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。

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.

目錄
第一章、導論	1
1-1 研究動機	1
1-2 研究目的	2
1-3 文獻回顧	3
1-4 研究內容	4
第二章、摺疊結構理論	5
2-1 紋理結構	5
2-1-1 摺疊結構–Miura（三浦摺疊）	8
2-1-2 摺疊結構–Eggbox	9
2-1-3 摺疊結構–Flower Tower	10
2-1-4 摺疊結構–Hypar	11
2-1-5 摺疊結構–Whirlpool（渦流）	12
2-1-6 摺疊結構–Huffman Stars-Triangles	13
2-1-7 摺疊結構–Waterbomb	14
2-1-8 摺疊結構–Lang Wedged Double Faced Tessellation	14
2-1-9 摺疊結構–Lang KNL Dragon	15
2-1-10 摺疊結構–Kirigami Honeycomb	16
2-2摺疊模型製造之程式開發- MATLAB	16
2-3摺疊軟體Origami Simulator介紹	17
2-4泊森比	20
第三章、摺疊結構軟體操作	22
3-1 摺疊生成軟體MATLAB操作	23
3-2 摺疊軟體Origami Simulator之操作	24
3-5本章小結	27
第四章、摺疊結構模擬成果	28
4-1摺疊結構–Miura	28
4-1-1泊森比-Miura	30
4-2 摺疊結構–Eggbox	43
4-2-1泊森比（Poisson’s Ratio，ν）-Eggbox	45
4-3 摺疊結構–Flower Tower	66
4-4 摺疊結構–Hypar	71
4-5	摺疊結構–Whirlpool	76
4-6	摺疊結構–Huffman Stars-Triangles	78
4-7 摺疊結構–Waterbomb	83
4-8摺疊結構–Lang Wedged Double Faced Tessellation	87
4-9 摺疊結構–Lang KNL Dragon	92
4-10 摺疊結構–Kirigami Honeycomb	94
第五章、結論與展望	99
5-1 結論	99
5-2 展望	99
參考文獻	101 
圖目錄
圖一	摺疊結構綜觀	2
圖二	本研究摺疊結構模擬圖	7
圖三	Miura結構伸縮圖	8
圖四	Miura三明治結構圖	9
圖五	Eggbox摺疊結構圖	10
圖六	衛星面板的摺紙圖與Flower Tower摺紙模擬圖對比	11
圖七	Hypar摺疊結構摺線圖	12
圖八	Whirlpool摺疊結構摺痕圖	13
圖九	Huffman Stars-Triangles摺疊結構摺痕圖	13
圖十	Waterbomb摺疊結構摺痕圖	14
圖十一	Lang Wedged Double Faced Tessellation摺疊結構摺痕圖	15
圖十二	Lang KNL Dragon摺疊結構摺痕圖	15
圖十三	Lang KNL Dragon摺疊結構的改變	16
圖十四	Kirigami Honeycomb摺疊結構摺痕圖	16
圖十五	軟體MATLAB頁面圖	17
圖十六	摺疊軟體Origami Simulator頁面圖	18
圖十七	簡易摺疊圖	18
圖十八	摺疊結構單元各方向勁度之說明與示意圖	18
圖十九	摺疊結構單元各方向勁度之影響示意圖	20
圖二十	橫向應變、縱向應變示意圖	21
圖二十一	摺疊結構生成模擬步驟一	22
圖二十二	摺疊結構生成模擬步驟二	23
圖二十三	摺疊軟體Origami Simulator之操作步驟	24
圖二十四	摺疊軟體Origami Simulator設定畫面	25
圖二十五	摺峰、摺谷與邊界顏色設定顯示圖	26
圖二十六	Miura摺疊結構之摺疊檢核	30
圖二十七	Miura橫向應變及縱向應變與摺疊比率之變化圖	32
圖二十八	Miura摺疊結構之摺疊比率與泊松比之關係圖	32
圖二十九	Miura橫向應變及縱向應變與摺痕軸勁度之變化圖	34
圖三十	Miura摺疊結構之摺疊比率與泊松比之關係圖	35
圖三十一	Miura橫向應變及縱向應變與摺面面部勁度之變化圖	37
圖三十二	Miura結構之面部勁度與泊森比關係	37
圖三十三	Miura橫向應變及縱向應變與摺痕摺疊勁度之變化圖	39
圖三十四	Miura橫向應變及縱向應變與摺面摺疊勁度之變化圖	41
圖三十五	Miura結構之摺面摺疊勁度與泊松比關係圖	42
圖三十六	Eggbox摺疊結構之摺疊檢核	45
圖三十七	Eggbox摺疊結構應變與摺疊比率之變化	46
圖三十八	Eggbox摺疊結構之摺疊比率與泊松比之關係圖	47
圖三十九	Eggbox橫向應變及縱向應變與軸勁度（Axial Stiffness）之變化圖	49
圖四十	軸勁度與泊森比關係	49
圖四十一	Eggbox摺疊結構摺疊比率0％時之模擬圖	50
圖四十二	Eggbox橫向應變及縱向應變與摺面面部勁度之變化圖	52
