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研究生:柯浩宇
研究生(外文):Hao-Yu Ke
論文名稱:結構最佳化之兩點分段適應近似法
論文名稱(外文):Two-Point Piecewise Adaptive Approximation for Structural Optimization
指導教授:鍾添東鍾添東引用關係
指導教授(外文):Tien-Tung Chung
口試委員:劉正良史建中
口試日期:2016-08-01
學位類別:碩士
校院名稱:國立臺灣大學
系所名稱:機械工程學研究所
學門:工程學門
學類:機械工程學類
論文種類:學術論文
論文出版年:2016
畢業學年度:104
語文別:英文
論文頁數:80
中文關鍵詞:結構最佳化連續近似最佳化兩點近似法有限元素分析非線性規劃
外文關鍵詞:Structural optimizationSequential approximate optimizationTwo-point approximation methodFinite element analysisNonlinear programming
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  • 被引用被引用:1
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本研究提出兩點分段適應近似法應用於結構最佳化上。為使數學最佳化理論能與結構設計結合,必須透過近似法將結構之行為諸如應力、位移、頻率等轉換成以設計變數表示的顯函數。最佳解便能透過解決數個由近似函數構成的最佳化問題得到。為確保近似品質,近似函數會考量函數的單調性來建立。由於許多結構行為對設計變數的變化近乎單調函數,兩點分段適應近似法確保建立單調的近似函數以確保近似品質,並在兩點微分值異號時亦能建立非單調函數以符合兩點靈敏度值。並且此近似法採用分段函數解決過往近似法中不當近似的產生。此研究亦整合最佳化程式、CAD軟體與有限元素分析軟體進行自動化結構最佳設計,並以多個結構最佳化的問題驗證本近似法於結構最佳化的實用性,並另實際應用於電路板等效有限元素模型建立與精密檢測平台的設計之中。

This study proposes a new two-point approximation method called two-point piecewise adaptive approximation (TPPAA) for structural optimization. For applying the mathematical optimization to structural design, several kinds of structural behavior, including stress, displacement and natural frequency, are represented as explicit functions of design variables by approximation technique. The optimum design can be found with sequential sub-problems solved, which is known as sequential approximate optimization (SAO). To ensure the approximation quality, structural behavior is approximated with considering the monotonicity. Monotonic functions are available in TPPAA when the first order derivatives of two successive design points have the same signs since many kinds of structural behavior vary quasi-monotonically with respect to design variables. Non-monotonic form can also be obtained when the two derivatives of two successive design points have different signs. TPPAA adopts the piecewise approximate functions to avoid inappropriate approximation that existing approximation schemes would encounter. In this study, a program integrating ANSYS, AutoCAD and Microsoft Visual C++ is developed for automated structural optimization. The practicability of TPPAA is examined in several structural optimization problems and the comparison of several approximation methods are also presented. Furthermore, TPPAA is applied to optimum design of large structures, such as effective FE model construction of PCB and design of high-accuracy measuring stage structure.

誌謝 i
中文摘要 iii
ABSTRACT iv
CONTENTS v
LIST OF FIGURES viii
LIST OF TABLES x
LIST OF SYMBOLS xiii
Chapter 1 Introduction 1
1.1 Introduction to structural optimization 1
1.2 Paper review 2
1.3 Strategies of research 5
1.4 Outline 6
Chapter 2 Application of approximation methods in structural optimization 7
2.1 Procedure of mathematical optimization 7
2.1.1 Selection of design variables 7
2.1.2 Defining objective function 8
2.1.3 Sensitivity analysis 8
2.1.4 Treatment of constraints 9
2.1.5 Application of approximation methods 10
2.1.6 Application of mathematical optimization 11
2.2 Single-point approximation methods 11
2.2.1 Direct linear approximation 12
2.2.2 Reciprocal approximation 12
2.2.3 Modified reciprocal approximation 13
2.2.4 Conservative and convex approximation 13
2.3 Two-point approximation 14
2.3.1 Two-point modified reciprocal approximation 14
2.3.2 Two-point exponential approximation 14
2.3.3 Linear-reciprocal approximation 15
2.3.4 Incomplete series expansion 16
2.3.5 Two-point adaptive nonlinearity approximation-3 17
2.4 Integrated optimization program 18
Chapter 3 The proposed approximation method 20
3.1 Modified incomplete series expansion 20
3.2 Two-point piecewise adaptive approximation 25
3.3 Modification for convex approximation 28
3.4 Modification for matching function value of previous design point 29
Chapter 4 Optimization of small scale structures 31
4.1 2-bar truss 31
4.2 3-bar truss optimization 33
4.3 4-bar truss optimization 35
4.4 6-bar truss optimization 38
4.5 10-bar truss optimization 39
4.6 25-bar truss optimization 41
4.7 Multi-section circular beam optimization 44
4.8 Multi-section tube beam optimization 46
4.9 Multi-section rectangular beam optimization 48
Chapter 5 Optimization of large scale structures 50
5.1 Effective finite element model construction for PCB 50
5.1.1 Material property identification for orthotropic thin plate 51
5.1.2 Effective FE model construction for PCB 55
5.2 Optimization of high-accuracy measuring stage 59
5.2.1 Optimization of gantry 59
5.2.2 Optimization of modified gantry 63
5.2.3 Optimization of y-stage 67
Chapter 6 Conclusion and suggestion 72
6.1 Conclusion 72
6.2 Suggestion 72
REFERENCES 74
Appendix: User manual of integrated optimization program 77
A.1 Program setting 77
A.2 Operation step 79
Vitae 80

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