結構最佳化軟體開發：應用於斜張橋設計

• Main Authors: 柯俊宇, Ke, Chun-Yu
• Other Authors: 指導教授：呂良正, 臺灣大學：土木工程學研究所
• Format: Thesis
• Language: English
• Published: 2014
• Subjects: 雙層最佳化; 斜張橋; 設計模式; 有限元素分析; 最佳化設計; 結構最佳化; 軟體開發; Anchorage; Barrios; Erskine; Helgeland; Helgeland Bridge; Huntington; Kuna; Pasco; Pylon
• Online Access: http://ntur.lib.ntu.edu.tw/handle/246246/260724; http://ntur.lib.ntu.edu.tw/bitstream/246246/260724/1/ntu-103-R01521212-1.pdf

斜張橋的材料使用效率高、建造相對簡便、在中長跨距相對經濟且十分美觀，也因此成為世界各地近五十年間最常採用之橋梁型態。但因其鋼索、主梁與橋塔間複雜的交互關係，造成其結構系統之高度靜不定，故斜張橋之設計實屬相當困難。採用傳統的設計方法於此種多變數與多束制條件之結構設計上，必然會耗費過多的時間與資源，且無法保證結果最佳之設計。因此，全世界橋梁工程師都非常渴望的便是一套能夠分析斜張橋最佳化設計問題之解決方案。 本研究為解決複雜的多目標最佳化問題，提出一套含多層最佳化流程之軟體系統架構，將各種結構分析軟體之結構資訊抽象化至統一的數學模型，以利採用不同最佳化演算法進行分析。基於該系統架構，本研究開發出一套功能強大的軟體以解決各種結構最佳化問題，稱為SODIUMM。該軟體已經過各種經典結構最佳化與斜張橋索力最佳化問題測試與驗證，確保其精度與效率，同時也展現其在分析模型的彈性以及最佳化參數設定的靈活度。 此外，為瞭解斜張橋設計參數在實務上的合理範圍以確保最佳解之可行性，本研究針對二十三座具代表性的斜張橋進行參數分析，統整出經驗設計參數範圍。再由參數之統計結果提出單塔與雙塔斜張橋之標準模型，藉以展示多種以雙層最佳化為基礎之斜張橋最佳化設計方法，並以此結果檢驗以往工程師所提出之經驗公式的正確性與適用範圍。最後，本研究基於各種斜張橋最佳化設計方法之結果，對現有之斜張橋提出建議，並針對各設計變數提出通用的最佳數值與概念性的設計方針。 Because of the aesthetic appeal, ease of erection, efficient utilization of materials, economical in long span bridges, and other countless advantages, cable-stayed bridges have found wide applications all over the world in recent 50 years. However, the design of cable-stayed bridge is very complex due to its three major structural components, stay-cables, girder, and pylon, are tightly coupled, which makes the structural system highly statically indeterminate. Design of such complex structure with a large number of design variables and constraints with traditional methods is inevitably time consuming and cannot guarantee the optimality of the final design. As a result, bridge engineers around the world are craving a methodology that is capable of solving the optimal configuration of cable-stayed bridges. In this research, a flexible software framework that integrates commercial structural analysis software and optimization algorithms with a multi-level optimization scheme is proposed for generalizing the structural information to a unified mathematical model that is applicable for any mathematical optimization algorithms and solving multi-objective optimization problems. Based on the proposed framework, a powerful software named “Structure Optimal Design Interface with Unified Mathematical Model” (SODIUMM), has been developed to solve various structure optimal design problems. Representative structural optimization problems and post-tensioning cable force optimization problems have been tested and validated to ensure the accuracy and efficiency of the SODIUMM. Those abundant optimization problems also reflect the flexibility of the software framework and the SODIUMM. Moreover, crucial design parameters are studied among 23 representative cable-stayed bridges in different classifications to provide practical design regions, which are used to examine the applicability of optimal solutions, and empirical design parameters. Standard cable-stayed bridge models for both single and double pylon configurations are proposed based on the empirical design parameters to demonstrate various optimal design schemes of cable-stayed bridges through bi-level optimization. Finally, from the optimal solutions of the standard cable-stayed bridge models, suggestions on specific bridges are made and general optimal values or conceptual guidelines are concluded in each respective design parameter. 