Contact Professor: Yeh-Liang Hsu (徐業良)

# 84碩士論文：從形式幾何最佳化到形態最佳化設計之整合

在進行形態最佳化設計時，必須先給定一個初始設計模型，進而設計出結構的最佳形態，然而在形態最佳化設計過程中，並無法改變結構的形式幾何，如果結構的初始設計“不佳”，則依據此形式幾何經過型態最佳化設計，所得之結果是在這個形式幾何之下的最佳設計，對整個結構來說可能不是最佳的，而結構最佳化設計的另一個領域，形式幾何最化設計，目的正好是幫助設計者尋找較佳的初始設計形式幾何，本研究擬整合形式幾何最佳化與形態最佳化為一完整的結構型態最佳化設計程序，將形式幾何最佳化設計作為概念設計，此階段著重在結構的整體特性，如：結構順從度，剛性或最小自然頻率等，並利用形式幾何最佳化設計所得的設計結果， 為形態最佳化設計的初始設計模型，在利用形態最佳化設計對結構進行細部設計，此階段著重在結構的區域特性，尤其以區域應力較為工程師所重視且重要的限制條件，並結合二維零次形態最佳化演算程序：骨架曲率函數法，進而求取結構的最佳設計型態。

# Integration of Structural Topology Optimization and Shape Optimization

An initial design model has to be defined before strating shape optimization. In shape optimization, the designer can not change the topology of the structure. If the topology of the initial design model is not optimal, the result, after shape optimization, using this initial topology, is only the optimum design under this topology. Therefore the purpose topology of the structure. This research attempts to integrate topology optimization and shape optimization into one complete design process. First,we use topology optimization as a conceptual design process. In topology optimization, the global property ( For example, compliance, stiffness, and smallest nature frequency, etc., ) is considered. The result from topology optimization is used to define the initial design model for shape optimization. Then shape optimization is viewed as the detail design process of the structure. In shape optimization, the local property is considered. Especially, the local stress is the most important constraints thatis consider by engineers. Finally, we use two dimensional zeroth order shape ptimization algorithm, namely the Skeleton Curvature Function Method, to find the optimal design of the structure.