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系統識別號 U0002-0803201113365400
中文論文名稱 以有限元素為基礎之形狀最佳化
英文論文名稱 Finite Element_based Shape Optimization
校院名稱 淡江大學
系所名稱(中) 土木工程學系碩士班
系所名稱(英) Department of Civil Engineering
學年度 99
學期 1
出版年 100
研究生中文姓名 游偲平
研究生英文姓名 Si-Ping You
學號 697380524
學位類別 碩士
語文別 中文
口試日期 2011-01-13
論文頁數 95頁
口試委員 指導教授-廖國偉
委員-楊亦東
委員-王人牧
中文關鍵字 最佳化  雙迴圈法  去偶合法  可靠度分析 
英文關鍵字 Optimization  DO  RBDO  Bi-level  double-loop  reliability analysis 
學科別分類 學科別應用科學土木工程及建築
中文摘要 可靠度最佳化設計可分為最佳化及可靠度兩方面來探討。最佳化分析包括整體設計的概念,使其最終結果符合所需;可靠度則是評估整體產品或系統品質的指標。若需求設定為考慮設計參數變異性的設計(Reliability-Based Design Optimization),簡稱RBDO,將設計參數的變異性考慮在最佳化的設計流程裡,藉著每次可靠度的分析評估,再利用最佳化來改善整體表現,依此重覆、持續的分析處理,直到達成最終最佳化設計,並符合設定之可靠度需求。
在處理可靠度最佳化的問題,必須分別處理可靠度與最佳化。其本質為一雙迴圈法(Double loop),雙迴圈法有一個很大的缺點,就是計算時間很長,計算量很大。因此為了有效率的去處理結構最佳化問題分析,本研究以雙層系統(the Bi-level system)的概念為出發點,希望利用上層和下層的雙層系統建立協同最佳化模式,並建立協調中心,負責整合最佳化與可靠度分析的結果,使兩者在同一時間裡進行計算,如此可靠度分析將無須等候最佳化之分析結果,接著以現有的商業套裝軟體,呈現其3D圖形之最佳化結果。文末以一個例題來說明,不但具有快速的計算效率,同時亦達到設計給定的可靠度指標。

英文摘要 This study presents a concurrent approach to evaluate the Reliability-Based Design Optimization (RBDO). The proposed approach prevents the RBDO from conducting the inherited double-loop calculation. Thus, the computational efficiency of performing a RBDO is improved. To concurrently perform a RBDO, the RBDO problem is reformulated as a system with a bi-level structure, which consists of upper and lower levels. The upper level has one sub-system, while the lower level includes two sub-systems. The sub-system in the upper level aims to minimize the discrepancy between results obtained from the two sub-systems in the lower level. The two major calculations in a RBDO problem, which are the reliability analysis (RA) and deterministic optimization (DO), are decomposed via two sets of linking variables. RA and DO serve as the two sub-systems in the lower level. The linking variables, which are "copies" of the design variables (DVs) and random design variables (RVs), connect the upper and lower levels to make three sub-systems as a whole. Once the RBDO is reformulated, the objective of the upper level is to minimize the difference of the linking variables obtained from each sub-system in the lower level. The main tasks in the lower level are to execute the deterministic optimization and reliability analysis. In the proposed method, the optimization and reliability analysis need not to be conducted sequentially. Instead, these two analyses are executed simultaneously to accelerate the RBDO process and to reduce the computational cost. Details of a RBDO solved by the bi-level algorithm is revealed through a numerical example provided in this study
論文目次 目錄
誌謝……………………………………………………………………I
中文摘要………………………………………………………………II
英文摘要………………………………………………………………III
目錄………………………………………………………………… IV
圖目錄……………………………………………………………… VIII
表目錄……………………………………………………………… X
第一章 緒論………………………………………………………………1
1.1前言…………………………………………………………1
1.2研究背景………………………………………………………………2
1.3研究動機與目的………………………………………………………………2
1.4研究流程與方法………………………………………………………………4
第二章 文獻探討………………………………………………………………6
2.1結構分析概念………………………………………………………………6
2.1.1有限元素法基本概念………………………………………………………………7
2.1.2有限元素法基本要素………………………………………………………………7
2.1.3有限元素法分析理論………………………………………………………………11
2.1.4有限元素法分析步驟………………………………………………………………15
2.2結構最佳化………………………………………………………………16
2.2.1結構尺寸最佳化………………………………………………………………17
2.2.2結構形狀最佳化………………………………………………………………18
2.2.3結構拓樸最佳化………………………………………………………………18
2.3最佳化理論………………………………………………………………19
2.3.1可靠度最佳化分析………………………………………………………………23
2.3.2多元系統最佳化………………………………………………………………25
第三章 形狀最佳化模式………………………………………………………………28
3.1形狀最佳化模式之建立………………………………………………………………28
3.2反應曲面法………………………………………………………………29
3.2.1反應曲面法之設計概念………………………………………………………………29
3.2.2反應曲面法的設計步驟………………………………………………………………30
3.2.3反應曲面法之數學模式………………………………………………………………31
3.2.4 RSM迴歸模型………………………………………………………………31
3.3可靠度演算法………………………………………………………………32
3.3.1正可靠度分析………………………………………………………………32
3.3.2逆可靠度分析………………………………………………………………33
3.3.3一階可靠度方法………………………………………………………………35
3.4 去偶合演算法………………………………………………………………38
3.4.1雙迴圈RBDO………………………………………………………………38
3.4.2去偶合技術………………………………………………………………40
3.4.3去偶合數學模型………………………………………………………………43
3.5 Bi-level RBDO架構………………………………………………………………47
第四章 分析模型之介紹………………………………………………………………49
4.1前言………………………………………………………………49
4.2有限元素分析系統………………………………………………………………49
