簡易檢索 / 詳目顯示

回結果列表
研究生： 陳志豪
Chen, Chih-Hao
論文名稱： 複合楔形體之反平面剪力變形分析
Analysis of Composite Wedges under Anti-Plane Shear Deformation
指導教授： 王建力
Wang, Chein-Lee
學位類別： 博士
Doctor
系所名稱： 工學院 - 資源工程學系
Department of Resources Engineering
論文出版年： 2009
畢業學年度： 97
語文別： 英文
論文頁數： 226
中文關鍵詞： 應變能密度 、應力強度因子 、III型 、裂紋 、反平面剪力 、楔形
外文關鍵詞： Wedge, Anti-Plane Shear, Mode III, Crack, Strain Energy Density, Stress Intensity Factor
相關次數： 點閱：127  下載：2 
分享至:
查詢本校圖書館目錄 查詢臺灣博碩士論文知識加值系統 勘誤回報

    • 本研究分析複合楔形體承受反平面剪力之變形問題。將楔形體考慮成一具有有限長半徑之扇形，利用有限梅林 (finite Mellin) 及拉氏 (Laplace) 積分變換法求解。探討的兩種複合楔形問題：雙層結合扇形、具有一裂紋終止於結合界面之結合扇形，承受反平面剪力作用於扇形之弧線上。解析此兩楔形相關問題之位移場及應力場，並推求其廣義應力強度因子、延伸 (extended) 應力強度因子、應變能密度及能量釋放率。結果顯示，位移與材料參數的數值有關，而應力及應力強度因子則與材料參數之比例有關，故單一材料之應力強度因子與材料參數無關。當雙材料之楔形角相等、作用力施加的角度相等，且軸向為自由邊界或固定邊界時，可將此複合楔形問題考慮成兩單一材料楔形問題，其結合界面之位移為零。利用高階項位移及應力解求得之應變能密度發現，應變能密度破壞準則不適用於本研究相關之裂紋發展問題，而以延伸應力強度因子配合最大剪力準則則計算出裂紋可能沿結合界面或沿一與楔形角度及材料參數相關之特定角度發展。另外，由能量釋放率計算結果驗證其與應力強度因子的關係。最後將結果退化成具有相等楔形角之複合楔形體，在承受一般剪應力作用下，比較解析結果與有限元素分析結果，比較結果良好。

    This study investigates problems of a composite wedge with a finite radius under anti-plane shear deformation. Two groups of wedge problem are considered: a perfectly bonded wedge and a circular shaft with a crack terminated at the interface; both problems are subjected to a pair of anti-plane shear loads on their arcs with various radial conditions. A solution procedure that applies a finite Mellin transform of the second kind in conjunction with the Laplace transform is proposed to derive analytical displacements and stress fields for the entire wedge. Explicit solutions for various cases are presented. It was found that if both the vertex and loading angles are fixed, free-free and clamped-clamped edge cases of the bonded wedge problem can be degenerated into single material cases for which the interface is clamped. Generalized and extended stress intensity factors (SIFs) are extracted from the obtained stress fields. An investigation of the generalized SIF shows that it depends not only on the values of the geometric and loading parameters, but also on the proportion of the material properties; thus, the generalized SIF is independent of the material properties for a single-material wedge. Using the extended SIFs applied to the maximum shear stress criterion for crack problems, the crack initiation can be calculated either in the direction along the interface or along a particular direction in front of the crack tip as long as the SIF in the direction exceeds its critical value. In addition, the strain energy density (SED) for the corresponding crack problems is calculated and discussed. It is demonstrated that the SED criterion cannot be used to predict the crack initiation direction for the studied cases when the higher-order terms of stress expansions are taken into account. The energy release rate (G) for an interfacial crack problem is calculated and its relationship with the SIF is verified. Some degenerate solutions are presented and used as weighted functions for the general loading cases. Finite element analyses are implemented to compare the analytical results, and good agreement is achieved.

