基因演算法於結構拓樸最佳化之應用

Continuum Structural Topology Optimization with Genetic Algorithms

吳啟誠(Qi-Cheng Wu)

指導教授 ： 黃仲偉

中原大學/工學院/土木工程研究所/碩士(2009年)

https://doi.org/10.6840/CYCU.2009.00780

摘要

摘要

結構拓樸最佳化設計可視為在設計領域之內尋求材料的最佳配置，不但可以節省材料的使用，同時亦可顯示出結構物受力後的內力傳遞路徑，在實務與應用上是相當重要的議題。本研究利用基因演算法二進位編碼的特性於求解單一材料的結構拓樸最佳化設計問題，並探討相關參數對拓樸最佳化的影響。由於基因演算法屬於零階的最佳化方法，迭代計算過程中無須計算目標函數和限制式的導數，故利用懲罰函數的觀念可以輕易地在結構拓樸最佳化設計中考慮不同的功能限制式。

數值模擬顯示出此種基因拓樸演算法可提供設計者較佳的結構拓樸形狀，而所考慮的限制條件亦可適當的反映在最後所得的拓樸形狀之中。由於基因演算法所需的計算量相當龐大，故本文分別利用微基因演算法、複合式基因演算法與適應性網格三種方式進行改善。數值結果顯示適應性網格法效果最佳，可大幅減少所需的計算量。

關鍵字

基因演算法 ； 拓樸最佳化 ； 懲罰函數 ； 微基因演算法 ； 複合式基因演算法 ； 適應性網格

並列摘要

Abstract

Structural topology optimization can be interpreted as seeking the optimal distribution of materials in the given design domain. The optimal topologies which can save materials and provide the load paths of the external loadings are important issues in practical designs and applications. In this paper, the single material structural topology optimization problem is solved by making use of the characteristics of binary codes of the genetic algorithm. The values of relevant parameters in the genetic algorithm are studied for the structural topology optimization problems. Because the genetic algorithm belongs to the zero-order optimization method, there is no need to calculate derivatives of the objective function and constraints in the iterative process. As a result, different constraints can be easily considered as penalty terms through the penalty function method.
Numerical examples demonstrate that the optimal structural topology can be obtained through the genetic algorithm. In addition, different constraints can be added into the pseudo-objective function and the corresponding final topology can reflect the presence of constraints. To reduce the computational cost, three methods that include micro genetic algorithm, compound genetic algorithm, and adaptive mesh are proposed. Numerical experiences show that the required enormous computation time of the genetic algorithm can be effectively reduced with the aids of the adaptive mesh.

並列關鍵字

Penalty function ； Genetic algorithm ； Topology optimization ； Micro-genetic algorithm ； Compound genetic algorithm ； Adaptive mesh

參考文獻

Baumgartner, A., Harzheim, L., and Mattheck C., 1992, “SKO (soft kill option): the biological way to find an optimum structure topology,” International Journal of Fatigue, Vol.14, No. 6, pp. 387-393.

Bendsøe, M. P., and Kikuchi, N., 1988, “Generating optimal topologies in structural design using a homogenization method,” Computer Methods in Applied Mechanics and Engineering, Vol. 71, pp.197-224.

Bendsøe, M. P., 1989, “Optimal shape design as a material distribution problem,” Structural Optimization, Vol. 1, pp. 193-202.

Carroll, D. L., 1996, “Chemical laser modeling with genetic algorithms,” AIAA Journal, Vol. 34, No. 2, pp. 338-346.

Chapman, C. D., Saitou, K., and Jakiela, M. J., 1994, “Genetic algorithm as an approach to configuration and topology design,” Journal of Mechanical Design, Vol. 116, No. 4, pp. 1005-1012.