拓樸優化是門廣泛應用在各領域的結構優化方法，能幫助設計者在給定的邊界條件與體積限制下計算出最佳的結構。在積層製造技術尚未發達前，複雜的拓樸結構製造上有相當高的難度，但現今積層製造技術已日趨成熟，大幅減低了拓樸結構製造的成本，也使更多拓樸設計能運用在實際生活上。目前已經有學者嘗試以拓樸優化設計通孔鞋中底結構，為了計算出高精度的設計，該設計採用大量的有限元素網格，因此需要大量的運算才能完成該拓樸結構。有鑑於此，本研究開發了一套快速的通孔鞋中底設計演算法，建立在桁架尺寸優化與體素後處理技術上，其優化後的模型為近似通孔之中底結構。演算法流程是先在設計空間中建立好桁架結構，將桁架中的桿件依應力大小分群，利用分群優化演算法計算出各桿件的最佳截面面積，接著將所有桿件做布林運算得出最佳的桁架結構，再利用體素後處理技術對結構做三維模糊卷積，以達到修邊與體積補償。本文最後分別以女鞋楦與男鞋楦自動生成中底通孔中底結構去驗證此演算法的可行性，證實此優化流程能快速且有效的優化出最佳中底結構。

Topology optimization (TO) is a method of structural optimization which widely used in many fields. The concept of TO is to get the best structure in the design domain under the volume constraints. Before additive manufacturing (AM) evolved to become a common method to produce components, the complicate topology structure is hard to be fabricated. However, AM was substantial growing in the past decades and the difficulty of topology structure fabrication had been dramatically reduced. Therefore, more and more topology structure can be used in our daily life. Now, some researcher started to use TO to design porous midsole structure. In order to calculate with high precision, the design needs amounted mesh in finite element and thus the computation task is very heavy. This research presents a fast approach of porous midsole design which is based on truss size optimization and post-processing of voxelization and gets the optimal porous-like structure. The algorithm flow starts with building the truss in the design domain and clustering the truss member by simulating each member stress with loading. Then it uses clustering optimization algorithm to find the best size of each truss member. After that, the algorithm uses Boolean operation to unite all members of the truss and 3D blur convolution to fillet the truss structure and compensate the volume error. In the final, we use two shoe lost to verify the feasibility of this methods and the results show that this is a fast and efficiency manner.

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