臺灣博碩士論文加值系統

優良的測力計需要較高的基頻以及較大的撓性以符合精度要求，這兩個互相衝突的要求很難同時滿足。本研究的目的是尋找適當的拓樸結構使得測力計能滿足這兩個設計規範。本研究設定測力計為桿件組成的平面構架，桿件的節點和截面尺寸為設計變數，目標函數為構架的基頻和自由端的面外靜力位移。在材料性質固定的前提下，在設計空間中，利用多目標粒子群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。多目標粒子群演算法則參考Coello提出MOPSO[1]，以網格劃分、指定適應性與輪盤選擇，維持粒子的多樣性。本研究嘗試數種不同的構架建構方式，發覺對稱於中心線的基部斜撐補強構架有最好的效能。首先固定截面尺寸，改變節點的位置得到最佳的拓樸形狀；接著再將所得的構架細分，藉由改變各段截面尺寸更進一步優化。最後將所得的最佳設計和前人的設計相比較。

A good load cell should have a wide band-width and large flexibility to meet the demand of high resolution. It’s very difficult to satisfy these two conflicting demands. This research aims to find a proper design, thorough topology optimization, of a load cell possessing both proper band-width and flexibility. The load cell studied in this thesis is a planar frame. The position of every joint and cross-section area of each rod are used as design variables. The objective functions are the fundamental frequency and the static deflection at the free end of the structure. The Pareto solutions in the design space are located by a multi-objective particle swarm optimization (MOPSO) algorithm. The values of the objective functions are determined using an in-house finite element method code. The MOPSO algorithm proposed by Coello [1], which introduces a mutation operator and a roulette-wheel selection scheme for maintaining the diversity of the particles, is employed to find the optimal designs. In this thesis, several schemes for constructing the frame of the load cell are tested. The symmetrical structures with angle braces have the best performance. In order to find proper designs in a feasible time, we first determine the primary frames under the restriction that the every rod has the same cross-sectional area. Then a primary design in the Pareto set is chosen and further optimized. In the final optimization process, the cross-sectional dimensions of each rod as well as the coordinates of each joint are used as design variables. The final optimal designs are compared with previous designs obtained using different topological optimization algorithms.

目錄
口試委員審定書 i
致謝 ii
摘要 iii
Abstract iv
目錄 v
圖目錄 vii
表目錄 xi
第一章 緒論 1
1.1 研究動機 1
1.2 文獻回顧 2
第二章 理論與方法 5
2.1 問題描述 5
2.2 有限元素模型 7
2.2.1 桿元素 8
2.2.2 樑元素 9
2.2.3 軸元素 11
2.2.4 元素組合 12
2.2.5 座標轉換 15
2.3 粒子群演算法 16
2.4 邊界條件 18
2.5 多目標粒子群演算法 20
2.5.1 決定Global Best 與Personal Best 21
2.5.2 更新Repository 23
2.5.3 突變 24
2.6 拓樸最佳化 26
2.6.1 平面構架結構 27
2.6.2 對稱V形結構 28
2.6.3 兩側支撐之懸臂樑結構 29
2.7 局部最佳化 30
第三章 結果與討論 32
3.1 驗證多目標函數粒子群演算法及參數討論 32
3.1.1 測試函數 32
3.1.2 參數影響討論 35
3.2 驗證有限元素程式 40
3.3 初步最佳化 42
3.3.1 平面構架 43
3.3.2 對稱V形結構 52
3.3.3 兩側支撐的懸臂樑結構 55
3.4 局部最佳化 59
3.4.1 最大、最小厚度 59
3.4.2 最大分割長度 74
3.5 數據比較 82
第四章 結論 86
參考文獻 88

參考文獻
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