結合結構分析軟體與最佳化設計軟體之斜張橋設計

Abstract

在現代橋梁設計中，斜張橋作為當今中長跨度橋梁中最為常用的橋型之一，其通透輕盈的美學效果以及良好的經濟性能受到了建築師和工程師的一致認同。但是斜張橋可供選擇變化的設計參數眾多，在設計過程中，設計者對於橋塔高度、橋塔傾斜角度、橋塔曲率半徑、鋼索錨碇位置、鋼索數目、鋼索預力大小等，常受限於設計時程緊迫只得以類似之工程案例推估，無法逐一探索其是否為最經濟配置，且由於其鋼索系統的高度靜不定以及非線性性質使其若要進行最佳化設計時不僅有大量的設計變數，還有複雜的結構分析過程。 本文從結構最佳化及其軟體架構開始談起，並了解到斜張橋結構最佳化的難度，然後通過蒐集世界各地27座斜張橋的資料，做了參數分析，結合實際工程提出了單塔以及雙塔斜張橋最佳化設計的初始模型。 在有了斜張橋最佳化的初始模型後，利用結構分析軟體SAP2000所提供的強大分析能力，可以在計算斜張橋結構時考慮到其各方面的非線性行為。接下來結合本研究團隊開發之結構最佳化軟體SODIUMM，通過其對最佳化參數設定的靈活度可以在斜張橋最佳化中加入B-spline技術，雙層最佳化技術。在應用了以上技術之後，從斜張橋的初始模型出發，對其進行了最佳化設計，在眾多的最佳化設計結果基礎上，本文分析了B-spline對於斜張橋鋼索預力最佳化之意義，探討了不同目標函數對最佳化結果的影響，提出了一些可供工程師參考的設計準則，例如最佳壓重與跨度比的關係。 斜張橋設計是一項複雜的工作，本研究旨在通過最佳化技術解決斜張橋設計中的一部分問題，為工程師提供一個有力的設計工具以及一些設計準則。

The Cable-stayed bridge is one of the most popular bridge types chosen by architects or structure engineer in modern bridge design because of its aesthetic appeal and economy. When designing cable-stayed bridges, a lot of design variables such as cable forces, pylon height, number of cables need to be decided and it might be time consuming for engineers to consider them in detail. In addition, as cable-stayed bridges are highly undetermined with severe nonlinearity, complex and time-consuming structural analyses needs to be performed. The research mainly focuses on the optimization design of cable-stayed bridge. Design parameters are studied among 27 representative cable-stayed bridges in different classifications to provide practical design region. Initial models of optimization design for both single and double pylon configurations are proposed based on the above study. SAP2000 is used to analyze cable-stayed bridge structure because of its powerful nonlinearity ability. And SODIUMM is a flexible structure optimization software that supports SAP2000 as its structure analysis software. The B-spline technique and multi-level optimization scheme are implemented in SODIUMM and several cable-stayed bridge optimization examples are presented. The effect of B-spline and different objective functions is discussed based on the presented optimal solutions. Some simple design suggestions are made for engineers like counter weight value. Design of cable-stayed bridge is a tough task. The research is aimed at solving some specific problems of cable-stayed bridges and provide engineers an efficient way and optimization pattern for cable-stayed bridge.