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研究生:江倚瑄
研究生(外文):Yi-Syuan Jiang
論文名稱:應用多目標基因演算法於測力計拓樸最佳化
論文名稱(外文):Topology Optimization of a Load Cell via a Multi-objective Genetic Algorithm
指導教授:盧中仁
口試委員:伍次寅蘇春熺
口試日期:2016-07-25
學位類別:碩士
校院名稱:國立臺灣大學
系所名稱:機械工程學研究所
學門:工程學門
學類:機械工程學類
論文種類:學術論文
論文出版年:2016
畢業學年度:104
語文別:中文
論文頁數:127
中文關鍵詞:多目標基因演算法NSGA-Ⅱ拓樸最佳化有限元素法古典平板理論
外文關鍵詞:multi-objective genetic algorithmNSGA-Ⅱtopology optimizationfinite element analysisClassical Plate Theory
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量測昆蟲振翅力的測力計需要較高的基頻以及較低的剛性以符合精度要求。本研究的目的是尋找測力計的最佳拓樸結構使其能有高基頻和低剛性。在材料性質固定的前提下,以矩形為設計範圍,利用多目標基因演算法尋找測力計的拓樸最佳化設計。以有限元素法計算所指定的目標函數值。多目標基因演算法則參考NSGA-Ⅱ的非受控排序法和群聚比較法,避免在演算過程中錯失較好的結果,並且維持族群的多樣性。
測力計的邊界條件和外力都對稱於中心線,因此本研究在計算過程中強制測力計結構有同樣的對稱性。另外也計算沒有強制對稱的測力計並比較其和對稱測力計的異同。為了節省計算時間,先以粗網格作全域設計範圍的初步拓樸最佳化,接著以初步最佳化的結果進行局部優化以減少需要計算的元素數量。最後以3D列印製造數個不同的最佳化設計的原型,量測這些原型的特性並和數值模擬的結果相比對。


A load cell for measuring the lift force generated by flapping wings of an insect must have a high fundamental frequency and low stiffness to meet the stringent precision requirements. This thesis aims to design a load cell that can record the waveform of the lift of an insect accurately. Starting from a rectangular shape with specified material properties, a multi-objective genetic algorithm, called NSGA-II, is employed to find the optimal shape of the load cell. A finite element analysis program is developed to determine the values of the objective functions. In NSGA-II, the non-dominated sorting method and crowded-comparison approach are used to increase the genetic diversity as well as keep the elite genes.
Because the boundary conditions and applied force are symmetric with respect to the central line of the load cell, we restrict the outcomes of the optimization program to symmetrical structures. The restriction is then removed. The performance of the asymmetrical optimal results thus generated is compared with that of the performance of the symmetrical ones. In order to reduce the computation time, the optimization is first performed on a coarse mesh for the generation of primitive structures. Then the meshes of some specified areas of a primitive optimal structure are refined. Optimization is performed on the refined meshes to determine the final topology of the load cell. In this way, the computational burden can be largely reduced. Prototypes of several optimal designs are manufactured by 3D printing. Experimental test results for the fundamental frequency and flexibility of these prototypes are compared with those of the numerical simulation.


口試委員審定書 I
致謝 II
摘要 III
ABSTRACT IV
目錄 V
圖目錄 VIII
表目錄 XIII
第一章 緒論 1
1.1 研究動機 1
1.2 參考文獻 2
第二章 理論與方法 5
2.1 拓樸最佳化 7
2.2 多目標基因演算法 8
2.2.1 非受控排序(nondominated sorting)法 9
2.2.2 群聚比較(crowded-comparison)法 13
2.2.3 基因複製、交換、突變 16
2.3 有限元素模型 18
2.4 元素連接性與矩陣奇異性篩選 22
2.5 網格加密和局部優化 25
2.6 對稱結構 30
2.7 演算法流程 31
第三章 結果與討論 33
3.1 有限元素法驗證 33
3.2 對稱結構最佳化設計 35
3.2.1 對稱結構初步最佳化 37
3.2.2 對編號11個體局部優化 41
3.2.3 對編號15個體局部優化 54
3.2.4 對稱結構奇數列最佳化 62
3.2.5 對稱結構偶數列和奇數列結果比較 72
3.3 非對稱結構最佳化設計 73
3.3.1 非對稱結構初步最佳化 75
3.3.2 非對稱結構局部優化 78
3.3.3 非對稱結構奇數列最佳化 86
3.3.4 非對稱結構偶數列和奇數列比較 96
第四章 實驗驗證 98
4.1 實驗設備與方法 98
4.2 實驗結果 101
第五章 結論 106
參考文獻 110
附錄 113
APPENDIX A. 測力計自然頻率模擬結果 113
APPENDIX B. 測力計頻譜圖 114
APPENDIX C. 程式使用步驟 116
APPENDIX D. 矩形平板厚度改為0.2 CM 119
APPENDIX E. 偶數列人工產生第0世代 122
APPENDIX F. 奇數列人工產生第0世代 125



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