博碩士論文 91322022 詳細資訊




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姓名 藍志浩(Chih-Hao Lan)  查詢紙本館藏   畢業系所 土木工程學系
論文名稱 考慮動態反應束制及關連性離散變數之結構最佳化設計
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摘要(中) 摘 要
本文主要針對含關連性離散變數、靜態和動態反應束制之結構輕量化設計問題,提出三種以離散拉格朗日法(Discrete Lagrangian Method, DLM)為基礎的搜尋策略,其中靜態反應束制包括位移、應力、挫屈應力及長細比束制,動態反應束制包括頻率及頻率反應振幅的束制。研究中,首先針對DLM中的拉格朗日乘子的更新公式提出修正,避免每次迭代可能必須反覆更新拉格朗日乘子的缺失。接著探討DLM應用於關連性離散變數以及動態反應束制條件下所遭遇的困難,並對此提出動態擴大鄰點搜尋及改善震盪現象策略。最後,為了確保DLM的求解品質,本研究亦提出一種藉由折減拉格朗日乘子啟動再搜尋的方法,使DLM有機會跳脫一個局部最佳解區域搜尋另一局部最佳解。數個結構輕量化設計問題將分別用來探討其適用性和影響求解品質與效率的相關參數,並藉由設計結果之比較,來探討本文所發展之三種搜尋法的優缺點。
摘要(英) Abstract
This research studies the minimum weight design of structures with linked discrete variables, static and dynamic response constraints. Three discrete Lagrangian based searching procedures are proposed in this report. The static response constraints include displacement, stress, buckling stress and slenderness ratio. The dynamic response constraints include frequency and frequency response amplitude. In this research, an update formula for the Lagrange multiplies is developed first. The difficulties in applying the DLM to solve for problems containing linked discrete variables and dynamic response constraints are then discussed. To resolve the difficulties, a dynamic extending neighborhood technique and an improving strategy for eliminating fluctuated searching trajectory are proposed. Finally, a restarting procedure for the DLM by scaling down the values of Lagrange multipliers is also proposed to help the search escaping from a local minimum to search for another one. The feasibility of three procedures is validated by several design examples. The results from comparative studies of the DLM against other discrete optimization algorithms are reported to show the solution quality of the proposed DLM procedures. The advantages and drawbacks of the three DLM algorithms are also discussed.
關鍵字(中) ★ 長細比束制
★ 關連性離散變數
★ 輕量化設計
★ 頻率反應振幅束制
★ 位移束制
★ 應力束制
★ 挫屈應力束制
★ 頻率束制
★ 離散拉格朗日法
關鍵字(英) ★ buckling stress constraints
★ linked discrete variable
★ slenderness ratio constraints
★ frequency constraints
★ minimum weight design
★ frequency response amplitude constraints
★ discrete Lagrangian method
★ stress constraints
★ displacement constraints
論文目次 目錄
中文摘要 I
英文摘要 III
目錄 V
表目錄 XI
圖目錄 XVII
第一章 緒論 1
1.1 研究動機與目的 1
1.2 文獻回顧 3