    摘要 I Abstract II Acknowledgements IV Table of Contents V List of Tables VIII List of Figures IX Nomenclature XV Chapter 1 Introduction 1 1.1 Background 1 1.2 Problem Statement 5 1.3 Objective and Scope 8 1.4 Literature Review 9 1.5 Layout of this Thesis 22 Chapter 2 Theory and Methodology 23 2.1 Basic Equations 23 2.2 Mellin Transform 26 2.3 Laplace Transform 28 2.4 Residue Theorem 29 Chapter 3 Solutions and Results 31 3.1 Solution Procedure 31 3.2 Problem Overview 32 3.3 Problem A (Composite Wedge with a Finite Radius) 36 3.3.1 Case 1: Traction-Traction-Free-Free (TTFF) 36 3.3.2 Case 2: Traction-Traction-Free-Clamped (TTFC) 44 3.3.3 Case 3: Traction-Traction-Clamped-Clamped (TTCC) 48 3.3.4 Case 4: Traction-Traction-Bonded-Bonded (TTBB) 51 3.3.5 Summary of Problem A 54 3.4 Problem B (Composite Circular Shaft with a Crack Terminated at the Interface) 57 3.4.1 Case 5: Traction-Traction-Free-Free-Free (TTFFF) 57 3.4.2 Case 6: Traction-Traction-Free-Free-Clamped (TTFFC) 63 3.4.3 Case 7: Traction-Traction-Free-Clamped-Clamped (TTFCC) 67 3.4.4 Case 8: Traction-Free-Traction-Free-Free (TFTFF) 70 3.4.5 Case 9: Traction-Free-Traction-Free-Clamped (TFTFC) 77 3.4.6 Case 10: Traction-Free-Traction-Clamped-Clamped (TFTCC) 80 3.4.7 Summary of Problem B 83 Chapter 4 Stress Intensity Factors 88 4.1 Problem A (Composite Wedge with a Finite Radius) 91 4.1.1 Case 1: Traction-Traction-Free-Free (TTFF) 91 4.1.2 Case 2: Traction-Traction-Free-Clamped (TTFC) 92 4.1.3 Case 3: Traction-Traction-Clamped-Clamped (TTCC) 95 4.2 Problem B (Composite Circular Shaft with a Crack Terminated at the Interface) 97 4.2.1 Case 5: Traction-Traction-Free-Free-Free (TTFFF) 97 4.2.2 Case 6: Traction-Traction-Free-Free-Clamped (TTFFC) 99 4.2.3 Case 7: Traction-Traction-Free-Clamped-Clamped (TTFCC) 101 4.2.4 Case 8: Traction-Free-Traction-Free-Free (TFTFF) 103 4.2.5 Case 9: Traction-Free-Traction-Free-Clamped (TFTFC) 105 4.2.6 Case 10: Traction-Free-Traction-Clamped-Clamped (TFTCC) 107 4.3 Composite Wedge with Equal Vertex Angles α=β 109 4.3.1 Case 1: TTFF with Vertex Angle α=β 109 4.3.2 Case 2: TTFC with Vertex Angle α=β 110 4.3.3 Case 3: TTCC with Vertex Angle α=β 112 4.4 Single-Material Wedge 115 4.4.1 Case 1: TTFF with μ1=μ2 115 4.4.2 Case 2: TTFC with μ1=μ2 115 4.5 Extended Stress Intensity Factors 117 4.5.1 Interfacial Crack Problems 117 4.5.2 Crack-Terminating Interface Problems 121 4.6 Summary 129 Chapter 5 Strain Energy Density and Energy Release Rate 131 5.1 Strain energy density (SED) 131 5.1.1 Interfacial Crack Problems 131 5.1.2 Crack-Terminating Interface Problems 135 5.2 Energy Release Rate (G) 143 5.3 Summary 145 Chapter 6 Degenerate Problems 147 6.1 Composite Wedge with Equal Vertex Angles 147 6.1.1 Case 1: TTFF with Vertex Angle α=β 147 6.1.2 Case 2: TTFC with Vertex Angle α=β 148 6.1.3 Case 3: TTCC with Vertex Angle α=β 149 6.2 Single-Material Wedge 157 6.2.1 Wedge with Free-Free Edge 157 6.2.2 Wedge with Free-Clamped Edge 159 6.2.3 Wedge with Clamped-Clamped Edge 160 6.2.4 A Cracked Circular Shaft with Anti-Symmetric Loadings 161 6.3 Summary 167 Chapter 7 Further Related Researches 