誌謝 I 摘要 III ABSTRACT V CONTENTS VII LIST OF TABLES XV LIST OF FIGURES XVII CHAPTER 1 INTRODUCTION 1 1.1 Research Purposes and Motivations 1 1.2 Literature Review 3 1.2.1 Structural Optimization 3 1.2.2 Integration of Commercial Structural Analysis Software 4 1.2.3 Previous Integrated Optimization Frameworks 6 1.2.4 Cable-Stayed Bridge Optimization 8 1.3 Thesis Organization 9 CHAPTER 2 STRUCTURE OPTIMAL DESIGN 11 2.1 Introduction 11 2.2 Statement of Optimization Problems 11 2.3 Structural Optimization 13 2.3.1 Sizing Optimization 15 2.3.2 Shape Optimization 16 2.3.3 Topology Optimization 17 Example 2.3.1 – Multi-material Topology Optimization of 3D Cantilever Beam 18 2.3.4 Optimal Design of Cable-Stayed Bridges 21 2.3.5 Multi-level Optimization Problems 22 2.4 Optimization Algorithms 23 2.4.1 Real-Coded Genetic Algorithm 23 2.4.2 IMSL Math Library – MinConNLP 25 2.4.3 Augmented Lagrangian Algorithm 25 2.4.4 COBYLA 26 2.4.5 MATLAB Optimization Toolbox – fmincon 27 2.4.6 Comparison 27 2.5 Optimization Procedure 29 2.6 Termination Conditions 30 2.7 Summary 30 CHAPTER 3 SOFTWARE DEVELOPMENT 33 3.1 Introduction 33 3.2 Programming Techniques 35 3.2.1 Object-Oriented Analysis and Design 35 3.2.1.1 Inheritance 36 3.2.1.2 Polymorphism 36 3.2.1.3 Encapsulation 36 3.2.2 Design Patterns 37 3.3 Requirements Analysis 37 3.3.1 User Requirements 38 3.3.1.1 Integration of Optimization Algorithms and Structural Analysis Software 38 3.3.1.2 Graphical User Interface 38 3.3.1.3 Visualization of Structure 39 3.3.1.4 Drag Selection 39 3.3.1.5 Real-Time Structure Visualization 39 3.3.1.6 Procedure Cancellation 40 3.3.1.7 Structure Model Output 40 3.3.2 Extensibility Requirements 40 3.3.2.1 Structural Analysis Software 41 3.3.2.2 Optimization Algorithm 41 3.3.2.3 Variables, Constraints, and Objective Function 41 3.3.3 Other Functionality Requirements 42 3.3.3.1 Restraints 42 3.3.3.2 Interpolation 42 3.3.3.3 User-defined Function 43 3.3.3.4 Virtual Variable 43 3.3.3.5 Multi-level Optimization 44 3.4 System Framework Architecture 44 3.4.1 Software Architecture 45 3.4.2 Document 46 3.4.3 Optimization 48 3.5 Module Framework Design 50 3.5.1 Document Creation 51 3.5.2 FEA Facade 52 3.5.3 Algorithm 53 3.5.4 Variable 55 3.5.5 Virtual Variable 56 3.5.6 Restraint 57 3.5.7 Interpolation 57 3.5.8 Function 58 3.6 Summary 60 CHAPTER 4 CABLE-STAYED BRIDGES 63 4.1 Introduction 63 4.2 Cable System 65 4.3 Mechanical Behaviors 67 4.3.1 Stiffness Distribution 67 4.3.2 Backstay Cables 68 4.3.3 Nonlinear Behaviors 69 4.4 Analysis Methodology 70 4.4.1 Cable Sag Effect 70 4.4.2 Large Deflection and P-Delta Effect 71 4.4.3 SAP2000 71 4.4.4 FrameCS 73 4.5 Representative Cable-Stayed Bridges 73 4.5.1 Single-Pylon Cable-Stayed Bridges with Sparse Stay-Cables 74 4.5.1.1 Kniebrucke 74 4.5.1.2 Oberkassel Bridge 75 4.5.1.3 Fleher Bridge 76 4.5.1.4 Dazhi Bridge 77 4.5.2 Single-Pylon Cable-Stayed Bridges with Dense Stay-Cables 78 4.5.2.1 East Huntington Bridge 78 4.5.2.2 Veterans'' Glass