博碩士論文 983202005 詳細資訊




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姓名 曾文傑(Wen-chieh Tseng)  查詢紙本館藏   畢業系所 土木工程學系
論文名稱 力法分析應用於HS-DLM混合搜尋法之桁架拓樸輕量化效率的研究
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摘要(中) 本文將力法分析應用於和聲搜尋(Harmony Search, HS)與離散拉格朗日法(Discrete Lagraingian Method, DLM)組成之混合演算法進行桁架拓樸結構輕量化設計,並比較力法與位移法之輕量化設計搜尋效率的快慢。
位移法分析時需求解方程式大小是由系統自由度的數量決定,具有高度通用性與自動化分析條件,被廣泛用於現今最佳化設計,而力法分析所需求解的方程式大小是系統贅餘度的數量決定,因此,當超靜定結構的贅餘度數量小於系統自由度數量時,力法在方程式求解的速度上佔有優勢,此外,力法分析中的力平衡矩陣,在結構拓樸與形狀相同下不會改變,因此不需重複將平衡矩陣拆解成對應贅力桿件的贅力矩陣和基元靜定結構的靜定矩陣。本文利用上述之力法分析上的優勢,結合HS隨機搜尋的能力在全域選定一個固定拓樸結構後,利用DLM健全的局部搜尋能力找出局部最佳解,在HS-DLM反覆的搜尋後,本文中所有算例皆可找出與文獻相同或是更好的解,證明了HS-DLM有不錯的搜尋能力,跟位移法分析結果比較後,也證明了力法分析較位移法有速度上的優勢。
摘要(英) This paper is study the efficiency between force method and displacement method applied to hybrid metaheuristic algorithm, namely HS-DLM,for topology optimization design of truesses wiht continuous and discrete variables.
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 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 when the topology and shape of truss is fixed in the redesign process making this method attractive and efficient.Using the HS(Harmony Search) global searching ability to find a fixed topology of truss, and find the constrained local minimum by applying DLM(Discrete Lagraingian Method). Afier a few iteration, the study shows that HS-DLM has great searching ability on the references’s cases and the force method has better efficiency of topology optimization design than displacement method.
關鍵字(中) ★ 矩陣力法
★ 和聲搜尋法
★ 離散拉格朗日法
★ 結構輕量化設計
關鍵字(英) ★ Force method
★ Harmony search
★ Discrete lagraingian method
★ Optimum structural design
論文目次 目錄 I
表目錄 VII
圖目錄 IX
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 最佳化分析方法回顧 3
1.2.2 結構最佳化設計 6
1.2.3 結構分析力法與位移法 8
1.3 研究方法與內容 10
第二章 結構分析方法 13
2.1 引言 13
2.2 矩陣位移法 13
2.2.1 建立元素勁度矩陣 14
2.2.2 建立座標轉換矩陣 15
2.2.3 建立元素諧和變位矩陣 17
2.2.4 計算全域座標的元素勁度矩陣 18
2.2.5 將元素勁度矩陣組合成系統勁度矩陣 19
2.2.6 求解出自由度位移 19
2.2.7 計算桿件內力 20
2.3 矩陣力法 20
2.3.1 建立內外力平衡矩陣 21
2.3.2 利用平衡矩陣選取贅力 24
2.3.3 計算力轉換矩陣 26
2.3.4 求解贅力 27
2.3.5 計算桿件內力和節點自由度位移 28
2.4 穩定結構判斷 28
2.4.1 位移法結構穩定判斷 30
2.4.2 力法結構穩定判斷 30
第三章 HS-DLM搜尋法 31
3.1 引言 31
3.2 最佳化問題之數學模式 31
3.3 HS理論回顧 32