168 7.1 Other Types of Materials 168 7.2 Mode III Fracture Toughness Test 169 Chapter 8 Summary and Conclusions 172 Appendix A Strain-Displacement Relations in Cylindrical Coordinates 176 Appendix B Finite Mellin Transform on a Laplace’s Operator 181 Appendix C Laplace Transform in the Tangential Direction of the Wedge 184 Appendix D J-integral of a Bi-Material Wedge in Mode III 187 Appendix E Explicit Solution Fields for the Single-Material Wedge 188 Appendix F Full-field Displacement and Stress Distributions of Composite Wedges with Finite Radii 197 References 213 VITA 224

    [1] Sanford, R.J., 2003. Principles of Fracture Mechanics. Prentice Hall, New Jersey.
    [2] Atkinson, C., Craster, R.V., 1995. Theoretical aspects of fracture mechanics. Progress in Aerospace Sciences, 31, 1-83.
    [3] Fineberg, J., Marder, M., 1999. Instability in dynamic fracture. Physics Reports, 313, 1-108.
    [4] Cartwright, J.A., Mansfield, C.S., 1998. Lateral displacement variation and lateral tip geometry of normal faults in the Canyonlands National Park, Utah. Journal of Structural Geology, 20, 3-19.
    [5] Roach, G.F., 1982. Green’s Functions (2nd edition). Cambridge University Press, Great Britain.
    [6] Shahani, A.R., 2005. Some problems in the antiplane shear deformation of bi-material wedges. International Journal of Solids and Structures, 42, 3093-3113.
    [7] Sinclair, G.B., 2004. Stress singularities in classical theory – I: Removal, interpretation, and analysis. Applied Mechanics Reviews, 57, 251-297.
    [8] Sinclair, G.B., 2004. Stress singularities in classical theory – II: Asymptotic identification. Applied Mechanics Reviews, 57, 385-439.
    [9] Tranter, C.J., 1948. The use of the Mellin transform in finding the stress distribution in an infinite wedge. The Quarterly Journal of Mechanics and Applied Mathematics, 1, 125-130.
    [10] Godfrey, D.E.R., 1955. Generalized plane stress in an elastic wedge under isolated loads. The Quarterly Journal of Mechanics and Applied Mathematics, 8, 226-236.
    [11] Williams, M.L., 1952. Stress singularities resulting from various boundary conditions in angular corners of plates in extension, Transactions of the ASME, Journal of Applied Mechanics, 19, 526-528.
    [12] Williams, M.L., 1957. On the stress distribution at the base of a stationary crack. Transactions of the ASME, Journal of Applied Mechanics, 24, 109-114.
    [13] Williams, M.L., 1959. The stresses around a fault or crack in dissimilar media. Bulletin of Seismological Society of America, 49, 199-204.
    [14] Bogy, D.B., 1968. Edge-bonded dissimilar orthogonal elastic wedges under normal and shear loading. Transactions of the ASME, Journal of Applied Mechanics, 35, 460-466.
    [15] Bogy, D.B., 1971. Two edge-bonded elastic wedges of different materials and wedge angles under surface tractions. Transactions of the ASME, Journal of Applied Mechanics, 38, 377-386.
    [16] Bogy, D.B., Wang, K.C., 1971. Stress singularities at interface corners in bonded dissimilar isotropic elastic materials. International Journal of Solids and Structures, 7, 993-1005.
