以整合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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陳冠廷(Kuan-Ting Chen) 查詢紙本館藏

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論文名稱

以整合力法為分析工具之結構離散輕量化設計效率的探討
(Discrete optimum design of structures using integrated force method)

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摘要(中)

本文主要是以整合力法(Integrated force method, IFM)搭配和聲搜尋(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離散結構之最佳化設計。探討整合力法與傳統贅力法、位移法所需結構分析時間之差異，並利用混合式搜尋法希望藉以提升最佳解之品質，藉以改善最佳解整體之計算效率。本文使用整合力法進行結構分析運算過程中，使用虛擬反矩陣法(Psedo-inverse method)與奇異值分解法(Singular Value Decomposition, SVD)求得諧和矩陣；另外透過有限元分析建立力平衡矩陣，透過諧和矩陣與力平衡矩陣即可直接求得各桿件內力，並藉此反求結構各自由度位移。本文藉由數個結構離散輕量化設計例比較本文方法之優異性，並於部分算例同時考慮LRFD鋼結構設計規範。結果顯示整合力法能夠較位移法節省許多計算時間，並且可有效利用HS-DLM混合搜尋法獲得可能之整體最佳解。

摘要(英)

In this article, the discrete structural optimization problem solves by using HS-DLM in conjunction with the integrated force method (IFM) of analysis is presented. In IFM, all the element forces are taken as the independent variables instead of the redundants as the prime unknowns.
The equilibrium matrix is generated automatically through the finite element analysis and the compatibility matrix is obtained directly using the displacement-deformation relations and singular value decomposition (SVD) technique. By combining the compatibility and equilibrium matrix, the structural element forces are obtained directly. And the displacement can de back-calculated through the element forces. The results of the analysis are compared with the results of the redundant force method and displacement method. The design examples have been demonstrated that integrated force method is efficient and equally viable as compared to the displacement method. The results also shows HS-DLM algorithm is reliable, and the solution quality of the optimum design problems studies in the literature is comparable to other optimal method.

關鍵字(中)

★ 整合力法
★ 和聲搜尋法
★ 離散拉格朗日法
★ 結構輕量化設計

關鍵字(英)

★ Harmony search method
★ Discrete lagrangian method
★ Optimum structural design
★ Integrated force method

論文目次

中文摘要 I
英文摘要 III
目錄 V
表目錄 XI
圖目錄 XV
第一章緒論 1
1.1 研究動機與目的 1
1.2 文獻回顧 4
1.2.1 最佳化方法 4
1.2.2　整合力法(Integrated Force Method, IFM) 9
1.3 研究方法與內容 12
第二章整合力法分析 13
2.1　前言 13
2.2整合力法之理論推導 14
2.3　整合力法分析程序 19
2.3.1　建立力平衡方程 20
2.3.2　產生諧和條件 30
2.3.3　組合平衡方程與諧和條件，求解桿件未知內力 34
2.3.4　藉由桿件內力，求解節點位移 36
2.4　整合力法運算流程算例 36
第三章 HS-DLM混合搜尋法 43
3.1　最佳化問題之數學模式 43
3.2　和聲搜尋法(HS)理論回顧 44
3.2.1　HS搜尋流程 50
3.3　離散拉格朗日法(DLM)理論回顧 52
3.3.1　加權離散拉格朗日函數 52
3.3.2　鄰點(Neighborhood) 54
3.3.3　離散梯度(Discrete Gradient, DG) 55
3.3.4　離散鞍點(Discrete Saddle Point, DSP) 56
3.3.5　一階搜尋公式與收斂準則 57
3.3.6　合向量策略 61
3.3.7　DLM演算程序 63
3.4　HS-DLM 混合式演算法 66
第四章數值計算例 71
4.1　分析流程 71
4.2.1　範例一 10桿平面桁架 74
4.2.2　範例二 25桿空間桁架 77
4.2.3　範例三 36桿空間桁架 81
4.2.4　範例四 72 桿空間桁架 86
4.2.5　範例五 132桿空間桁架 91
4.2.6　範例六 160桿空間桁架 97
4.2.7　範例七 200桿空間桁架 102
4.2.8　範例八 582桿空間桁架 106
4.2.9　範例九單跨雙層平面構架 110
4.2.10　範例十雙跨五層平面構架 114
4.2.11　範例十一單跨八層平面構架 117
4.3 考慮極限設計法與構材束制條件 121
4.3.1 範例十二　單層樓8桿空間構架 121
4.3.2 範例十三　雙垮三層平面構架 127
4.3.3 範例十四　四層樓84桿空間構架 130
第五章　建議與結論 135
5.1　結論與建議 135
5.2　未來研究方向 138
參考文獻 139
附錄A　10桿平面桁架細部資料及設計結果 149
A.1　細部設計資料 149
A.2　HS-DLM-IFM 設計結果 150
附錄B　25桿空間桁架細部資料及設計結果 153
B.1　細部設計資料 153
B.2　HS-DLM-IFM 設計結果 155
附錄C　36桿空間桁架細部資料及設計結果 157
C.1　細部設計資料 157
C.2　HS-DLM-IFM 設計結果 159
附錄D　72桿空間桁架細部資料及設計結果 161
D.1　細部設計資料 161
D.2　HS-DLM-IFM 設計結果 163
附錄E　132桿穹頂桁架細部資料及設計結果 167
E.1　細部設計資料 167
E.2　HS-DLM-IFM 設計結果 171
附錄F　160桿空間桁架細部資料及設計結果 179
F.1　細部設計資料 179
F.2　HS-DLM-IFM設計結果 184
附錄G　200桿平面桁架細部資料及設計結果 195
G.1　細部設計資料 195
G.2　HS-DLM-IFM設計結果 199
附錄H　582桿空間桁架細部資料及設計結果 207
H.1　細部設計資料 207
H.2　HS-DLM-IFM 設計結果 214
附錄I　單跨雙層平面構架細部資料及設計結果 225
I.1　細部設計資料 225
I.2　HS-DLM-IFM 設計結果 227
附錄J　雙跨五層平面構架細部資料及設計結果 229
J.1　細部設計資料 229
J.2　HS-DLM-IFM 設計結果 232
附錄K　單跨八層平面構架細部資料及設計結果 235
K.1　細部設計資料 235
K.2　HS-DLM-IFM 設計結果 242

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指導教授

莊德興(Der-shin Juang)

審核日期

2011-8-26

推文