鄧佳怡

學號：402380512 (Jia-Yi Deng)

論文名稱

摺疊模型之實作與結構力學分析 (Implementation and Structural Mechanics Analysis of Origami Folding Models)

關鍵詞

摺疊結構、摺紙、泊森比、勁度、應變 (Folding structures, Origami, Poisson’s ratio, Stiffness, Strain)

DOI

https://doi.org/10.6846/TKU.2019.00409

中文摘要

摺疊結構為結構力學與工程科學之一新興研究領域，其優點在於透過摺疊單元的配置，得以調整結構本身的勁度，進而達到更好的結構承載效率，並且因為其摺疊紋理的特殊結構型式，結構除能收縮至一定的限制空間大小外，亦能使得結構大幅增進承載之能力。摺疊結構，為現代創新結構設計的代表之一，從大型的人造衛星天線的「三浦摺疊」結構，乃至山毛櫸樹葉的摺疊結構，小至蛋白質分子也擁有摺疊結構，並發揮其效用。結構經摺疊後，可以改變其勁度（或柔度），以此為增強原有系統的機械力學與空間使用之性能。

本研究對多個摺疊模組進行摺疊分析，摺疊結構模擬計有：Miura、Eggbox、Flower Tower、Hypar、Whirlpool、Huffman Stars-Triangles、Waterbomb、Lang Wedged Double Faced Tessellation、Lang KNL Dragon、Kirigami Honeycomb，尤以 Miura 與 Eggbox 為主，除對摺疊紋理形成過程做一詳細觀察外，更以結構力學的角度，探討系統在各摺疊程度狀態下，所具有之不同力學性能，本研究針對了摺疊單元各方向之勁度：含有摺痕軸勁度（Axial Stiffness）、摺面面部勁度（Face Stiffness）、摺痕摺疊勁度（Fold Stiffness）、摺面摺疊勁度（Facet Crease Stiffness），對具不同摺疊比例狀態結構之影響進行探討，當中結構力學性質影響是以泊森比（Poisson’s ratio）數據做一完整呈現與比較。

英文摘要

The folded structure is an emerging research field in structural mechanics and engineering science. Its advantage is that the stiffness of the structure itself can be adjusted through the configuration of the folding unit, thereby achieving better structural bearing efficiency, and because of the special structure of the folded texture, In addition to shrinking the structure to a certain size of the restricted space, the structure can also greatly enhance the capacity of the structure. Folding structure, one of the representatives of modern innovative structure design, from the “Sanpu folding” structure of large artificial satellite antennas, to the folding structure of beech leaves, as small as protein molecules also have a folded structure and exert its utility. After the structure is folded, its stiffness (or flexibility) can be changed to enhance the mechanical and spatial performance of the original system.

In this study, multiple folding modules were analyzed for folding. The folding structure simulations were: Miura, Eggbox, Flower Tower, Hypar, Whirlpool, Huffman Stars-Triangles, Waterbomb, Lang Wedged Double Faced Tessellation, Lang KNL Dragon, and Kirigami Honeycomb. Based on Miura and Eggbox, in addition to a detailed observation of the folding texture formation process, the mechanical properties of the system are discussed in terms of structural mechanics. The study is aimed at the various directions of the folding unit. Stiffness: Axial Stiffness, Face Stiffness, Fold Stiffness, Facet Crease Stiffness, different folds. The influence of the proportional state structure is discussed. Among them, the influence of structural mechanics is a complete presentation and comparison with Poisson’s ratio data.