    [17] Bogy, D.B., 1972. The plane solution for anisotropic elastic wedges under normal and shear loading. Transactions of the ASME, Journal of Applied Mechanics, 39, 1103-1109.
    [18] Kuo, M.C., Bogy, D.B., 1974. Plane solutions for the displacement and traction-displacement problems for anisotropic elastic wedges. Transactions of the ASME, Journal of Applied Mechanics, 41, 197-202.
    [19] Kuo, M.C., Bogy, D.B., 1974. Plane solutions for traction problems on orthotropic unsymmetrical wedges and symmetrically twinned wedges. Transactions of the ASME, Journal of Applied Mechanics, 41, 203-208.
    [20] Hein, V.L., Erdogan, F., 1971. Stress singularities in a two-material wedge. International Journal of Fracture Mechanics, 7, 317-330.
    [21] Erdogan, F., Biricikoglu, V., 1973. Two bonded half planes with a crack going through the interface. International Journal of Engineering Science, 11, 745-766.
    [22] Erdogan, F., Aksogan, O., 1974. Bonded half planes containing an arbitrarily oriented crack. International Journal of Solids and Structures, 10, 569-585.
    [23] Erdogan, F., Gupta, G.D., 1975. Bonded wedges with an interface crack under anti-plane shear loading. International Journal of Fracture, 11, 583-593.
    [24] Shahani, A.R., Adibnazari, S., 2000. Analysis of perfectly bonded wedges and bonded wedges with an interface crack under antiplane shear loading. International Journal of Solids and Structures, 37, 2639-2650.
    [25] Shahani, A.R., 2003. Mode III stress intensity factor for edge-cracked circular shafts, bonded wedges, bonded half planes and DCB’s. International Journal of Solids and Structures, 40, 6567-6576.
    [26] Shahani, A.R., 2006. Mode III stress intensity factors in an interfacial crack in dissimilar bonded materials. Archive of Applied Mechanics, 75, 405-411.
    [27] Chue, C.H., Liu, T.J.C., 2004. Electro-elastic analysis of a bimaterial piezoelectric wedge with an interface crack under antiplane concentrated forces and inplane surface charges. International Journal of Solids and Structures, 41, 4179-4196.
    [28] Hwang, E.H., Choi, S.R., Earmme, Y.Y., 1992. Inclined edge crack in two bonded elastic quarter planes under out-of-plane loading. International Journal of Fracture, 56, R39-R49.
    [29] Sih, G.C., Chen, E.P., 1981. Cracks in composite materials: A compilation of stress solutions for composite systems with cracks, in Mechanics of Fracture. Sih, G.C. (ed.), 6, Martinus Nijhoff Publishers, Hague.
    [30] Choi, S.R., Chong, C.H., Chai, Y.S., 1994. Interfacial edge crack in two bonded dissimilar orthotropic quarter planes under anti-plane shear. International Journal of Fracture, 67, 143-150.
    [31] Theocaris, P.S., 1974. The order of singularity at a multi-wedge corner of a composite plate. International Journal of Engineering Science, 12, 107-120.
    [32] Fenner, D.N., 1976. Stress singularities in composite materials with an arbitrarily oriented crack meeting an interface. International Journal of Fracture, 12, 705-721.
    [33] Erdogan, F., Arin, K., 1976. Fracture and contact problems for an elastic wedge. Journal of Elasticity, 6, 57-71.
    [34] Bassani, J.L., Erdogan, F., 1979. Stress intensity factors in bonded half planes containing inclined cracks and subjected to antiplane shear loading. International Journal of Fracture, 15, 145-158.
    [35] Bera, R., Patra, B., 1979. On the shear of an elastic wedge as a mixed boundary value problem. Acta Mechanica, 33, 307-316.
    [36] Naylor, D., 1963. On a Mellin type integral transform. Journal of Mathematics and Mechanics, 12, 265-274.