圖四十三	Eggbox結構之面部勁度與泊森比關係圖	52
圖四十四	Eggbox結構之面部勁度與泊森比關係	54
圖四十五	Eggbox結構之面部勁度與泊森比關係	54
圖四十六	Eggbox橫向應變及縱向應變與摺疊勁度（Fold Stiffness）之變化圖	56
圖四十七	Eggbox結構之摺痕摺疊勁度與泊森比關係圖	57
圖四十八	Eggbox結構之摺疊勁度與泊森比關係	58
圖四十九	Eggbox結構之摺痕摺疊勁度與泊森比關係	59
圖五十	Eggbox橫向應變及縱向應變與摺面摺痕勁度（Facet Crease Stiffness）之變化圖	61
圖五十一	Eggbox結構之摺面摺痕勁度與泊森比狀況	61
圖五十二	Eggbox橫向應變及縱向應變與摺面摺痕勁度（Facet Crease Stiffness）之變化圖	63
圖五十三	Eggbox結構之摺面摺痕勁度與泊森比狀況	63
圖五十四	Eggbox橫向應變及縱向應變與摺面摺痕勁度（Facet Crease Stiffness）之變化圖	65
圖五十五	Eggbox結構之摺面摺痕勁度與泊森比狀況	65
圖五十六	Flower Tower摺疊結構之摺疊檢核	67
圖五十七	Flower Tower橫向應變及縱向應變與摺疊比率之變化圖	70
圖五十八	Flower Tower摺疊結構之摺疊比率與泊松比之關係圖	70
圖五十九	Hypar摺疊結構之摺疊檢核	72
圖六十	Hypar橫向應變及縱向應變與摺疊比率之變化圖	75
圖六十一	Hypar摺疊結構之摺疊比率與泊松比之關係圖	75
圖六十二	Whirlpool摺疊結構之摺疊檢核	77
圖六十三	Huffman Stars-Triangle摺疊結構之摺疊檢核	80
圖六十四	Huffman Stars-Triangle橫向應變及縱向應變與摺疊比率之變化圖	82
圖六十五	Huffman Stars-Triangle摺疊結構之摺疊比率與泊松比之關係圖	82
圖六十六	Waterbomb摺疊結構之摺疊檢核	84
圖六十七	Waterbomb橫向應變及縱向應變與摺疊比率之變化圖	86
圖六十八	Waterbomb摺疊結構之摺疊比率與泊松比之關係圖	87
圖六十九	Waterbomb摺疊結構之摺疊檢核	89
圖七十	Lang Wedged Double Faced Tessellation橫向應變及縱向應變與摺疊比率之變化圖	91
圖七十一	Lang Wedged Double Faced Tessellation摺疊結構之摺疊比率與泊松比之關係圖	92
圖七十二	Lang KNL Dragon摺疊結構之摺疊檢核	94
圖七十三	Kirigami Honeycomb摺疊結構之摺疊檢核	96
圖七十四	Kirigami Honeycomb橫向應變及縱向應變與摺疊比率之變化圖	98
圖七十五	Kirigami Honeycomb摺疊結構之摺疊比率與泊松比之關係圖	98
表目錄
表一	摺疊軟體Origami Simulator設定面顏色、設定摺疊最大應變量	25
表二	摺疊軟體Origami Simulator設定面部顏色、設定最大應變量	26
表三	Miura結構橫向應變及縱向應變與摺疊比率之變化	30
表四	Miura結構之軸勁度與應變狀況	33
表五	Miura結構之面部勁度與應變狀況	36
表六	Miura摺痕摺疊勁度與應變狀況	38
表七	Miura結構之摺痕摺疊勁度與泊森比關係圖	39
表八	Miura摺面摺疊勁度與應變狀況	40
表九	Eggbox橫向應變、縱向應變即泊森比與摺疊比率之變化	46
表十	Eggbox軸勁度（Axial Stiffness）與應變狀況	48
表十一	Eggbox結構之面部勁度（Face Stiffness）與應變狀況	51
表十二	Eggbox結構之面部勁度（Face Stiffness）與應變狀況	53
表十三	Eggbox結構之摺痕摺疊勁度與應變狀況	55
表十四	Eggbox結構之摺痕摺疊勁度（Fold Stiffness）與應變狀況	57
表十五	Eggbox結構之摺面摺痕勁度（Facet Crease Stiffness）與應變狀況	60
表十六	Eggbox結構之摺面摺痕勁度（Facet Crease Stiffness）與應變狀況	62
表十七	Eggbox結構之摺面摺痕勁度（Facet Crease Stiffness）與應變狀況	64
表十八	Flower Tower結構橫向應變及縱向應變與摺疊比率之變化	68
表十九	Hypar結構橫向應變及縱向應變與摺疊比率之變化	73
表二十	Huffman Stars-Triangle結構橫向應變及縱向應變與摺疊比率之變化	81
表二十一	Waterbomb結構橫向應變及縱向應變與摺疊比率之變化	85
表二十二	Lang Wedged Double Faced Tessellation結構橫向應變及縱向應變與摺疊比率之變化	90
表二十三	Kirigami Honeycomb結構橫向應變及縱向應變與摺疊比率之變化	97

中文文獻
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