- 學位論文
應用移動漸近線法於結構拓樸最佳化之研究
Structural Topology Optimization by Method of Moving Asymptotes
摘要
本論文是應用移動漸近線法於結構拓樸最佳化之研究。研究中使用ANSYS做為結構分析的工具，並利用拓樸設計方法中之複合材料分配法配合移動漸近線法以獲得最佳結構外形。在本文中使用移動漸近線法和對偶法找出初始的拓樸結構外形，再使用混合法同時保留必要元素與排除非必要元素來減少不合理之情形外，並應用B-spline函數之概念，定義設計參數上下限來平滑結構外形。本研究之目的為在滿足結構固定體積之限制條件下達到最小順從度之目標。研究顯示利用移動漸近線法快速收歛的優點，可以在最佳化的過程中迅速的得到最佳拓樸設計。 本研究以七個不同結構範例探討結構最佳化設計問題，其結果顯示，吾人採用移動漸近線法搭配拓樸最佳化理論，無論在二維或是三維的結構上，都可以得到較平滑的結構外形，達到更具實用性之設計。
並列摘要
A methodology of topology optimization design by Method of Moving Asymptotes was used in this study. The finite element analysis software ANSYS was used for structural analysis. The optimum shape design was obtained by the concept of material distribution borrowed from density method with Method of Moving Asymptotes and dual method. In addition to using the element growth-removal combined method simultaneously to grow and remove the essential element and the non-essential element, the concept of B-spline curve was used to smooth the design shape. The objective of the structural topology design is to find the minimum structural compliance subject to the desired structural volume. The advantage of Method of Moving Asymptotes is that the optimum topology design can be obtained efficiently in the design cycles. Seven examples were discussed in the numerical examples. By using Method of Moving Asymptotes, the final results of optimum topology design was better than the first stage design in two or three dimensional structures. After the proposed design algorithm, the primitive optimum design can be improved to more practical design in this study.