4.3應用軟體………………………………………………………………50
4.4連桿模型之構成………………………………………………………………51
4.4.1元素選擇………………………………………………………………51
4.4.2邊界條件及網格劃分………………………………………………………………52
4.4.3模型建立之流程………………………………………………………………53
第五章 例題分析與結果討論……………………………………………………………… 57
5.1前言………………………………………………………………57
5.2連桿問題………………………………………………………………57
5.3撰寫程式的流程………………………………………………………………59
5.4連桿之結果討論………………………………………………………………61
第六章 結論與未來展望………………………………………………………………70
6.1 結論………………………………………………………………70
6.2未來展望………………………………………………………………70
參考文獻………………………………………………………………72
附錄………………………………………………………………75























圖目錄
圖 1.1 研究流程圖.................................................................................4
圖 2.1 三維節點自由度示意圖...........................................................10
圖 2.2 結構最佳化分類圖...................................................................17
圖 2.3 定然式最佳化分析示意圖.......................................................23
圖 2.4 系統分析示意圖.......................................................................25
圖 2.5 ATC的構架圖...........................................................................26
圖 3.1 形狀最佳化系統模式架構圖...................................................28
圖 3.2 正可靠度分析圖.......................................................................32
圖 3.3 逆可靠度分析圖.......................................................................34
圖 3.4 雙迴圈法示意圖.......................................................................39
圖 3.5 SORA設計之流程....................................................................41
圖 3.6 去偶合法示意圖(SORA)..........................................................43
圖 3.7 懸臂梁最佳化外力為100.........................................................45
圖 3.8 懸臂梁最佳化外力為180.........................................................46
圖 3.9 懸臂梁最佳化外力為150.........................................................47
圖 3.10 Bi-level RBDO架構...................................................................48
圖 4.1 連桿原始設計模型...................................................................49
圖 4.2 C3D8R元素...............................................................................52
圖 4.3 連桿邊界條件及載重示意圖...................................................53
圖 4.4 建立分析模型之流程...............................................................55
圖 4.5 ABAQUS後處理之雲層圖(平面)............................................56
圖 4.6 ABAQUS後處理之雲層圖(立體面)........................................56
圖 5.1 建立連桿問題之雙層系統.......................................................58
圖 5.2 選逆可靠度...............................................................................59
圖 5.3 選定可靠度方法.......................................................................60
圖 5.4 各變數分佈情形.......................................................................62
圖 5.5 各變數收斂情形.......................................................................63
圖 5.6 應力分佈情形...........................................................................63
圖 5.7 體積分佈情形...........................................................................64
圖 5.8 最終設計之模型.......................................................................65
圖 5.9 ABAQUS分析結果(平面)........................................................65
圖 5.10 ABAQUS分析結果(立體面)..................................................66










表目錄
表 2.1 各元素節點數目表.......................................................................8
表 2.2 各維度元素示意...........................................................................9
表 2.3 各維度網格示意表.....................................................................10
表 4.1 連桿設計尺寸.............................................................................54
表 5.1 連桿之隨機變數.........................................................................58
表 5.2 為連桿之分析結果.....................................................................64
表 5.3 單迴圈的效率.............................................................................67
表 5.4 Bi-level RBDO的效率.................................................................68
表 5.5 單迴圈和Bi-leve RBDO比較....................................................68

參考文獻 參考文獻
[1] K. Wieghardt, “Uber einen Grenzubergang der Elastizitaslehre und seine Anwendung auf die Statik hochgradig statisch unbestimmter Fachwerke”, Verhandlungen des Vereins z.Beforderung des Gewerbefleisses. Abhandlungen, vol 85, pp 139-176, 1906.