1.2.1 離散最佳化方法 3
1.2.2 動態反應束制 5
1.3 研究方法與內容 6
1.3.1 動態反應束制條件 7
1.3.2 拉格朗日乘子放大倍數 7
1.3.3 動態擴大鄰點搜尋策略 8
1.3.4 DLM演算法震盪現象之改善策略 8
1.3.5 DLM的再搜尋策略 8
第二章 DLM演算法 11
2.1 離散最佳化問題之數學模式 11
2.2 DLM理論回顧 12
2.2.1 加權離散拉格朗日函數 12
2.2.2 鄰點 12
2.2.3 離散梯度 13
2.2.4 離散鞍點 14
2.2.5 轉換函數 15
2.2.6 收斂準則與一階搜尋公式 15
2.2.7 一階搜尋公式之修改 17
2.2.8 DLM演算程序 20
2.3 合向量策略 22
2.4 動態擴大鄰點搜尋策略 24
2.5 動態擴大鄰點搜尋策略之數值算例 27
2.5.1 22桿平面桁架 27
2.5.2 10桿平面桁架(I) 30
2.6 DLM演算法震盪現象之改善策略 33
2.7 震盪現象改善策略之數值算例 36
2.7.1 3桿平面桁架 36
2.8 討論 40
第三章 設計程序 41
3.1 引言 41
3.2 固定鄰點之搜尋程序 42
3.3 動態擴大鄰點與改善震盪現象之搜尋程序 44
3.4 DLM的再搜尋程序 44
3.4.1 測試算例 45
3.4.1.1 25桿空間桁架(I) 48
3.4.2 討論 60
第四章 數值算例與參數研究 65
4.1 目標函數與束制條件 65
4.2 測試流程介紹 69
4.3 DLM-1與DLM-2之參數研究 70
4.3.1 10桿平面桁架(I) 71
4.3.1.1 DLM-1參數研究 71
4.3.1.2 DLM-2參數研究 75
4.3.1.3 結果比較 80
4.3.2 10桿平面桁架(II) 82
4.3.2.1 DLM-1參數研究 84
4.3.2.2 DLM-2參數研究 93
4.3.2.3 結果比較 101
4.3.3 10桿平面桁架(III) 105
4.3.3.1 DLM-1參數研究 106
4.3.3.2 DLM-2參數研究 110
4.3.3.3 結果比較 114
4.4 其他算例設計結果 116
4.4.1 25桿空間桁架(I) 116
4.4.2 25桿空間桁架(II) 120
4.4.3 25桿空間桁架(III) 123
4.4.4 25桿空間桁架(IV) 133
4.4.5 25桿空間桁架(V) 141
4.4.6 160桿空間桁架 143
4.4.7 200桿平面桁架(I) 147
4.4.8 200桿平面桁架(II) 151
4.4.9 單跨八層平面構架 154
4.4.10 單跨雙層平面構架 158
4.4.11 單跨七層平面構架 172
第五章 結論與建議 179
5.1 結論與建議 179
5.2 未來研究方向 182
參考文獻 183
附錄A 22桿平面桁架細部資料及設計結果 191
A.1 細部設計資料 191
A.2 DLM設計結果 192
附錄B 10桿平面桁架(I)細部資料及設計結果 193
B.1 細部設計資料 193
B.2 DLM設計結果(I) 195
B.3 DLM設計結果(II) 196
附錄C 3桿平面桁架細部資料及設計結果 197
C.1 細部設計資料 197
C.2 DLM設計結果 198
附錄D 25桿空間桁架(I)細部資料及設計結果 199
D.1 細部設計資料 199
D.2 DLM設計結果(I) 201
D.3 DLM設計結果(II) 203
附錄E 10桿平面桁架(II)細部資料及設計結果 205
E.1 細部設計資料 205
E.2 DLM設計結果 206
附錄F 10桿平面桁架(III)細部資料及設計結果 209
F.1 細部設計資料 209
F.2 DLM設計結果 210
附錄G 25桿空間桁架(II)細部資料及設計結果 211
G.1 細部設計資料 211
G.2 DLM設計結果 212
附錄H 25桿空間桁架(III)細部資料及設計結果 213
H.1 細部設計資料 213
H.2 DLM設計結果 215
附錄I 25桿空間桁架(IV)細部資料及設計結果 219
I.1 細部設計資料 219
I.2 DLM設計結果 221
附錄J 25桿空間桁架(V)細部資料及設計結果 225
J.1 細部設計資料 225
J.2 DLM設計結果 226
附錄K 160桿空間桁架細部資料及設計結果 227
K.1 細部設計資料 227
K.2 DLM設計結果 231
附錄L 200桿平面桁架(I)細部資料及設計結果 239
L.1 細部設計資料 239
L.2 DLM設計結果 242
附錄M 200桿平面桁架(II)細部資料及設計結果 247
M.1 細部設計資料 247
M.2 DLM設計結果 250
附錄N 單跨八層平面構架細部資料及設計結果 255
N.1 細部設計資料 255
N.2 DLM設計結果 260
附錄O 單跨雙層平面構架細部資料及設計結果 261
O.1 細部設計資料 261
O.2 DLM設計結果 265
附錄P 單跨七層平面構架細部資料及設計結果 267
P.1 細部設計資料 267
P.2 DLM設計結果 270
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指導教授 莊德興(Der-Shih Juang) 審核日期 2005-7-20
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