應用多領域最佳化方法與拓樸最佳化之研究 詹天佐、紀華偉
E-mail: [email protected]
摘 要
拓樸最佳化最大問題主要在於計算時間冗長，計算資源耗費龐大。目前有關拓樸最佳化設計的研究，大部分使用單一系統
，亦即在一個最佳化問題中同時處理所有變數。 本文利用多領域最佳化方法，將單一結構系統分解成若干次系統，進行同 步最佳化設計。各次系統最佳化之協調機制藉由分配各次系統滿足其他系統的限制條件之責任達成。結果顯示，本文所提 出的同步次系統最佳化方法，可以獲得良好拓樸設計，提供拓樸最佳化平行運算的可能性，有效減少設計時間。
關鍵詞 : 多領域最佳化 ; 非層次分解法 ; 拓樸最佳化
目錄
封面內頁 簽名頁 授權書..………iii 中文摘要………
………v 英文摘要………vi 誌謝………
………vii 目錄………viii 圖目錄………
………x 表目錄………xiii 第 一章 緒論………1 1.1前言………
……1 1.2研究目的………2 1.3文獻回顧………
………2 1.4論文大綱………6 第二章 研究方法與理論推導………
………8 2.1拓樸最佳化方法………8 2.1.1均質法………
………10 2.1.2密度函數法………11 2.1.3模擬生物成長方法………
………13 2.2最佳化演算法………14 2.3目標函數與制限條件………
………16 2.4結構順從度對設計變數靈敏度分析………17 2.5多領域最佳化………
………20 2.5.1全域靈敏度公式法………20 2.5.2同步次系統最佳化方 法………23 2.5.3責任分配機制………27 第三章 應用軟體與程式設 計流程………30 3.1 ANSYS有限元分析軟體………30 3.1.1 ANSYS之 分析檔………32 3.1.2 ANSYS分析檔指令………34 3.2連續線 性規劃法應用於多領域最佳化設計問題………35 3.2.1邊界限制………36 3.3最佳化 程式流程.………37 第四章 實例分析與討論………39 4.1範例一
：二維懸臂樑結構之多領域拓樸最佳化………40 4.2 範例二：下方受單一負荷之簡支撐平板………49 4.3 範例三：下 方受多重負荷之簡支撐平板………56 4.4 範例四：腳踏車車架結構問題………62 4.5 範例五：非對稱負 荷懸臂樑結構………70 第五章 結論與未來發展………77 參考文獻………
………79 附錄A ANSYS有限元分析樣本檔範例………83 參考文獻
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