[2] W. Riedel, “Beitrage zur Losung des ebenen Problems eines elastischen Korpers mittels der Airyschen Spannungsfunktion”, Zeitschrift fur Angewandte Mathematik und Mechanik, vol 7, no 3, pp 169-188, 1927.
[3] A. L. Yettram and H. M. Husain, “Plane Framework Models for Plates in Extension”, JEMDiv, vol 92, no EMI, pp 157-168, 1966.
[4] A. Hrennikoff , “Solution of problems of elasticity by the framework method”, Journal of Applied mechanics, 1941.
[5] A. Hrennikoff, “A Lattice analogy for the solution of stress problems”, Journal of the ICE, 1943.
[6] S. Levy, “Structural Analysis and Influence Coefficients for Delta Wings”, JAeroS, vol 20, no 7, pp 449-454, 1953.
[7] R. W. Clough, “The Finite Element Method in Plane Stress Analysis”, Proceedings of the Second Conference on Elecrtonic Computation, American Society of Civil Engineers, New York, pp345-377, 1960.
[8] 吳佳璋、黃俊銘, “MSC.FEA 有限元素結構分析-基礎與實例演練”, 全華出版社, 2006.
[9] http://staff.pccu.edu.tw/~wrchen/fem.htm 有限元素介紹網站
[10] M. A. Bhatti, “Fundamental Finite Element Analysis and Applications: with Mathematica and MATLAB Computations”, Wiley, 2005.
[11] A. G. M. Michell, “The Limits of Economy of Material in Framed Structures”, Philosophy Magazine, Series 6, vol 8, pp 589-597, 1904.
[12] L. A. Schmit, “Structural Design by Systematic Synthesis”, Proceedings of the 2nd Conference on Electronic Computation, ASCE, New York, pp 105-122, 1960.
[13] R. T. Haftka and R. V. Grandhi, “Structural Shape Optimization-A Survey”, Computer Methods in Applied Mechanics and Engineering, vol 57, pp 91-106, 1986.
[14] U. Kirsch, “Structural Optimization”, Springer-Verlag, 1993.
[15] D. B. Ashok and R. C. Tirupathi, “Optimization Concepts and Applications in Engineering”, prentice hall, 1999.
[16] Kuo-Wei Liao & C. Ha, “Application of reliability-based optimization to earth-moving machine: hydraulic cylinder components design process”, Journal of Structural and Mutidisciplinary Optimization, Online First, Springer, 2007.
[17] O. Ditlevsen and H. O. Madsen, “Structural Reliability Methods”,Wiley, 1996.
[18] K. W. Liao, “Evaluation of System Reliability Using Multi-Level Optimization Technique“, 7th World Congress on Structural and Multidisciplinary Optimization, 2007.
[19] 葉怡成, “實驗計劃法-製程與產品最佳化“ ,五南圖書出版公司, 2001.
[20] Jae-Ohk Lee, Young-Soon Yang, Wom-Sun Ruy, “A comparative study on reliability and target-performance-based probabilistic structural designoptimization”, Comp. and Struc. vol 80, pp 257-269, 2002.
[21] B. D. Youn, K. K. Choi and Y. H. Park, “Hybrid Analysis Method for Reliability-Based Design Optimization” , ASME, J. Mech. Design, vol 125, pp 221-232, 2003.
[22] J. Tu, K. K. Choi and Y. H. Park, “A New Study on Reliability-Based Design Optimization”, Journal of Mechanical Design, 1999.
[23] A. Hasofer and N. Lind , “Exact and invariant second-moment code format”, Journal of the Engineering Mechanics Division, vol 100, no EM1, pp 111-121, 1974.
[24] Y. M. Yoo, E. J. Haug, and K. K. Choi, “Shape Optimal Design of an Engine Connecting Rod”, Journal of Mechanisms, Transmissions, and Automation in Design, vol 106/415, pp 415-419, 1984.
[25] http://www.simutech.com.tw/html/front/bin/home.phtml 士盟科技官方網站
[26] S. Kodiyalam and G. N. Vanderplaats. “Shape optimization of three dimensional continum structures viaforce approximation techniques“ , AIAA Journal, vol 27, pp 1256-1263, 1989.
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