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研究生:邱義汎
研究生(外文):Yi-Fan Ciou
論文名稱:結合梁、柱元素之開孔結構最佳化設計
論文名稱(外文):Optimal Design of Structures with Openings Using Beam and Column Elements
指導教授:呂良正呂良正引用關係
指導教授(外文):Liang-Jenq Leu
口試委員:黃仲偉王建凱
口試日期:2016-07-15
學位類別:碩士
校院名稱:國立臺灣大學
系所名稱:土木工程學研究所
學門:工程學門
學類:土木工程學類
論文種類:學術論文
論文出版年:2016
畢業學年度:104
語文別:中文
論文頁數:80
中文關鍵詞:結構最佳化梁柱元素結構開孔拓樸最佳化多層最佳化
外文關鍵詞:structural optimizationbeam elementsstructural openingstopology optimizationmulti-layer optimization
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現實的建築物通常都有梁柱系統,然而拓樸最佳化較難直接應用在現實的建築結構上,由於設計或施工層面的問題,無梁柱之系統較難施作,因此本研究期望拓樸的設計建構在有梁柱系統的架構下,因此使用了梁元素及柱元素來進行拓樸最佳化,讓拓樸最佳化更有可能應用在實際建築物上。結構物不可避免會有開門或開窗甚至配置管線,因此會有開孔的行為,而開孔會對結構物的勁度造成影響,因此本研究也希望透過最佳化的方式來將開孔造成的勁度影響降到最低。
本團隊曾經提出使用最陡梯度法當作是孔洞位置最佳化中孔洞的移動標準,因此本研究想多使用幾種演算法來比較其效果,其中局域演算法以Pattern search表現較佳,全域演算法以模擬退火法(Simulated Annealing)表現較佳,因此結合兩者之優點先使用全域的模擬退火法(SA),再使用局域的Pattern search來做最佳化,其表現比只做其中一種還要好,此種以全域演算法之結果當作起始值,在使用局域演算法使之收斂,在孔洞位置最佳化表現不錯,應該也可以適用在其他最佳化上。
本研究透過例題驗證加入柱元素之效果,且柱元素的勁度會影響拓樸形狀,在若加入柱元素的勁度不足,可能會使拓樸形狀較不規則。在同時加入梁元素和柱元素時,其兩者為剛接或是鉸接會對拓樸造成影響,在低樓層時影響較不明顯,高樓層時差異才會比較大。透過不同的外力形式的例題發現,若外力的形式是側向力,則拓樸形狀就會有較多的斜撐狀45度角桿件或是交叉桿件,若外力形式為垂直載重,則拓樸形狀會呈現墩柱狀或是拱橋狀。
孔洞位置最佳化結合拓樸最佳化的問題中,可以看出孔洞會往原本拓樸材料較少的地方移動,進一步驗證多層最佳化的可靠性。


Real buildings usually use beams and columns system, but topology optimization is difficult to apply in this system. This research expect to use topology optimization design in the buildings with beams and columns system. We use beam elements and column element to combine topology optimization, that topology optimization is more likely to make the application in the real buildings. There are many structures with openings like door, windows or room for pipes. Stiffness of structures will decrease because of openings. This research also expect to use optimization design to reduce the effect of stiffness.
Our team have used the steepest descent method to determine the positions of openings. Therefore, this research want to use many kinds of algorithms to compare the effect. Pattern search and simulated annealing are better than other algorithms. We use simulated annealing to get the result, and then take the result using for the pattern search. The performance of using this method is better than only using one algorithm. This method is good for optimization of positions.
This research verifies that the stiffness of column elements will affect the result of topology optimization. If stiffness of column elements is too small, the result of topology optimization will be irregular. Because the displacement fields between different elements do not match, it causes this result. The connection types between beam and column elements will also affect the result of topology optimization, but it only performs when the floor is high enough. The forms of force also affect the result of topology. Vertical force and lateral force cause different topology result.


口試委員會審定書 #
誌謝 i
摘要 iii
Abstract v
目錄 vii
圖目錄 xi
第一章 緒論 1
1.1 研究動機 1
1.2 文獻回顧 1
1.3 研究內容 2
第二章 結構最佳化方法 5
2.1 前言 5
2.2 最佳化問題描述 5
2.3 結構最佳化分析方法與工具介紹 6
2.3.1 數學規劃法(Mathematical Programming,MP ) 7
2.3.2 最佳化條件法(optimum criteria method,OC) 8
2.4 固體等向性懲罰函數法(Solid Isotropic Material with Penalization,SIMP) 8
2.4.1 SIMP之基本概念 9
2.4.2 敏感度因子(Sensitivity Number) 9
2.4.3 棋盤化效應 11
2.4.4 停止條件 12
2.4.5 SIMP設計流程 12
2.5 多層最佳化 13
2.6 多重載重狀況 13
2.7 小結 14
第三章 孔洞位置最佳化 21
3.1 前言 21
3.2 孔洞位置最佳化問題 21
3.2.1 問題描述 21
3.2.2 置入孔洞的方式 22
3.2.3 孔洞移動後材料之回填 22
3.2.4 孔洞的移動準則 22
3.2.5 Matlab內建最佳化演算法 23
3.2.6 最佳化流程 25
3.3 例題探討與比較 27
3.4 小結 28
第四章 結合梁、柱元素之最佳化 35
4.1 前言 35
4.2 梁、柱元素之性質 35
4.2.1 梁、柱元素之斷面性質 35
4.2.2 梁、柱元素之勁度矩陣 35
4.3 結合梁元素與Q4元素 36
4.3.1 梁元素與Q4元素的連接方式 36
4.3.2 梁元素與柱元素的連接方式 37
4.3.3 最佳化流程 37
4.4 例題探討與比較 39
4.4.1 加入柱元素之拓樸最佳化 39
4.4.2 加入柱元素之孔洞位置最佳化 42
4.4.3 加入柱元素之孔洞位置結合拓樸最佳化 43
4.4.4 加入梁元素及柱元素之拓樸最佳化 44
4.4.5 加入梁元素及柱元素之孔洞位置最佳化 46
4.5 小結 46
第五章 結論與未來展望 71
5.1 結論 71
5.2 未來展望 71
參考文獻 75



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