City Skyway 79 4.5.2.3 Rugen Bridge 80 4.5.2.4 Eilandbrug 81 4.5.2.5 Erasmusbrug 82 4.5.2.6 Bickensteg 83 4.5.2.7 Samuel Beckett Bridge 84 4.5.2.8 Gaoping River Cable-Stayed Bridge 85 4.5.2.9 Shezi Bridge 86 4.5.3 Double-Pylon Cable-Stayed Bridges with Sparse Stay-Cables 87 4.5.3.1 Erskine Bridge 87 4.5.3.2 Stromsund Bridge 88 4.5.3.3 Beeckerwerther Bridge 89 4.5.4 Double-Pylon Cable-Stayed Bridges with Dense Stay-Cables 90 4.5.4.1 Pasco-Kennewick Bridge 90 4.5.4.2 Sunshine Skyway Bridge 91 4.5.4.3 Helgeland Bridge 92 4.5.4.4 Barrios de Kuna Bridge 93 4.5.5 Special Cable-Stayed Bridges 94 4.5.5.1 Alamillo Bridge 94 4.5.5.2 Puerto Madero Footbridge 95 4.5.5.3 Turtle Bay Sundial Bridge 96 4.6 Empirical Design Parameters 97 4.6.1 Pylon Height 97 4.6.2 Girder Depth 99 4.6.3 Cable Anchorage Spacing 103 4.6.4 Span Ratio 104 4.7 Standard Cable-Stayed Bridges 106 4.7.1 General Design Parameters 106 4.7.2 Standard Single-Pylon Cable-Stayed Bridge 107 4.7.3 Standard Double-Pylons Cable-Stayed Bridge 109 4.8 Summary 110 CHAPTER 5 APPLICATIONS OF SODIUMM 111 5.1 Sizing Optimization 111 Example 5.1.1 – Sizing Optimization of 10-bar 2D Cantilever Truss 111 Example 5.1.2 – Sizing Optimization of 30-bar 3D Truss 115 5.2 Shape Optimization 118 Example 5.2.1 – Shape Optimization of 13-bar Simply-supported Truss 118 Example 5.2.2 – Shape Optimization of 37-bar Simply-supported Truss Bridge 120 5.3 Shape and Sizing Combined Optimization 122 Example 5.3.1 – Shape and Sizing Combined Optimization of 18-bar Truss 122 5.4 Optimal Design of Cable-Stayed Bridges 127 5.4.1 Post-tensioning Cable Force 127 Example 5.4.1 – Optimal Cable Forces of a Simple Cable-Stayed Bridge 128 Example 5.4.2 – Optimal Cable Force of a Harp-type Cable-Stayed Bridge 131 Example 5.4.3 – Optimal Cable Forces of a Fan-type Cable-Stayed Bridge 136 Example 5.4.3* – Optimal Cable Forces of a Fan-type Cable-Stayed Bridge 141 Example 5.4.4 – Optimal Cable Forces of a 3D Semi-Fan Cable-Stayed Bridge. 146 5.4.2 Pylon Height 150 Example 5.4.5 – Optimal Pylon Height of Single-Pylon Cable-Stayed Bridge 151 Example 5.4.6 – Optimal Pylon Height of Double-Pylon Cable-Stayed Bridge 155 5.4.3 Locations of Cable Anchorages 159 Example 5.4.7 – Optimal Cable Anchorage Locations of Single-Pylon C-S Bridge 160 Example 5.4.8 – Optimal Cable Anchorage Locations of Double-Pylon C-S Bridge 164 5.4.4 Span Ratio 168 Example 5.4.9 – Optimal Span Ratio of Single-Pylon Cable-Stayed Bridge 169 Example 5.4.10 – Optimal Span Ratio of Double-Pylon Cable-Stayed Bridge 173 5.4.5 Inclined Pylon 177 Example 5.4.11 – Optimal Pylon Angle of Single-Pylon Cable-Stayed Bridge 178 Example 5.4.12 – Optimal Pylon Angle of Double-Pylon Cable-Stayed Bridge 185 5.4.6 Curved Pylon 189 Example 5.4.13 – Optimal Pylon Curve of Dazhi Bridge 190 5.4.7 Manual Iterative Operation 196 Example 5.4.14 – Optimal Pylon Shape and Cable Anchorage Locations 197 5.5 Optimization of Mathematical Problems 201 Example 5.5.1 – Optimization of Mathematical Problem: Rosenbrock Function 201 Example 5.5.2 – Optimization of Mathematical Problem: Himmelblau''s function 203 5.6 Summary 205 CHAPTER 6 CONCLUSIONS AND FUTURE WORK 207 6.1 Conclusions 207 6.2 Future Work 208 REFERENCES 211