臺灣博碩士論文加值系統

本研究提出一個全新的拓樸最佳化(Topology Optimization)架構，稱為基於MMC(Moving Morphable Component)方法之混合式拓樸最佳化，用於設計撓性機構(Compliant Mechanism)。此架構以MMC拓樸最佳化為基礎，融合了啟發式演算法(Metaheuristic Algorithm)和梯度式演算法(Gradient-based Algorithm)。由於撓性機構的運動通常涉及大形變，演算法使用非線性有限元素分析以獲取準確的結構響應。混合式拓樸最佳化分為三個階段：啟發式搜索(Metaheuristic Search)、部件擴增(Component Augmentation)和梯度式搜索(Gradient-based Search)。首先，啟發式搜索利用極少量的B樣條尋找機構骨幹。接著，部件擴增將機構骨幹轉換為梯度式搜索的初始猜值。最後，梯度式搜索找出機構的最佳拓樸。本研究透過三個設計問題展示混合式拓樸最佳化的效用。此外，本研究也針對混合式拓樸最佳化的效能做進一步的分析，包括運算加速、對特定參數的敏感度和初始猜值的影響。本研究提出的架構不僅能消除拓樸最佳化對人為設定初始猜值的依賴性，還能夠高效率地運行啟發式搜索。

This study proposes a novel topology optimization framework called MMC (Moving Morphable Component)-based Hybrid Topology Optimization for compliant mechanism design. Based on MMC Topology Optimization, this framework incorporates both metaheuristic and gradient-based algorithms into the optimization process. Due to the fact that compliant mechanisms usually undergo large deformation, the algorithms employ nonlinear finite element analysis to obtain accurate structure responses. The Hybrid Topology Optimization consists of three main stages: Metaheuristic Search, Component Augmentation, and Gradient-Based Search. In the first stage, a small number of splines are used to search for the backbone structure of the mechanism. Then, in the second stage, the backbone structure is converted into an initial guess for the next stage. Finally, the algorithm identifies the optimized topology in the third stage. This study demonstrates the effectiveness of the proposed framework through three design problems. Furthermore, additional analyses are conducted to evaluate the framework’s performance, including computational acceleration, sensitivity to specific parameters, and the influence of initial guesses. The proposed framework not only eliminates the dependency on initial guesses decided by designers in conventional topology optimization methods but also enables efficient execution of the metaheuristic search.

目錄
致謝辭 i
口試委員會審定書 ii
摘要 iii
Abstract iv
圖目錄 vii
表目錄 x
符號說明 xi
第一章 緒論 1
1.1 撓性機構 1
1.2 撓性機構的設計方法 2
1.3 研究動機與目標 3
1.4 論文架構 3
第二章 文獻回顧 4
2.1 結構最佳化 4
2.1.1 尺寸最佳化 6
2.1.2 形狀最佳化 6
2.1.3 拓樸最佳化 7
2.2 MMC拓樸最佳化 9
2.3 使用啟發式演算法之拓樸最佳化 11
第三章 基於MMC方法之混合式拓樸最佳化 13
3.1 拓樸表示式 13
3.1.1 構成單元 14
3.1.2 水平集函數 16
3.1.3 階躍函數 18
3.2 有限元素分析 20
3.2.1 數值分析模型 20
3.2.2 非線性有限元素分析 21
3.2.3 超彈性材料添加法 22
3.2.4 APDL 副程式 24
3.3 混合式拓樸最佳化的核心概念 24
3.4 階段一：啟發式搜索 26
3.4.1 基因演算法 27
3.5 階段二：部件擴增 28
3.5.1 結點植入 29
3.5.2 樣條增生 30
3.6 階段三：梯度式搜索 31
3.6.1 敏感度分析 33
3.6.2 MMA 35
3.6.3 收斂條件 37
第四章 實例應用 38
4.1 位移反向器 38
4.2 撓性夾爪 45
4.3 等力夾爪 50
第五章 混合式拓樸最佳化性能探討 60
5.1 使用平行處理實現運算加速 60
5.2 樣條增生對最佳化結果的影響 63
5.3 啟發式搜索的重要性 66
5.4 相關文獻整理 68
第六章 結論與未來展望 70
6.1 結論 70
6.2 未來展望 71
參考文獻 73

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