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中文論文名稱 應用逐次線性規劃法結合移動限制技術於結構最佳化設計之研究
英文論文名稱 Optimum Design of Structures by Sequential Linear Programming with Adaptive Move Limit Techniques
校院名稱 淡江大學
系所名稱(中) 航空太空工程學系碩士班
系所名稱(英) Department of Aerospace Engineering
學年度 95
學期 2
出版年 96
研究生中文姓名 黃建翰
研究生英文姓名 chian-Han Huang
學號 694370122
學位類別 碩士
語文別 中文
口試日期 2007-07-04
論文頁數 58頁
口試委員 指導教授-張永康
委員-陳步偉
委員-洪健君
中文關鍵字 有限元素法  靈敏度分析  移動限制  逐次線性規劃法 
英文關鍵字 Finite Element Method  Sensitivity analysis  Move limit  Sequential Linear Programming 
學科別分類 學科別應用科學航空太空
中文摘要 本研究採用逐次線性規劃法於結構之最佳化設計,研究中採用ANSYS有限元素分析軟體作為結構分析之工具。本研究採用中心差分法計算結構反應之靈敏度以及改良之移動限制以加快程式收歛之效率。吾人可用泰勒展開式將非線性工程問題簡化為線性問題,並利用單體法逐次搜尋的方式得到最佳值。為了能自動化地執行結構最佳化,吾人將最佳化軟體和有限元素分析軟體整合為一系統程式。
本研究將以結構輕量化設計及提高結構之第一自然振動頻率為目的,並求得各結構在滿足限制條件時之最佳設計值。數值分析中將用六個範例並與文獻比較以證明結合移動限制技術之逐次線性規劃法可以有效獲得結構之最佳化設計。
英文摘要 The Sequential Linear Programming (SLP) is adopted in optimum design of structures in this study. The finite element model of structures was analyzed by ANSYS software. Since sensitivity can provide the optimal search direction and move limit calculation. The central difference method was used to obtain structure response sensitivity and the move limit. The nonlinear problem can be linearized by Taylor’s series expansion. In order to execute the structure optimization in an automatic fashion, The optimization software and finite element analysis software were combined together in a system program.
The objectives of this study are minimum weight design and maximum the first natural frequency of different structure problem. Six numerical examples will be compare with the results of other literatures to demonstrate the capability of the proposed method.
論文目次 中文摘要 ………………………………………………………………I
英文摘要 …………………………………………………………… II
目錄 …………………………………………………………………III
圖目錄 …………………………………………………………………V
表目錄 ………………………………………………………………VI
符號說明 ……………………………………………………………VII
第一章 緒論 ………………………………………………………1
1-1 研究動機 …………………………………………1
1-2 文獻回顧 …………………………………………2
1-3 本文架構 …………………………………………5

第二章 結構分析 …………………………………………………6
2-1 有限元素分析 ……………………………………6
2-2 靈敏度分析 ………………………………………9

第三章 最佳化方法 ………………………………………………11
3-1 逐次線性規劃法 …………………………………11
3-2 移動限制 …………………………………………13
3-3 程式執行流程 ……………………………………15
第四章 數值分析與討論 …………………………………………18
4.1範例一:十桿件桁架結構最佳化設計 ……………………20
4.2範例二:壓電複合梯形斜板結構之自然頻率最大化設計…22
4.3範例三:懸臂壓電多層複材薄板結構之輕量化設計 ……25
4.4範例四:簡支壓電層疊薄板結構之外型定位控制 ………28
4.5範例五:直昇機尾桁結構最佳化設計 ……………………31
4.6範例六:單層懸臂薄板結構最佳化設計……………………33

第五章 結論 ………………………………………………………35

參考文獻 ………………………………………………………………36

圖目錄

圖一 程式流程圖………………………………………………………39
圖二 範例一十桿件桁架結構外型圖…………………………………40
圖三 範例一十桿件桁架結構收斂圖…………………………………41
圖四 範例二壓電複合梯形斜板結構外型圖…………………………42
圖五 範例二壓電複合梯形斜板結構收斂圖…………………………43
圖六 範例三懸臂壓電多層複材薄板結構外型圖……………………44
圖七 範例三懸臂壓電多層複材薄板結構收斂圖……………………45
圖八 範例四簡支壓電層疊薄板結構外型圖…………………………46
圖九 範例四簡支壓電層疊薄板結構收斂圖…………………………47
圖十 範例五直昇機尾桁結構外型圖…………………………………48
圖十一 範例五直昇機尾桁結構收斂圖………………………………49
圖十二 範例六單層懸臂薄板結構外型圖……………………………50
圖十三 範例六單層懸臂薄板結構收斂圖……………………………51


表目錄

表一 範例一有限元素分析初始值與最佳值之比較…………………52
表二 範例二有限元素分析初始值與最佳值之比較…………………53
表三 範例三有限元素分析初始值與最佳值之比較…………………54
表四 範例四有限元素分析初始值與最佳值之比較…………………55
表五 直昇機尾桁之桿件分類…………………………………………56
表六 範例五有限元素分析初始值與最佳值之比較…………………57
表七 範例六有限元素分析初始值與最佳值之比較…………………58
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