- 學位論文
結構最佳化軟體開發：應用於斜張橋設計
Development of Structure Optimal Design Software: Applications in Cable-Stayed Bridge Design
摘要
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。
並列摘要
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.