3.3.1 HS搜尋流程 33
3.3.2 HS於束制條件處理方法 38
3.4 DLM理論回顧 41
3.4.1 鄰點 41
3.4.2 加權離散拉格郎日函數 43
3.4.3 離散梯度與離散鞍點 43
3.4.4 轉換函數與收斂準則 45
3.4.5 一階搜尋公式 46
3.4.6 DLM演算程序 48
3.5 HS-DLM 混合式演算法 51
3.5.1 引言 51
3.5.2 HS-DLM用於尺寸拓樸最佳化 52
第四章 數值算例 57
4.1 測試流程介紹 57
4.2 HS-DLM之參數研究 58
4.2.1 45桿平面桁架 58
4.2.2 HMCR與PAR 59
4.2.3 HM中解的限制與HMS的大小 68
4.2.4 HS-DLM與HS-RDLM 80
4.2.5 小結 81
4.3 力法與位法分析效率 82
4.6.1 類型(一) 10桿平面桁架(I) 82
4.6.2 類型(一)39桿平面桁架 88
4.6.3 類型(一)45桿平面桁架 93
4.6.4 類型(一)72桿空間桁架 96
4.6.5 類型(二)10桿平面桁架(II) 100
4.6.6 類型(二)10桿平面桁架(III) 102
4.6.7 類型(二)11桿平面桁架 104
4.6.8 類型(二)12桿平面桁架 106
4.6.9 類型(二)15桿平面桁架 109
4.6.10 類型(二)25桿空間桁架 114
4.6.11 類型(二)20桿2×2網格桁架 117
4.6.12 類型(二)42桿3×3網格桁架 120
4.6.13 類型(二)72桿4×4網格桁架 123
4.6.14 類型(二)110桿5×5網格桁架 126
4.6.15 類型(二)215桿10×5網格桁架 129
4.4 小結 132
第五章 結論與建議 133
5.1 結論與建議 133
5.2 未來研究方向 134
參考文獻 135
附錄A 10桿平面桁架(I)細部資料及設計結果 145
A.1 10桿平面桁架(I)細部設計資料(參考圖 4- 35) 145
A.2 10桿平面桁架(I)設計結果 146
附錄B 39桿平面桁架細部資料及設計結果 147
B.1 39桿平面桁架細部設計資料(參考圖 4- 41) 147
B.2 39桿平面桁架設計結果 148
附錄C 45桿平面桁架細部資料及設計結果 149
C.1 45桿平面桁架細部設計資料(參考圖 4- 45) 149
C.2 45桿平面桁架設計結果 150
附錄D 72桿空間桁架細部資料及設計結果 151
D.1 72桿空間桁架細部設計資料(參考圖 4- 47) 151
D.2 72桿空間桁架設計結果 152
附錄E 10桿平面桁架(II)細部資料及設計結果 154
E.1 10桿平面桁架(II)細部設計資料(參考圖 4- 49) 154
E.2 10桿平面桁架(II)設計結果 155
附錄F 10桿平面桁架(III)細部資料及設計結果 156
F.1 10桿平面桁架(III)細部設計資料(參考圖 4- 51) 156
F.2 10桿平面桁架(III)設計結果 158
附錄G 11桿平面桁架細部資料及設計結果 159
G.1 11桿平面桁架細部設計資料(參考圖 4- 52) 159
G.2 11桿平面桁架設計結果 160
附錄H 12桿平面桁架細部資料及設計結果 161
H.1 12桿平面桁架細部設計資料(參考圖 4- 54) 161
H.2 12桿平面桁架設計結果 162
附錄I 15桿平面桁架細部資料及設計結果 163
I.1 15桿平面桁架細部設計資料(參考圖 4- 56) 163
I.2 15桿平面桁架設計結果 164
附錄J 25桿空間桁架細部資料及設計結果 165
J.1 25桿空間桁架細部設計資料(參考圖 4- 62) 165
J.2 25桿空間桁架設計結果 167
附錄K 20桿2×2網格桁架細部資料及設計結果 168
K.1 20桿2×2網格桁架細部設計資料(參考圖 4- 64) 168
K.2 20桿2×2網格桁架設計結果 169
附錄L 42桿3×3網格桁架細部資料及設計結果 170
L.1 42桿3×3網格桁架細部設計資料(參考圖 4- 67) 170
L.2 42桿3×3網格桁架設計結果 171
附錄M 72桿4×4網格桁架細部資料及設計結果 172
M.1 72桿4×4網格桁架細部設計資料(參考圖 4- 70) 172
M.2 72桿4×4網格桁架設計結果 174
附錄N 110桿5×5網格桁架細部資料及設計結果 175
N.1 110桿5×5網格桁架細部設計資料(參考圖 4- 73) 175
N.2 110桿5×5網格桁架設計結果 177
附錄O 215桿10×5網格桁架細部資料及設計結果 178
O.1 215桿10×5網格桁架細部設計資料(參考圖 4- 76) 178
O.2 215桿10×5網格桁架設計結果 180
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指導教授 莊德興 審核日期 2013-8-26
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