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中文論文名稱 摺疊模型之實作與結構力學分析
英文論文名稱 Implementation and Structural Mechanics Analysis of Origami Folding Models
校院名稱 淡江大學
系所名稱(中) 土木工程學系碩士班
系所名稱(英) Department of Civil Engineering
學年度 107
學期 2
出版年 108
研究生中文姓名 鄧佳怡
研究生英文姓名 Jia-Yi Deng
學號 606380029
學位類別 碩士
語文別 中文
口試日期 2019-06-27
論文頁數 104頁
口試委員 指導教授-王建凱
委員-王建凱
委員-董奕鍾
委員-李家瑋
中文關鍵字 摺疊結構  摺紙  泊森比  勁度  應變 
英文關鍵字 Origami structures  structural mechanics  origami simulation  poisson’s ratio  stiffness  folding strain 
學科別分類 學科別應用科學土木工程及建築
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.
論文目次 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
參考文獻 中文文獻
[1] 鄭惟仁(2017),「最佳設計力學於摺疊結構之研究 Optimal Mehcanics of Origami Folding Structures」,碩士論文,淡江大學土木工程學系。
國外文獻
[1] Amanda Ghassaei, Erik D. Demaine, Neil Gershenfeld, “Fast, Interactive Origami Simulation using GPU Computation”, in Origami 7: Proceeding of the 7 th International Meeting on Origami in Science, Mathematics and Education (OSME 2018), Oxford, England, 5-7 September 2018.
[2] Erik D. Demaine, Jason S. Ku, and Robert J. Lang, “A New File Standard to Represent Folded Structures”, in Abstracts from the 26th Fall Workshop on Computational Geometry, October 27–28, 2016, to appear.
[3] Erik D. Eemaine, Martin L. Demaine, Vi Hart, Gregory N. Price, and Tomohiro Tach (2015). “(Non)existence of Pleated Folds: How Paper Folds Between Creases”, Graphs and Combinatorics, 27(3):377-397.
[4] Evgueni T. Filipov, Glaucio H. Paulino, Tomohiro Tachi (2015). “A Bar and Hinge Model for Scalable Structural Analysis of Origami”, P. Sharma, Annual SES Technical Meeting, Texas A&M University.
[5] Evgueni T. Filipov, Tomohiro Tachi, and Glaucio H. Paulino (2015) . “Miura Tubes and Assemblages: Theory and Applications”, American Physical Society March Meeting, March 2-6, 2015, San Antonio, TX.
[6] Evgueni T. Filipov, Tomohiro Tachi, and Glaucio H. Paulino (2015). “Origami tubes assembled into stiff, yet reconfigurable structures and metamaterials”, PNAS, Vol. 112, No.40, 12321-12326.
[7] Evgueni T. Filipov, Tomohiro Tachi, and Glaucio H. Paulino (2016) . “Origami tubes with reconfigurable s-polygonal crossections”, Proceedings of the Royal Society - A , Vol. 472, No. 2185, 20150607.
[8] Hani Buri and Yves Weinand. (2008) , “ORIGAMI – Folded Plate Structures, Architecture”, 10th World Conference on Timber Engineering, Miyazaki.
[9] Hongbin Fang, Suyi Li and K. W. Wang (2016) , “Self-locking degree-4 vertex origami structures”, Proceedings of the Royal Society – A, Vol. 472(2195).
[10] Hiromi Yasuda , Tomohiro Tachi , Mia Lee and Jinkyu Yang (2016),” Origami-based tunable truss structures for non-volatile mechanical memory operation”, (submitted)
[11] Jesse L. Silverberg, Jun-Hee Na , Arthur A. Evans , Bin Liu , Thomas C. Hull , Christian D. Santangelo , Robert J. Lang , Ryan C. Hayward and Itai Cohen(2015),” Origami structures with a critical transition to bistability arising from hidden degrees of freedom”, Nature Materials 14, 389–393
[12] Keyao Song, Xiang Zhou, Shixi Zang, Hai Wang and Zhong You (2017), ” Design of rigid-foldable doubly curved origami tessellations based on trapezoidal crease patterns”. Proceedings of the Royal Society – A, Vol. 473,20170016.
[13] Mahadevan, L. and Rica, S. (2005), “Self-Organized Origami”, Science 307(5716), p. 1740.
[14] Mark Schenk and Simon D. Guest (2010). “Origami Folding: A Structural Engineering Approach”, 5th International Conference on Origami in Science, Mathematics and Education and Folding Convention, Singapore.
[15] Mark Schenk and Simon D. Guest (2013)., “Geometry of Miura-folded metamaterials”, PNAS, Vol. 110, N0.9, 3281.
[16] Nishiyama, Yutaka (2012). “Miura folding: Applying origami to space exploration.” International Journal of Pure and Applied Mathematics 79.2: 269-279.
[17] Paul T. Boggs and Jon W. Tolle (1995), ”Sequential Quadratic Programming”, in Acta Numerica, 1995, Vol. 4 of Acta Numer., Cambridge Univ. Press, Cambridge,, pp. 1–52.
[18] Pedro M. Reis1, Francisco López Jiménez, and Joel Marthelot (2015). “Transforming architectures inspired by origami”, PNAS, Vol. 112, No.40, 12234-12235.
[19] Robert J. Lang (1996),” A computational algorithm for origami design”, In Computational Geometry: 12th Annual ACM Symposium, pages 98–105, Philadelphia, Pennsylvania
[20] Seffen, K.A. (2011). Compliant Shell Mechanisms, accepted for Philosophical Transactions of the Royal Society - Special Theme issue on the “Geometry and Mechanics of Layered Structures and Materials”.
[21] Tomohiro Tachi (2009). “Simulation of Rigid Origami”, n Origami 4: The Fourth International Conference on Origami in Science, Mathematics, and Education, edited by Robert Lang, pp. 175-187, A K Peters, Wellesley, MA.
[22] Tomohiro Tachi (2010). “Freeform Variations of Origami”, Journal for Geometry and Graphics, Vol. 14, No. 2, 203–215.
[23] Wojciech Gilewski, Jan Jan Pełczyński and Paulina Stawarz (2014).” A Comparative Study of Origami Inspired Folded Plates”, Procedia Engineering 91. 220-225
[24] Yutaka Nishiyama (2012).” Miura Folding: Applying Origami to Space Exploration”, Department of Business Information, Faculty of Information Management, Osaka University of Economics, 2, Osumi Higashiyodogawa Osaka, 533-8533, Japan
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