本文使用李宗豪所開發的最佳化設計系統(李宗豪2005)作為最佳化設計工具,針對橋梁形式與構件配置位置做最佳化設計。有鑑於橋梁在設計上多由經驗決定,為了增加橋梁的經濟性,本研究將利用一個兩階段的最佳化流程,配合有限元素商業軟體ABAQUS,將橋梁設計的種種參數列入最佳化設計變數中, 在先前的研究中,拓樸最佳化和尺寸形狀最佳化以一個兩階段流程的方式分開進行,利用拓樸最佳化得到的結果,作為尺寸形狀最佳化的初始設計,再以尺寸與形狀最佳化進行細部設計。本研究針對兩階段流程的第一階段,也就是拓樸最佳化的部分做進一步的開發,主要是企圖在這個階段中,找尋最佳支承位置或者多重材料之分配方式的同時完成拓樸最佳化。得到需要的拓樸型式後,就可以依先前研究的流程,利用各種不同的判斷方法連接桿件,進行尺寸、形狀和預拉力的最佳化,利用電腦反覆運算分析得到用量最省、工程造價最低且均滿足所有限制條件下最經濟的橋梁形式,以提升橋梁實務施做時的便利與準確。另外,本研究也針對拓樸最佳化的移除準則做簡化,讓反覆運算的迭代次數明顯減少,同時得到與過去的移除準則相近的拓樸結果。
Since engineers make use of experience to design bridge structures, to be more economic, this research carries out an optimization procedure to find the design variables in the bridge structure. This research uses the optimization system developed by Li(2005)to carry out topology, sizing and shape optimization in bridge structure design. In the past, a two-step procedure is used in topology optimization and sizing, shape optimization. First, topology optimization is used to find the rough structure appearance. After that, sizing and shape optimization is used to find the detail design of bridge structure. Based on the first step, this research finds the optimal position of supports and the distribution of multiple-material. According to different kinds of remove criterion, including energy, tension, and compression, evolutionary structural optimization (ESO) can find various kinds of bridge appearance. Then combining topology and sizing, shape optimization, this research carries out a procedure to decide the connecting point and element for sizing and shape optimization. Also, a simple remove criterion is used in this research to reduce the iteration numbers. The criterion can provide results which are similar to previous researches with less iteration.