以力法為分析工具之結構離散輕量化設計效率的探討

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林俊榮(Jing-Long Lin) 查詢紙本館藏

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土木工程學系

論文名稱

以力法為分析工具之結構離散輕量化設計效率的探討
(On the Computational Efficiency of Using Force Method in Discrete Structural Optimization)

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摘要(中)

本文主要是以矩陣力法配合離散拉格朗日法(Discrete Lagrangian Method, DLM)進行離散結構最佳化設計，並與位移法比較設計所需時間，藉以探討其對最佳化整體計算效率改善情況。一般的最佳化設計研究多數以位移法分析為主，位移法分析時所需求解的方程式數量是系統自由度的數量，而力法所需要求解的方程式數量則是系統贅餘度數，因此當超靜定結構的贅餘度數小於系統自由度數量的情況下，其所需要的分析時間會低於位移法所需的時間；此外，力法分析中的力平衡矩陣不會變更，不需重覆找出對應於贅力的平衡矩陣和基元靜定結構的平衡矩陣，因此應用力法於需要反覆求解之的最佳化問題時，比位移法更具優勢。DLM為一種鄰點搜尋法，其具備非常強健之搜尋能力，由過去的研究結果顯示此法求解能力極佳，本文同時考慮合向量移動策略來改善DLM求解大型結構的效能，並能加快DLM的求解效率。本文最後將以數個傳統結構離散輕量化設計例來展示以力法作為結構分析工具的優點，並比較力法和位移法所需的計算時間。

摘要(英)

In this paper, the discrete structural optimization problem solved by using discrete Lagrangian method (DLM) in conjunction with force method of analysis is presented. DLM belongs to the neighborhood searching methods. In the past, the analysis module built in the DLM algorithm is based on the displacement approach. To improve the searching efficiency of the method, the force method of analysis will be considered in this study. Most structural optimization algorithms published in the literature were developed based on the displacement method of analysis which is incorporated inside the optimization routine. In the displacement method, the number of equations needed to be solved is the number of degrees of freedom for the system whereas that for the force method is the number of redundant forces. If the number of degrees of freedom is greater than for the number of redundant in a structural system, the displacement method requires much more computer time than the force method does. Furthermore, the equilibrium matrix in the force method does not change in the redesign process making this method attractive and efficient. The DLM (Discrete Lagrangian Method) is an adaptation of usual Lagrange multiplier method to structural optimization problems using available sections have shown that it is robust and validate. To enhance the efficiency and robustness of the search for optimal larger structural design problems, an enhancing strategy for accelerating the search speed of the DLM. The advantage of using force method and the efficiency improvement of the force method will be discussed for discrete sizing optimization problems of structures.

關鍵字(中)

★ 結構輕量化設計
★ 力法

關鍵字(英)

★ Force Method
★ Structural Optimization

論文目次

中文摘要 ....................................... i
英文摘要 ....................................... iii
致謝 ........................................... v
目錄 ........................................... vii
表目錄 ......................................... xiii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　力法 .................................... 5
1.2.2　離散拉格朗日演法......................... 7
1.3　研究方法與內容 ............................ 8
第二章　矩陣力法分析 ........................... 10
2.1　前言 ...................................... 10
2.2　矩陣力法分析程序 .......................... 11
2.2.1　建立內外力平衡矩陣[B] ................... 12
2.2.2　利用[B]矩陣選取贅力 ..................... 24
2.2.3　計算力轉換矩陣 .......................... 26
2.2.4　求解贅力 ................................ 27
2.2.5　計算桿件內力和節點自由度位移 ............ 29
2.3　空間構架算例 .............................. 30
第三章　DLM演算法 .............................. 44
3.1　離散最佳化問題之數學模式 .................. 44
3.2　DLM理論回顧 ............................... 45
3.2.1　加權離散拉格朗日函數 .................... 45
3.2.2　鄰點 .................................... 46
3.2.3　離散梯度 ................................ 47
3.2.4　離散鞍點 ................................ 48
3.2.5　收斂準則與一階搜尋公式 .................. 49
3.2.6　合向量移動策略 .......................... 53
3.2.7　DLM搜尋程序 ............................. 56
第四章　數值計算例 ............................. 59
4.1　結構離散最佳化問題之目標函數與束制條件 .... 60
4.2　數值算例設計結果 .......................... 62
4.2.1　10桿平面桁架............................. 63
4.2.2　25桿空間桁架 ............................ 67
4.2.3　22桿平面桁架 ............................
4.2.4　36桿空間桁架 ............................ 75
4.2.5　72桿空間桁架 ............................ 78
4.2.6　132桿空間桁架 ........................... 80
4.2.7　160桿空間桁架 ........................... 84
4.2.8　200桿平面桁架 ........................... 88
4.2.9　單跨單層平面構架 ........................ 93
4.2.10 單跨雙層平面構架 ........................ 96
4.2.11 雙跨五層平面構架 ........................ 98
4.2.12 單跨八層平面構架 ........................ 101
第五章　結論與建議 ............................. 105
5.1　結論 ...................................... 105
5.2　未來研究方向 .............................. 106
參考文獻 ....................................... 108
附錄A　10桿平面桁架細部資料及設計結果 .......... 116
A.1　細部設計資料 .............................. 116
A.2　DLM-f設計結果 ............................. 117
附錄B　25桿空間桁架細部資料及設計結果 .......... 118
B.1　細部設計資料 .............................. 118
B.2　DLM-f設計結果 ............................. 120
附錄C　22桿平面桁架細部資料及設計結果 .......... 122
C.1　細部設計資料 .............................. 122
C.2　DLM-f設計結果 ............................. 124
附錄D　36桿空間桁架細部資料及設計結果 .......... 126
D.1　細部設計資料 .............................. 126
D.2　DLM-f設計結果 ............................. 128
附錄E　72桿空間桁架細部資料及設計結果 .......... 130
E.1　細部設計資料 .............................. 130
E.2　DLM-f設計結果 ............................. 132
附錄F　132桿穹頂桁架細部資料及設計結果 ......... 136
F.1　細部設計資料 .............................. 136
F.2　DLM-f設計結果 ............................. 140
附錄G　160桿空間桁架細部資料及設計結果 ......... 150
G.1　細部設計資料 .............................. 150
G.2　DLM-f設計結果 ............................. 155
附錄H　200桿平面桁架細部資料及設計結果 ......... 167
H.1　細部設計資料 .............................. 167
H.2　DLM-f設計結果 ............................. 170
附錄I　單跨單層平面構架細部資料及設計結果 ...... 178
I.1　細部設計資料 .............................. 178
I.2　DLM-f設計結果 ............................. 179
附錄J　單跨雙層平面構架細部資料及設計結果 ...... 180
J.1　細部設計資料 .............................. 180
J.2　DLM-f設計結果 ............................. 182
附錄K　雙跨五層平面構架細部資料及設計結果 ...... 184
K.1　細部設計資料 .............................. 184
K.2　DLM-f設計結果 ............................. 附錄L　單跨八層平面構架細部資料及設計結果 ...... 190
L.1　細部設計資料 .............................. 190
L.2　DLM-f設計結果 ............................. 198

參考文獻

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指導教授

莊德興(Der-Shin Juang)

審核日期

2011-4-7

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