應用元素交換法於三維結構拓樸最佳化

Abstract

過往一些對於結構拓樸最佳化之研究及程式，多限於二維平面空間，大大限制了結構拓樸最佳化之適用範圍。而本研究嘗試將現有結構拓樸最佳化之應用，拓展至三維立體空間，如此將能更廣泛地運用於各種問題。 由於三維之結構分析將更為複雜且艱難，故本研究中使用有限元素商業軟體ABAQUS作為分析引擎，利用ABAQUS模型資料輸入檔及結果輸出檔案，使用自行以MATLAB開發之元素交換法演算程式進行讀取、演進及修改，再呼叫ABAQUS進行分析，以迭代得到最佳化之拓樸形狀。 而本研究團隊近年所主要使用之演進式結構最佳化系列方法，如ESO、BESO、GESO、EEM等等，此系列方法使用離散設計變數，相較於其他使用連續設計變數之方法，於拓樸形狀容易界定範圍，且須定義之材料種類與變化較少，更適合於ABAQUS中使用；且本系列方法運算上較為容易，實際應用之可能性較高。本研究選擇使用此系列之EEM方法（Element Exchange Method，簡稱為EEM; Rouhi et al. 2010），此方法之特點在於保有BESO雙向演化之優點，卻簡化BESO繁瑣的投影策略，使最佳化設計具有更大之自由度。 本研究中之程式設計方面，先探討ABAQUS資料輸入與輸出之規則，再進行MATLAB之程式撰寫。MATLAB程式分為資料擷取模組、最佳化演算模組、模型修改模組、分析程式驅動模組；並增加不可設計領域、同步交換、多組受力組合、自動決定初始拓樸之設定。 而後以文獻中所提供之例題，與此演算程式所產生之結果相互比對，發現結果吻合。再以一些自行設計之例題加以測試，從結果中可發現，最後之拓樸形狀均符合結構猜想，且材料均發揮出較佳之效能。

For the past research of structural topology optimization, mostly limited to two-dimensional space, greatly limiting the scope of application. To widely use in more kinds of issues, an attempts to expand the subject into three-dimensional space is proposed in this thesis. Since the three-dimensional structural analysis will be more complex and difficult, in this thesis, the FEM commercial software ABAQUS is used as an analysis engine, and MATLAB is used to do the iteration. Element Exchange Method（EEM; Rouhi et al. 2010）uses a series of discrete design variables, more suitable for ABAQUS than other methods of continuous design variables. In this thesis, the first part is about coding the structure topology optimization. We investigated the writing rules of ABAQUS input and output file, then used MATLAB to read and write. In the MATLAB code, there are four module: data acquisition, optimization, model modification, and analyzes driving. In addition, we added four features: non-design area, synchronous exchanging, multiple combinations of force, and determine the initial topology automatically. The second part is testing. We used examples from past research, and some own designed example to do the optimization. The result shape shows that the materials have a better performance.