    [37] Dempsey J.P., Sinclair, G.B., 1979. On the stress singularities in the plane elasticity of the composite wedge. Journal of Elasticity, 9, 373-391.
    [38] Dempsey J.P., Sinclair, G.B., 1981. On the singular behavior at the vertex of a bi-material wedge. Journal of Elasticity, 11, 317-327.
    [39] Sinclair, G.B., 1980. On the singular eignefunctions for plane harmonic problems in composite regions. Transactions of the ASME, Journal of Applied Mechanics, 47, 87-92.
    [40] Munz, D., Fett, T., Yang, Y.Y., 1993. The regular stress terms in bonded dissimilar materials after a change in temperature. Engineering Fracture Mechanics, 44, 185-194.
    [41] Munz, D., Yang, Y.Y., 1992. Stress singularities at the interface in bonded dissimilar materials under mechanical and thermal loading. Transactions of the ASME, Journal of Applied Mechanics, 59, 857-861.
    [42] Yang, Y.Y., Munz, D., 1994. Determination of the regular stress term in a dissimilar materials joint under thermal loading by the Mellin transform. Journal of Thermal Stresses, 17, 321-336.
    [43] Yang, Y.Y., Munz, D., 1995. Stress distribution in a dissimilar materials joint for complex singular eigenvalues under thermal loading. Journal of Thermal Stresses, 18, 407-419.
    [44] Yang, Y.Y., Munz, D., 1997. Stress singularities in a dissimilar materials joint with edge tractions under mechanical and thermal loading. International Journal of Solids and Structures, 34, 1199-1216.
    [45] Yang, Y.Y., 1998. Asymptotic description of the logarithmic singular stress field and its application. International Journal of Solids and Structures, 35, 3917-3933.
    [46] Yang, Y.Y., 1999. The type of stress singularities in a two-dissimilar-materials joint under thermal loading. Journal of Thermal Stresses, 22, 101-121.
    [47] Ma, C.C., 1995. Plane solution of thermal stress for anisotropic bimaterial elastic wedge. Journal of Thermal Stresses, 18, 219-245.
    [48] Hwu, C., Lee, W.J., 2004. Thermal effect on the singular behavior of multibonded anisotropic wedges. Journal of Thermal Stresses, 27, 111-136.
    [49] Delale, F., Erdogan F., Boduroglu, H., 1982. Stress singularities at the vertex of a cylindrically anisotropic wedge. International Journal of Fracture, 19, 247-256.
    [50] Delale, F., 1984. Stress singularities in bonded anisotropic materials. International Journal of Solids and Structures, 20, 31-44.
    [51] Ting, T.C.T., 1986. Explicit solution and invariance of the singularities at an interface crack in anisotropic composites. International Journal of Solids and Structures, 22, 965-983.
    [52] Ma, C.C., Hour B.L., 1989. Analysis of dissimilar anisotropic wedges subjected to antiplane shear deformation. International Journal of Solids and Structures, 25, 1295-1309.
    [53] Ma, C.C., Hour B.L., 1990. Antiplane problems in composite anisotropic materials with an inclined crack terminating at a bimaterial interface. International Journal of Solids and Structures, 26, 1387-1400.
    [54] Ma, C.C., Wu, H.W., 1990. Analysis of inplane composite wedges under traction-displacement or displacement-displacement boundary conditions. Acta Mechanica, 85, 149-167.
    [55] Chen, D.H., Nisitani, H., 1992. Singular stress field in two bonded wedges. Transactions of the JSME, Series A, 68, 457-464. (in Japanese)
    [56] Chen, D.H., Nisitani, H., 1993. Singular stress filed near the corner of jointed dissimilar material. Transactions of the ASME, Journal of Applied Mechanics, 60, 607-613.
