(44.192.112.123) 您好!臺灣時間:2021/02/28 06:20
字體大小: 字級放大   字級縮小   預設字形  
回查詢結果

詳目顯示:::

我願授權國圖
: 
twitterline
研究生:蕭培需
研究生(外文):Pei-Hsu Hsiao
論文名稱:一個用於分析異向彈性彎曲問題的新邊界積分法
論文名稱(外文):A New Boundary Integral Equation Formulation for Bending Problems of Anisotropic Plates
指導教授:吳光鐘
指導教授(外文):Kuang-Chong Wu
口試委員:張正憲邱佑宗陳世豪
口試委員(外文):Jeng-Shian ChangYu-Tsung ChiuShih-Hao Chen
口試日期:2014-07-25
學位類別:碩士
校院名稱:國立臺灣大學
系所名稱:應用力學研究所
學門:工程學門
學類:機械工程學類
論文種類:學術論文
論文出版年:2014
畢業學年度:102
語文別:中文
論文頁數:72
中文關鍵詞:邊界積分法異向彈性板板理論對稱性史磋法
外文關鍵詞:anisotropic platesclassical plate theoryboundary integral equationsStroh-like formalismBetti’s reciprocal work theorem
相關次數:
  • 被引用被引用:5
  • 點閱點閱:114
  • 評分評分:系統版面圖檔系統版面圖檔系統版面圖檔系統版面圖檔系統版面圖檔
  • 下載下載:0
  • 收藏至我的研究室書目清單書目收藏:0
本文發展一個分析對稱性複合疊層板彎曲問題的新的邊界積分方程式。此積分方程式的推導係運用一個分析古典板之方法。該法將板彎曲問題的解以類似二維異向彈力問題的史蹉解的形式來表示。傳統邊界積分方程式均利用Betti的互換功定理及適當的格林函數)來導得,但本文則使用柯西積分定理來推導。本研究所將發展之邊界積分方程式的優點之一是可同時得到線性相依之兩對偶積分方程組,無論邊界條件的形式為何,待解的方程式均可透過兩對偶以適定的第二型Fredholm積分方程式表示。本法的另一優點是邊界上所有的應力或彎矩分量均可直接得到,無須另作數值微分。
本文並計算方形板受板緣彎矩作用,板面受集中力或分布力,及含孔洞之無限板在遠處受彎矩等之算例,數值結果與解析解比較顯示本法之準確性極高。


A new boundary integral formulation for the numerical solution of bending problems of anisotropic plates is proposed in this work. The formulation is based on a Stroh-like formalism developed for the classical plate theory. In contrast to the conventional formulation, which is derived from Betti’s reciprocal work theorem with appropriate Green’s functions, the proposed formulation makes use of Cauchy’s integral theorem.
An advantage of the new formulation is that it provides dual sets of boundary integral equations, which are linearly dependent. With the dual sets, the integral equations to be solved can always be cast into the form of well-posed Fredholm integral equations of the second type regardless of the types of boundary conditions. Another advantage is that all stress or moment components can be obtained directly without additional numerical differentiations. Numerical examples are given to demonstrate the effectiveness and efficiency of the proposed boundary integral formulation.


口試委員會審定書 i
誌謝 ii
中文摘要 iii
ABSTRACT iv
目錄 v
圖目錄 vii
表目錄 ix
第1章 導論 1
1.1 研究動機與文獻回顧 1
1.2 本文大綱 2
第2章 複合材料層板理論 3
2.1 應力應變關係 3
2.2 位移場假設 4
2.3 應變與位移關係 4
2.4 組成律 5
2.5 平衡方程式 8
2.6 統御方程式 9
第3章 解析解 10
3.1 Stroh-Like理論 10
3.2 橢圓坐標系映射到單位圓坐標系 13
3.3 之計算 18
第4章 數值方法 21
4.1 廣義柯西公式(Generalized Cauchy''s Formula) 21
4.2 雙邊界積分方程式 22
4.3 彎矩問題之邊界積分方程式 24
4.4.1 方形板受集中力 25
4.4.2 方形板受均勻分布力 28
4.5 座標轉換 31
4.6 孔洞邊界環向彎矩轉換 32
4.7 數值解法 35
第5章 數值分析結果 42
5.1 正交性材料平板施加均勻彎矩 42
5.1.1 方形板加 43
5.1.2 方形板加 44
5.2 方形板受集中力 46
5.2.1 方形板邊界之計算 47
5.2.2 方形板內部計算 48
5.3 方形板受分布力 50
5.3.1 等向性材料 50
5.3.2 正交性材料 52
5.4 含孔洞無限板受 54
5.4.1 等向性材料 54
5.4.2 正交性材料 56
5.5 含孔洞無限板受 59
5.5.1 等向性材料 59
5.5.2 正交性材料 61
5.6 正交性含孔洞無限板受 (30度) 65
第6章 結論與未來展望 68
6.1 結論 68
6.2 未來展望 69
參考文獻 70

