先，提出一種新型式不同懲罰強度的外懲罰函數法。研究此種懲罰函數法的收斂特性並與可適性懲罰函數法與非固定式懲罰函數法相比較，進而提出一個可動態調整懲罰程度的評估程序。此評估程序能依據族群對限制條件的違反個數與違反程度來決定所要使用的懲罰程度。最後，本文發展出一套結合遺傳演算法與ANSYS有限元素法分析軟體的整合程式。利用此程式，可對一些測試的範例及實際工程結構設計問題進行分析。從分析結果可知，利用提出的評估程序所決定的動態懲罰程度，對於大部分的分析範例皆能得到一個十分滿意的收斂結果。

This thesis studies the effect of constraint handling for structural optimization with genetic algorithms. First, a new form of the traditional exterior penalty function method with different penalty levels are introduced. The convergent characteristics of this new penalty function are investigated and compared with characteristics of the adaptive penalty function method and non-stationary penalty function method. Then, an evaluation process that can dynamically adjust the level of the penalty term is provided. This evaluation process determines the penalty level according to the violated constraint numbers and the level of constraint violation in the population. Finally, an integrated program combining genetic search algorithms and the ANSYS finite element software is developed. With this developed program, design processes of some test examples and practical structural design problems are given. From these results, it shows that the dynamic penalty level determined by the proposed evaluation process will give quite satisfactory convergent result for most cases.

第一章 緒論1
1.1簡介1
1.2文獻回顧2
1.3研究的目的與動機4
1.4研究的策略與方法5
1.5論文大綱介紹6
第二章 結構最佳化設計理論8
2.1結構最佳化設計的問題形式8
2.2有限元素法與機械結構分析12
2.3數值最佳化方法─非線性規劃法19
2.4遺傳演算法理論23
2.4.1遺傳演算法24
2.4.2遺傳演算法之理論基礎27
2.4.3遺傳演算法的運算子30
2.4.4遺傳演算法於最佳化設計35
第三章 遺傳演算法在最佳設計的應用37
3.1目標函數與設計變數的處理37
3.1.1遺傳演算法的目標函數37
3.1.2遺傳演算法的設計變數39
3.2遺傳演算法限制條件的處理40
3.2.1內懲罰函數法41
3.2.2外懲罰函數法42
3.2.3可適性懲罰函數法44
3.2.4非固定式懲罰函數法48
3.3遺傳演算法運算子的處理49
3.3.1個體數的給定49
3.3.2選擇法的給定49
3.3.3交配與突變運算子的處理52
3.4懲罰函數法與選擇壓力對最佳化收斂的關係53
3.5程式的流程與規劃55
第四章 最佳化設計─小型結構實例60
4.1三桿結構最佳化設計61
4.2十桿結構最佳化設計63
4.3二十五桿結構最佳化設計66
4.4薄壁懸臂軸結構最佳化設計69
4.5雙桿格架結構最佳化設計73
4.6數值函數實例76
4.6.1數值函數範例一76
4.6.2數值函數範例二79
4.7結果討論82
第五章 最佳化設計─大型結構實例84
5.1線切割放電加工機結構最佳化設計84
5.1.1線切割放電加工機靜態特性最佳化設計85
5.1.2線切割放電加工機動態特性最佳化設計89
5.2奈米級三次元量測儀的結構最佳化分析91
5.3結果討論95
第六章 結論與建議96
6.1結論與研究成果96
6.2建議與未來發展方向97
參考文獻98
附錄102

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