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研究生:洪崇倫
研究生(外文):Chong-Lun Hong
論文名稱:裂紋與剛性線異質物之互制研究
論文名稱(外文):Interactions of Rigid Line and Cracks
指導教授:宋見春
指導教授(外文):Jen-chun Sung
學位類別:碩士
校院名稱:國立成功大學
系所名稱:土木工程學系碩博士班
學門:工程學門
學類:土木工程學類
論文種類:學術論文
論文出版年:2008
畢業學年度:96
語文別:中文
論文頁數:109
中文關鍵詞:剛性線異質物裂紋應力強度因子奇異積分方程式正交性材料
外文關鍵詞:Singular integral equationCracksOrthotropic materialRigid line inclusionStress intensity factors
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本文探討無限域異向性線彈性體,內含一線剛性異質物與一裂紋之互制行為,應用無限域內含一中央線剛性異質物,受一差排作用之基本解,將此問題轉換為一組以未知差排密度函數分佈於裂紋面上之奇異積分方程,利用數值方法求解此積分方程並間接推得裂紋尖端之應力強度因。受均佈拉曳力作用下,文中探討線剛性異質物與裂紋尺寸、線剛性異質物與裂紋尖端距離、裂紋傾角以及異向性材料之異向程度等對應力強度因子之影響。
The interacting problem of a rigid line and a crack embedded in the anisotropic elastic medium of infinite extent under uniform loading at infinity is investigated. Based on the Stroh formalism and with the Green’s function for a point dislocation, a system of singular integral equations for the unknown dislocation densities defined on the crack faces is derived. Numerical method is then used to calculate the solutions to the system of equations. Results are presented graphically for the stress intensity factors for orthotropic and monoclinic materials for the medium subjected to different uniform loading at infinity. The effects of the distance between a rigid line and the crack on stress intensity factors are discussed in some detail.
目錄
摘要.................................................................................................................I
英文摘要.....................................................................................................II
誌謝.............................................................................................................III
目錄.............................................................................................................IV
表目錄........................................................................................................VI
圖目錄......................................................................................................VII

第一章 緒論...............................................................................................1
1.1 前言.............................................................................................1
1.2 文獻回顧.....................................................................................2
1.3 研究方法與本文綱要.................................................................3
第二章 理論基礎....................................................................................6
2.1 位移函數與應力函數.................................................................6
2.2 S、H和L矩陣............................................................................10
第三章 問題推演..................................................................................12
3.1 問題敘述...................................................................................13
3.2 公式推演...................................................................................14
3.3 應力強度因子...........................................................................20
第四章 數值方法..................................................................................23
4.1奇異積分方程組之正規化.........................................................24
4.2正規奇異積分方程組之離散化.................................................24
第五章 數值結果與探討...................................................................28
5.1平行裂紋之探討.........................................................................29
5.2傾斜裂紋之探討.........................................................................51
第六章 結論與展望.............................................................................66
參考文獻....................................................................................................68
附錄A............................................................................................................70
附錄B............................................................................................................75
B.1 平行裂紋之探討(剪力條件)...................................................75
B.2 傾斜裂紋之探討(剪力條件)...................................................95
自述
Ballarini, R., Shah, S. P. and Keer, L. M., “Failure characteristics of short anchor bolts embedded in a brittle material,” Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences, Vol. 404, No. 1826, 35-54 (1986).
Ballarini, R., “An integral equation approach for rigid line inhomogeneity problems,” International Journal of Fracture 33, R23-R26 (1987).
Ballarini, R., Keer, L. M. and Shah, S. P., “An analytical model for the pull-out of rigid anchors,” International Journal of Fracture 33, 75-94 (1987).
Ballarini, R., “A rigid line inclusion at a biomaterial interface,” Engineering Fracture Mechanics, Vol. 37, No. 1, 1-5 (1990).
Ballarini, R., “A certain mixed boundary value problem for a biomaterial interface,” International Journal of Solids and Structures, Vol. 32, No 3/4, 279-289 (1995).
Eshelby, J. D., Read, W. T. and Shockley, W., “Anisotropic elasticity with applications to dislocation theory,” Acta Metallurgica, Vol. 1, 251-259 (1953).
Erdogan, F. and Gupta, G. D., “On the numerical solution of singular integral equations,” Quarterly of Applied Mathematics, Vol. 30, 525-534 (1972).
Gerasoulis, A. and Srivastav, R. P., “A method fo the numerical solution of singular integral equations with a principal value integral,” International Journal of Engineering Science, Vol. 19, 1293-1298 (1981).
Gerasoulis, A., “The use of piecewise quadratic polynomials for the solution for singular integral equations of cauchy type,” Computational Mathematics with Applications, Vol. 8, No. 1, 15-22 (1982).
Isida, M., “Elastic analysis of cracks and stress intensity factors (in Japanese)” Fracture Mechanics and Strength of Materials 2, Baifuukan, 181-184 (1976).
Lekhnitskii, S. G., Theory of Elasticity of an anisotropic Elastic Body. Holden-Day, San Francisco, California. (1963).
Li, Qianqian, “Line inclusions in anisotropic elastic solids,” Ph.D. Thesis, University of Illinois at Chicago. (1988).
Li, Qianqian, and Ting T. C. T., “Line inclusions in anisotropic elastic solids,” Transactions of the ASME, Journal of Applied Mechanics, Vol. 56, 556-563 (1989).
Liou, J. Y. and Sung, J. C., “On the equivalence of the Lekhnitskii and Stroh formalisms,” European Journal of Mechanics, (revised) (2008)
Muskhelishvili, N. I., Singular Integral Equations, J. R. Radok, trans., Noordhoff, Groningen, The Netherlands. (1945).
Stroh, A. N., “Dislocations and cracks in anisotropic elasticity,” Phil. Mag. Vol. 3, 625-646 (1958).
Theocaris, A. and Ioakimidis, N. I., “Numerical integration methods for the solution of singular integral equations,” Quarterly of Applied Mathematics, Vol. 35, 173-182 (1977).
Ting, T. C. T., Anisotropic Elasticity: Theory and Application. Oxford University Press. (1996).
彭文彬,〝二維異向性裂紋交互作用之探討〞,碩士論文,國立成功大學土木工程學系,2000。
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