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研究生:林志豐
研究生(外文):Lin, Chih Fong
論文名稱:機械結構之有限元素法拓樸最佳化設計與分析
論文名稱(外文):FEM Based Topological Optimization for Mechanical Structural Design and Analysis
指導教授:史建中
指導教授(外文):C.J.Shih
學位類別:碩士
校院名稱:淡江大學
系所名稱:機械工程學系
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:2001
畢業學年度:89
語文別:中文
論文頁數:88
中文關鍵詞:廣義霍普菲爾神經網路最佳化拓樸最佳化尺寸最佳化有限元素法
外文關鍵詞:Generalized Hopfield Neural NetworkTopological OptimizationSize OptimizationFinite element method
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本文的內容主要分為尺寸最佳化設計和拓樸最佳化設計二個部份,在尺寸最佳化方面,提出廣義霍普菲爾神經網路最佳化和可行方向法最佳化等兩種方法來結合有限元素分析。在廣義霍普菲爾網路應用方面,網路的系統能量必朝向平衡狀態前進,即最小化系統之能量。只要將最佳化問題之目標函數及限制條件與網路的能量函數間找出一個合適的對應關係,則可將原最佳化設計問題轉換成一般的聯立常微分方程式,設計者無需習用最佳化特別數值方法,僅需解聯立常微分方程式即可。在可行方向法結合有限元素分析方面,則是以一階泰勒展開法求得限制函數的近似函數,而泰勒展開法中所需的值則由有限元素分析提供。在拓樸最佳化方面,分別對結構強度和撓性作最佳化設計研究。以結構強度為設計考量方面則是求得最能抵抗外力的結構形態,再引入結構撓性,則可設計出既能抵抗外力,又兼具在指定輸出位置上能夠表現出設計者欲求的位移方向。本文是以材料分配法,將正常化密度當做為拓樸最佳化的設計變數,以總體積使用率做為限制函數,對固定設計領域實行拓樸最佳化設計,求得滿足載力與拘束條件下的最佳結構。本文亦建立一般靜平衡受力之固體元素拓樸結構設計及撓性放大機構之設計,桁架與板狀物為本文之兩種解析例題,屬於多目標最佳化設計之題型,結果顯示,其指定位置之放大效果亦已達到。根據本文之基礎,未來預期將拓樸最佳化與尺寸最佳化作結合,再探討平滑邊界的修飾最佳化策略,進一步應用在實際所需之撓性放大機構上。
This paper develop the size optimization method using Generalized Hopfield Neural Network (GHN) and the topological optimization method using material distribution. The feature of GHN method shows that the original optimization problem can transform to a set of ordinary differential problem and it does not need the specialized optimization algorithm. However, the large scale problems have to be applied so that the algorithm needs to be further modified.Truss and solid elements have been adopted as the target to develop topological optimization. The material density is design variables and the limiting volume is the general constraint. A typical flexible structure and printer head have been applied to examine the method. The strategies developed in this study can be the basis for further topological optimum design.
中 文 摘 要..............................................................................Ⅰ
英 文 摘 要..............................................................................Ⅲ
表 目 錄VII
圖 目 錄VIII
符號說明.......................................................................................... V
第一章 緒論1
1-1 動機與目的1
1-2 文獻回顧3
1-3研究方法與步驟7
第二章 結合有限元素法的最佳結構設計9
2-1霍普菲爾神經網路最佳化9
2-1-1 GHN結合懲罰函數法之最佳化11
2-1-2結合有限元素軟體的最佳化設計13
2-2可行方向法的最佳化設計15
2-3 設計例題18
第三章 拓樸最佳化設計與分析32
3-1 拓樸最佳化設計原理32
3-2 拓樸最佳化32
3-3設計例題41
第四章 撓性放大機構之拓樸最佳化設計63
4-1 撓性放大機構之分析63
4-2 撓性放大機構之拓樸最佳化設計67
4-3撓性桁架機構設計72
4-4點陣式印字頭的放大機構之拓樸設計78
第五章 結論84
參考文獻85
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[20] Lau Gih Keong, Du Hejun, Lim Mong King, "Systematic Design of Displacement-amplifying Mechanisms for Piezoelectric Stacked Actuators Using Topology Optimization", School of Mechanical and Production Engineering, Nanyang Technological University Nanyang Avenue, Singapore, 2000.
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