[1]Lekhnitskii, S.G., Anisotropic Plate, Gordon and Breach, London, 1968.
[2]Timoshenko, S. and Woinowsky-Krieger S., Theory of Plates And Shells, New York, McGraw-hill, 1959.
[3]Cheng, Z. Q., and Reddy, J. N., Octet Formalism For Kirchhoff Anisotropic Plates, Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences, Vol.458, p. 1499, 2002.
[4]Chen, W. H., and Huang T. F., Three-dimensional interlaminar stress analysis at free-edges of composite laminate, Computers and structures, Vol. 32, pp.1275-1286, 1989.
[5]Bezine, G., Boundary Integral Formulation for Plate Flexure with Arbitrary Boundary Conditions, Mechanics Research Communications, Vol. 5, p. 197, 1978.
[6]Jones R. M., Mechanics of Composite Materials, Washinton, DC:Scripts, 1974.
[7]Stern, M., A General Boundary Integral Formulation for the Numerical Solution of Plate Bending Problems, International journal of solids and structures, Vol. 15, p. 769, 1979.
[8]Wu, K. C., Chiu, Y. T., and Hwu, Z. H., A New Boundary Integral Equation Formulation for Linear Elastic Solids, Journal of applied mechanics, Vol. 59, p. 344, 1992.
[9]Wu, K. C., and Chen, C. T., Stress Analysis of Anisotropic Elastic V-Notched Bodies, International journal of solids and structures, Vol. 33, p. 2403, 1996.
[10]Wu, K. C. A new boundary integral equation method for analysis of cracked linear elastic bodies. Journal of the Chinese Institute of Engineers, Vol. 27, pp.937-941, 2004.
[11]Shi, G., and Bezine, G., A General Boundary Integral Formulation for the Anisotropic Plate Bending Problems, Journal of composite materials, Vol. 22, p. 694, 1988.
[12]N. I. Muskhelishvili, Some basic problems of the mathematical theory of elasticity :fundamental equations, plane theory of elasticity, torsion and bending. The Netherlands: Noordhoff International, 1963.


[13]Pan, E., Yang, B., Cai, G., and Yuan F. G., Stress analyses around holes in composite laminates using boundary element method, Engineering analysis with boundary elements, Vol. 25, pp.31-41, 2001.
[14]Pan, E., Exact solutions for simply supported and multilayered magneto-electro-elastic plates, Journal of applied mechanics, Vol. 68, pp.608-618, 2001.
[15]Lu, P., Mahrenholtz, O., Extension of the Stroh formalism to the analysis of bending of anisotropic elastic plates, Journal mechanics physics solids, Vol. 42, pp.1725-1741, 2001.
[16]Nishioka T and Atluri S N, Stress analysis of holes in angle –ply laminates: an
Efficient assumed stress special-holes-element approach and a simple estimation
Method, Computers and structures, Vol. 15, pp.135-147, 1982.
[17]Hwu, C., Anisotropic elastic plates with holes/cracks/inclusions subjected to out of plane bending moments, International journal of solids and structures, Vol. 39, pp. 4905-4925, 2002.
[18]Hwu, C., Green’s function of two-dimensional anisotropic plates containing an elliptic hole, International journal of solids and structures, Vol. 27, pp.1705-1719, 1991.
[19]Hwu, C., Stroh-Like Formalism for the Coupled Stretching–Bending Analysis of Composite Laminates, International journal of solids and structures, Vol. 40, pp. 3681, 2003.
[20]Hwu, C., Extended Stroh-Like Formalism for electro-elastic composite laminates and its applications to hole problems, Smart material and structures, Vol. 14, pp. 56-68, 2004.
[21]T. C.-T. Ting, Anisotropic Elasticity: Theory and Applications. New York/Oxford: Oxford University Press, 1996.
[22]T. C.-T. Ting, A modified Lekhnitskii formalism a la Stroh for anisotropic elasticity and classifications of the matrix N., 1999.
[23]Cheng, Z. Q., &; Reddy, J. N. Structure and properties of the fundamental elastic plate matrix. ZAMM&;#8208;Journal of Applied Mathematics and Mechanics/Zeitschrift fur Angewandte Mathematik und Mechanik, Vol. 85, pp.721-739, 2005.
[24]Hwu, C. Boundary integral equations for general laminated plates with coupled stretching–bending deformation. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Science, Vol. 466, pp.1027-1054, 2010a.
[25]Hwu, C. Some explicit expressions of Stroh-like formalism for coupled stretching–bending analysis. International Journal of Solids and Structures, Vol. 47, pp.526-536, 2010b.
[26]Lu, P. Stroh type formalism for unsymmetric laminated plate. Mechanics research communications, Vol. 21, pp.249-254, 1994.
[27]Dos Reis, A., Lima Albuquerque, E., Luiz Torsani, F., Palermo Jr, L., &; Sollero, P. Computation of moments and stresses in laminated composite plates by the boundary element method. Engineering Analysis with Boundary Elements, Vol. 35, pp.105-113, 2011.
[28]Rizzo, F. J. An integral equation approach to boundary value problems of classical elastostatics. Quart. Appl. Math, Vol. 25, pp.83-95, 1967.
[29]Rizzo, F. J., &; Shippy, D. J. A method for stress determination in plane anisotropic elastic bodies. Journal of Composite Materials, Vol. 4, pp.36-61, 1970.
[30]Zhao, Z., &; Lan, S. Boundary stress calculation—a comparison study. Computers &; structures, Vol. 71, pp.77-85, 1999.


QRCODE
 
 
 
 
 
                                                                                                                                                                                                                                                                                                                                                                                                               
第一頁 上一頁 下一頁 最後一頁 top
系統版面圖檔 系統版面圖檔