本研究探討隨機化對於拓樸最佳化之結果影響,並運用結合基因演算法之結構最佳化演進法(GESO)以及元素交換法(EEM)此兩種拓樸最佳化方法來進行例題探討以及比較。 在進行最佳化時,並非皆能夠找到全域最佳解,常會找到區域最佳解,拓樸最佳化中也會遇到此種問題。因此若是加入隨機化步驟,希望進入區域最佳解時,能夠因為隨機使得當時的解能夠重新有機會再度找到全域最佳解。過去本研究團隊相關研究中所使用之拓樸最佳化設計方法包括結構最佳化演進法(ESO)以及雙向結構最佳化演進法(BESO)等,於拓樸最佳化中對於隨機化的加入之探討並不多,多只限於演算法之探討。 有鑑於此,具有隨機化之拓樸最佳化方法變成為研究目標,其中將結合基因演算法之結構最佳化演進法與原先結構最佳化演進法進行比較,探討其置入基因演算法概念之效果,比較後可以觀察出隨機化之效果。再來利用元素交換法進行例題比較,此方法之基本概念簡單並且操作容易,並且在其中步驟也具有隨機化之特性,而且在所得到之拓樸結果達到不錯的適應性。因此元素交換法便成為本研究中之主軸。 雖然元素交換法之適應性不錯,但仍然有諸多缺點包括體積比之固定、對稱性限制等問題。因此本研究將此些問題加以改善,提出一改良型元素交換法使得其成為更具有彈性且適應性極高的方法。在解決先前研究中(呂其翰2010)之雙重材料分配在材料由硬變軟以及由軟變硬情況下,不須增加額外的手段即可一次解決。而在大量的例題,其中包括2D以及3D結構設計下也得到適應性高的驗證。最終將元素交換法推展至多重材料分配之三種材料以上問題上,也得到了不錯的結果。
The scope of this research is to study the effects of stochastic methods used in topology optimization, namely “Genetic Evolutionary Structural Optimization (GESO)” and “Element Exchange Method (EEM)”. Usually the optimization problems, yields local optimum rather than global optimum. This local optimum problem also appears in topology optimization. By using stochastic methods, the local optimum solution gets chance to approach global optimum. In the past few years, the studies on topology optimization methods such as “Evolutionary Structural Optimization (ESO)” and “Bi-directional Evolutionary Structural Optimization (BESO)” by this research group have not studied the stochastic methods used in topology optimization. In view of the study in the past few years, this research aims to use the stochastic methods in topology optimization. The effect participated by genetic algorithm in GESO is studied here. Further, this research compares the cases by using Element Exchange Method, which has a simple basic concept and can be operated easily, to get the topology results which shows that the EEM is a high flexibility method. Because of the high flexibility in EEM, this research uses EEM as a main topology optimization method. Although the Element Exchange Method is a highly flexible method in topology optimization, it still has some limitations such as the fixed volume ratio, the limitation of symmetry problem, etc. To improve EEM and solve its weaknesses, this research proposes a new approach - “Modified Element Exchange Method (MEEM)”, which has more flexibility and more advantages. MEEM is also found to produce good results for multi-material problems in topology optimization.