臺灣博碩士論文加值系統

近年來，摺紙文化啟發了很多科學研究與實際應用，而其中一種結構「三浦」(Miura)的摺紙設計更被學者們廣泛的研究，且具輕量化、高可變性、高即時變形能力等等的構件，已經廣泛應用於航太工程、家具裝飾與心血管支架等。然而這樣的結構卻未出現在土木結構上，國內的相關研究亦屈指可數。本文的目的在於評估三浦摺紙力學性能，並利用摺紙結構的優點應用在土木領域。
首先由三浦結構的幾何切入，藉由多次的投影技巧，將整個幾何關係公式化，尤其是單一細胞單元到多層結構的幾何尺寸、負波松比與密度；其次，提出一桁架桿件與抗彎彈簧模型分別模擬面內拉剪與面外撓曲，考慮在不同外力與邊界條件下，建立簡化的分析方法來替代複雜的有限元素分析。最後，比較簡化桁架與有限元素軟體，簡化桁架有更簡單更有效率的優點，並且可以被應用於更複雜的折紙結構模擬與最佳化幾何參數問題。

Recently, origami inspires many scientific studies and practical application. One of famous origami forms is Miura-origami, which has been widely studied by many researchers. It is deployable, self-adaptable, light-weight, and has been applied on aerospace engineering, biological engineering, furniture and so forth. However, little research has been explored for civil engineering in Taiwan. This thesis aims to investigate the mechanical properties of Miura-origami and utilize its advantages to the field of civil engineering.
First, geometry plays a key role in the mechanical properties of Miura-origami. The geometric relations of origami can be formulated by use of projection to three planes in space, especially for Poisson’s ratio and density from unit Miura cell to stacking of individual folded layers. Second, truss members and rotational springs are utilized to simulate the behaviors of in-plane stretching and shearing and out-of-plane bending of flat panel. When various force and boundary conditions are imposed, this simplified structural model is developed to replace more complicated finite element analysis.
Finally, the results indicate that such a simplified method is simpler and more efficient than the finite element one. This simplicity makes it well suited for simulating more complex origami structures and finding their optimized geometric parameters.

中文摘要 i
英文摘要 ii
誌謝 iii
目錄 iv
圖目錄 v
第一章 緒論 1
1.1 研究背景與動機 1
1.2 文獻回顧 2
1.3 研究內容與流程 3
第二章 Miura三浦摺紙的基本幾何 4
2.1單細胞幾何 5
2.2單層Miura-origami 10
2.3多層Miura-origami幾何 12
2.4小結 17
第三章 分析方法 18
3.1平面內拉力、壓力與剪力 22
3.1.1 公式推導 22
3.1.2 模型驗證 25
3.2面外撓曲 30
3.2.1 公式推導 31
3.2.2 模型驗證 36
第四章 案例分析 38
4.1單細胞結構 38
4.1.1 集中載重 39
4.1.2 均佈載重 46
4.2 多細胞結構 50
4.3 小結 60
第五章 結論與建議 61
5.1結論 61
5.2建議 62
5.3未來展望 62
參考文獻 64

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