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研究生： 吳承祐
Cheng-You Wu
論文名稱： 改良型無限制條件之多目標函數拓樸最佳化方法
An Advanced Unconstrained Multicriterion Topology Optimization Method
指導教授： 林其禹
Chyi-Yeu Lin
口試委員: 黃育熙
Yu-Hsi Huang
史建中
Chien-Jong Shih
學位類別： 碩士
Master
系所名稱： 工程學院 - 機械工程系
Department of Mechanical Engineering
論文出版年： 2015
畢業學年度： 103
語文別： 中文
論文頁數： 93
中文關鍵詞： 結構最佳設計 、拓樸最佳化 、多目標函數 、無限制條件
外文關鍵詞： structural optimization, topology optimization, multicriterion, Unconstrained
相關次數： 點閱：228  下載：6 
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    • 本文提出一個簡單而且穩健之改良型無限制條件之多目標函數拓樸最佳化方法，於實施拓樸最佳化之迭代過程中，以結構順從度及材料重量作為多目標函數，搭配加權係數的組合，除以獲得最小順從度與材料使用率之結構為目標之外，在迭代過程中經由加權係數之適當調整，亦可獲得滿足應力限制值之結構最佳化設計。
    這種創新建構的無限制條件拓樸最佳化問題，除可擴大最佳化過程中可能搜尋的範圍，亦可減少最佳化求解所需之電腦運算次數，提升執行效率外，對不同的初始值相對不敏感，具高度穩健性。
    本文提供三個二維例子，二個懸臂樑及一個L型懸臂樑之結構設計問題，同時進行實例驗證與比較，證實本文提出多目標無限制條件之迭代式加權係數調整技術，具有簡單、穩健且有效率之優點。

    This paper provides a simple but robust algorithm, the Advanced Unconstrained Multicriterion Topology Optimization method (AUMTO), which can obtain the minimum-compliance optimal structure that simultaneously meets the additional stress and/or displacement limits.
    This innovative unconstrained multicriterion function approach can expand the searching domain to increase the probability of getting the global optimum, reduce the computation time, and be robust to the variations of different initial design selections.
    The robustness, simplicity and high efficiency of the AUMTO algorithm are fully demonstrated by the three illustrative problems including two cantilever beams and one L-shaped cantilever beam.

    中文摘要……………………………………………………………I 英文摘要……………………………………………………………II 謝誌…………………………………………………………………III 目錄…………………………………………………………………IV 符號索引……………………………………………………………VII 圖索引………………………………………………………………IX 表索引………………………………………………………………XI 第一章 緒論………………………………………………………1 1.1前言……………………………………………………………1 1.2研究動機………………………………………………………2 1.3文獻回顧………………………………………………………3 1.4論文架構………………………………………………………9 第二章 結構設計最佳化…………………………………………10 2.1尺寸最佳化……………………………………………………10 2.2形狀最佳化……………………………………………………10 2.3拓璞最佳化……………………………………………………11 2.4最佳化問題定義………………………………………………12 2.5最佳化方法……………………………………………………13 2.5.1最佳材料分佈法……………………………………………13 2.5.2進化式結構最佳化…………………………………………19 2.5.3雙方向之進化式結構最佳化………………………………19 2.5.4全應力方法…………………………………………………21 2.5.5迭代式材料限制調整技術…………………………………21 2.5.6最佳化方法小結……………………………………………22 第三章 多目標函數拓樸最佳化方法……………………………24 3.1無限制條件之多目標函數拓樸最佳化方法…………………24 3.2改良型無限制條件之多目標函數拓樸最佳化方法…………27 3.3處罰函數拓樸最佳化…………………………………………31 3.4二值結構門檻值技術…………………………………………33 第四章 實例驗證…………………………………………………35 4.1懸臂樑(A)……………………………………………………35 4.1.1應力限制750 psi之分析…………………………………36 4.1.2應力限制1,000 psi之分析………………………………41 4.2懸臂樑(B)……………………………………………………46 4.2.1應力限制750 psi之分析…………………………………46 4.2.2應力限制1,000 psi之分析………………………………51 4.3 L型懸臂樑……………………………………………………55 4.3.1應力限制600 MPa 之分析…………………………………56 4.3.2應力限制800 MPa 之分析…………………………………60 4.4不同初始設計對最佳化結果之差異分析……………………64 4.4.1懸臂樑(B)應力限制750 psi之差異分析…………………64 4.4.2 L型懸臂樑應力限制600 MPa 之差異分析………………67 第五章 結論與展望………………………………………………71 5.1結論……………………………………………………………71 5.2展望……………………………………………………………72 參考文獻…………………………………………………………73

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