結合線性規劃法與改良式調和搜尋演算法於結構拓樸最佳化之研究

Structural Topology Optimization by Linear Programming and Improved Harmony Search Algorithms

陳柏均(Bo-Jyun Chen)

指導教授 ： 張永康

淡江大學/工學院/航空太空工程學系碩士班/碩士(2017年)

https://doi.org/10.6846/TKU.2017.00036

摘要

本論文是結合線性規劃法與改良式調和搜尋演算法於結構拓樸最佳化之研究。研究中以ANSYS做為結構分析工具，並使用複合材料分配法做為拓樸設計方法，再以線性規劃法與改良式調和搜尋演算法獲得最佳結構之材料分佈。在本文中利用線性規劃法找出初始結構外形，再以改良式調和搜尋演算法改善模糊元素與結構不連續之情形，以求得更佳之結構外形，最後再以B-spline函數之概念，定義設計變數上下限來平滑結構外形。本研究應用以上演算法，可達到最小結構順從度，並滿足體積限制之要求，更能獲得較合理之結構材料分佈。本研究以六個不同範例執行結構拓樸最佳化設計，其結果顯示本研究所採用之方法能處理大量變數之結構拓樸設計問題，並能得到明確的結構幾何形狀。

關鍵字

拓樸最佳化 ； 線性規劃法 ； 調和搜尋演算法

並列摘要

A methodology of topology optimization design by Linear Programming and Improved Harmony Search Algorithms was used in this study. The finite element analysis software ANSYS was used for structural analysis. The optimal topology design was obtained by the concept of material distribution borrowed from density method with Linear Programming and Improved Harmony Search Algorithms. In this paper, the first stage optimum structure was obtained by Linear Programming. The second stage optimum design structure was determined by eliminating the unnecessary and discontinuity element with Improved Harmony Search Algorithms. The final stage optimum design of structure was obtained by using B-spline function to smooth the design shape. Application of the above algorithms, the minimum compliance and reasonable topology design shape can be obtained.
There are six different structures were discussed in this study. The final results of optimum design were better than initial design. The proposed algorithm in this study was proved effectively.

並列關鍵字

Topology Optimization ； Linear Programming ； Harmony Search Algorithm

參考文獻

[16] 陳聖宗，「應用調和搜尋演算法於結構最佳化之研究」，淡江

[33] 劉宇哲，「改良式調和搜尋演算法於結構之最佳化設計」，淡江

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