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論文名稱(中文) 磁電彈複材疊層板之偶合邊界元素設計
論文名稱(英文) Coupled Stretching-Bending Boundary Element Design for Magneto-Electro-Elastic Composite Laminates
校院名稱 成功大學
系所名稱(中) 航空太空工程學系
系所名稱(英) Department of Aeronautics & Astronautics
學年度 106
學期 2
出版年 107
研究生(中文) 游閏喬
研究生(英文) Jun-Chiao Yu
學號 P46054236
學位類別 碩士
語文別 中文
論文頁數 77頁
口試委員 指導教授-胡潛濱
口試委員-楊文彬
口試委員-夏育群
中文關鍵字 磁電彈材料  延伸類史磋公式  邊界元素法  伸張彎曲偶合  複材疊層板 
英文關鍵字 magneto-electro-elastic material  extended Stroh-like formalism  boundary element method  coupled-stretching-bending  composite laminates plate 
學科別分類
中文摘要 偶合異向性彈性力學的延伸類史磋公式,可以利用矩陣維度擴充的便利與規律性,將原先僅能用於彈性材料,延伸應用到壓電材料與磁電彈材料皆能同時使用的通解,接著利用邊界元素法,並找出磁電彈材料無限板的基本解,使彈性、壓電與磁電彈材料都能使用相同基本解來處理無限板的問題,而不需要重新尋找各別材料的基本解。由於多數商業軟體僅能處理彈性複材疊層板的偶合問題,藉由擴充完之方程式編寫進本師門研發之異向性彈性力學分析軟體AEPH中,進而讓程式能利用邊界元素法來處理磁電彈複材疊層板與偶合相關的問題。
最後利用商業軟體ANSYS、史磋公式解析解法及二維邊界元素法,分別處理對稱/非對稱彈性、壓電和磁電彈複材疊層板受軸向均佈拉伸或均佈面外彎矩,經由比對與分析其物理特性,來證明本方法的正確性。
英文摘要 On the basis of the convenient and regular features that extended Stroh-like formalism for coupled-stretching-bending anisotropic elasticity can be extended from the elastic material to the piezoelectric and magneto-electro-elastic materials by expanding the related matrix dimension. Through the boundary element method, the fundamental solution for the magneto-electro-elastic material infinite plate can be found, the elastic, piezoelectric and magneto-electro-elastic materials can also employ the same fundamental solution without finding solutions individually at the same time. Because of the most commercial software only can solve elastic composite laminates coupled-stretching-bending problem, our research group develop the structure engineering analysis software, AEPH, which can apply boundary element method to solve the magneto-electro-elastic material coupled-stretching-bending problem. To verify the correctness of this method, the elastic, piezoelectric and magneto-electro-elastic symmetric/unsymmetric plate under the axial distributed tension or out of plane bending, are presented and compared with the commercial software, ANSYS, Stroh analytical solution and two dimension boundary element method.
論文目次 摘要 I
Abstract II
致謝 IX
目錄 X
表目錄 XII
圖目錄 XIII
符號索引 XIV
第一章 緒論 1
1.1 研究目的與動機 1
1.2 文獻回顧 2
1.3 本文架構 3
第二章 偶合磁電彈力學分析 4
2.1 基本方程式 4
2.2 延伸類史磋公式 8
2.3 材料特徵關係 10
第三章 邊界元素設計 14
3.1 邊界積分方程式 14
3.2 基本解 16
3.3 邊界元素方程式 21
3.4 應力應變分析 26
3.5 內部點分析 31
第四章 AEPH程式設計 33
4.1 程式架構介紹 33
4.2 控制參數輸入 35
4.3 數值輸出與儲存 38
4.4 大域座標與局部座標的轉換 39
第五章 數值模擬與討論 41
第六章 結論 46
參考文獻 47
附表 49
附圖 59
附錄 71
參考文獻 [1] Green, A., “A note on stress systems in aelotropic materials,” Philosophical Magazine, Vol. 34, pp. 416-418, 1943.
[2] Brebbia, C.A., Telles, J.C.F. and Wrobel, L.C., “Boundary Element Techniques,” Springer-Verlag, New York, 1984.
[3] Sokolnikoff, I.S., Mathematical Theory of Elasticity. McGraw Hill, 2nd Edition, 1956.
[4] Hwu, C., “Boundary Integral Equations for General Laminated Plates with Coupled Stretching-Bending Deformation,” Proceedings of the Royal Society, Series A, Vol.466, pp.1027-1054, 2010.
[5] Hwu, C., “Boundary Element Formulation for the Coupled Stretching-Bending Analysis of Thin Laminated Plates,” Engineering Analysis with Boundary Elements, Vol. 36, pp. 1027-1039, 2012.
[6] Hwu, C., “Green's Function for the Composite Laminates with Bending Extension Coupling,” Composite Structures, Vol. 63, pp. 283-292, 2004
[7] Eshelby, J.D., Read, W.T. and Shockley, W., “Anisotropic Elasticity with Applications to Dislocation Theory,” Acta Metallurgica, Vol. 1, pp. 251–259, 1953.
[8] Stroh, A.N., “Dislocations and Cracks in Anisotropic Elasticity,” Philosophical Magazine, Vol. 7, pp. 625–646, 1958.
[9] Stroh, A.N., “Steady State Problems in Anisotropic Elasticity,” Journal of Mathematical Physics, Vol. 41, pp. 77–103, 1962.
[10] Ting, T.C.T., Anisotropic Elasticity: Theory and Applications, Oxford Science Publications, New York, 1996.
[11] Hwu, C., “Stroh-Like Formalism for the Coupled Stretching-Bending Analysis of Composite Laminates,” International Journal of Solids and Structures, Vol. 40, No.13-14, pp 3681–3705, 2003.
[12] Hwu, C. and Hsieh, M.C., “Extended Stroh-Like Formalism for the Electro-Elastic Composite Laminates and Its Applications to Hole Problems,” Smart Materials and Structures, Vol. 14, pp. 56-68, 2005.
[13] Ugural, A.C, Stresses In Plate and Shells. WCB/McGraw-Hill, 2nd Edition, 1999.
[14] Hwu, C., “Anisotropic Elastic Plates,” Springer, New York, 2010.
[15] Hsieh, M.C. and Hwu, C., “Extended Stroh-Like Formalism for Magneto-Eletro-Elastic Composite Laminates,” International Conference on Computational Mesomechanics associated with Development and Fabrication of Use-Specific Materials, Tokyo, Japan, pp.325-332, 2003.
[16] Hwu, C. and Yen, W.J., “Green’s Functions of Two-Dimensional Anisotropic Plates Containing an Elliptic Hole,” Int. J. Solids and Structures, Vol. 27, No.13, pp. 1705-1719, 1991.
[17] Yin, W.L., “General Solutions of Anisotropic Laminated Plates,” ASME Journal of Applied Mechanics, Vol. 70, No. 4, pp. 496–504, 2003.
[18] Yin, W.L., “Structures and Properties of the Solution Space of General Anisotropic Laminates,” International Journal of Solids and Structures, Vol. 40, pp. 1825–1852, 2003.
[19] Hwu, C., “Boundary Integral Equations for Unsymmetric Laminated Composites,” Advances in Boundary Element Techniques XI, Proceedings of the 11th International Conference on Boundary Element Techniques, Berlin, Germany, pp. 231-236, 2010.
[20] AEPH程式設計手冊
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