    [57] Chen, D.H., Mori, Y., 1992. Stress singularities for a V-notch with its tip on the bimaterial interface. Transactions of the JSME, Series A, 58, 2381-2386. (in Japanese)
    [58] Chen, D.H., Mori, Y., 1994. Stress singularities for crack with tip on bimaterial interface of isotropic and anisotropic phases. Transactions of the JSME, Series A, 60, 2228-2235. (in Japanese)
    [59] Pageau S.S., Joseph, P.F., Biggers, S.B.Jr., 1994. The order of stress singularities for bonded and disbonded three-material junctions. International Journal of Solids and Structures, 31, 2979-2997.
    [60] Pageau S.S., Gadi, K.S., Biggers, S.B.Jr., Joseph, P.F., 1996. Standardized complex and logarithmic eigensolutions for n-material wedges and junctions. International Journal of Fracture, 77, 51-76.
    [61] Pageau S.S., Joseph, P.F., Biggers, S.B.Jr., 1995. A finite element analysis of the singular stress fields in anisotropic materials loaded in antiplane shear. International Journal for Numerical Methods in Engineering, 38, 81-97.
    [62] Pageau S.S., Joseph, P.F., Biggers, S.B.Jr., 1995. Finite element analysis of anisotropic materials with singular inplane stress fields. International Journal of Solids and Structures, 32, 571-591.
    [63] Pageau S.S., Biggers, S.B.Jr., 1996. A finite element approach to three-dimensional singular stress states in anisotropic multi-material wedges and junctions. International Journal of Solids and Structures, 33, 33-47.
    [64] Seweryn, A., Molski, K., 1996. Elastic stress singularities and corresponding generalized stress intensity factors for angular corners under various boundary conditions. Engineering Fracture Mechanics, 55, 529-556.
    [65] Stump, D.M., 1996. Elastic stresses under a wedge loaded with finite length strip of facial pressure and shear. International Journal of Fracture, 82, R25-R31.
    [66] Dunn, M.L., Suwito, W., Cunningham, S., 1997. Stress intensities at notch singularities. Engineering Fracture Mechanics, 57, 417-430.
    [67] Dunn, M.L., Suwito, W., Cunningham, S., May, C.W., 1997. Fracture initiation at sharp notches under mode I, mode II, and mild mixed mode loading. International Journal of Fracture, 84, 367-381.
    [68] Qian, J., Hasebe, N., 1997. Property of eigenvalues and eigenfunctions for an interface V-notch in antiplane elasticity. Engineering Fracture Mechanics, 56, 729-734.
    [69] Kargarnovin, M.H., Shahani, A.R., Fariborz, S.J., 1997. Analysis of an isotropic finite wedge under antiplane deformation. International Journal of Solids and Structures, 34, 113-128.
    [70] Shahani, A.R., 2007. On the antiplane shear deformation of finite wedges. Applied Mathematical Modelling, 31, 141-151.
    [71] Shahani, A.R., 1999. Analysis of an anisotropic finite wedge under antiplane deformation. Journal of Elasticity, 56, 17-32.
    [72] Kargarnovin, M.H., Fariborz, S.J., 2000. Analysis of a dissimilar finite wedge under antiplane deformation. Mechanics Research Communications, 27, 109-116.
    [73] Chue, C.H., Liu, W.J., 2007. Antiplane electro-mechanical field of a piezoelectric finite wedge under shear loading and at fixed-grounded boundary conditions. International Journal of Solids and Structures, 44, 2540-2552.
    [74] Liu, W.J., Chue, C.H., 2007. Electroelastic analysis of a piezoelectric finite wedge with mixed type boundary conditions under a pair of concentrated shear forces and free charges. Theoretical and Applied Fracture Mechanics, 48, 203-224.
    [75] Chen, H.P., 1998. Stress singularities in anisotropic multi-material wedges and junctions. International Journal of Solids and Structures, 35, 1057-1073.
    [76] Lin, Y.Y., Sung, J.C., 1998. Stress singularities at the apex of a dissimilar anisotropic wedge. Transactions of the ASME, Journal of Applied Mechanics, 65, 454-463.
    [77] Chue, C.H., Tseng, C.H., Liu, C.I., 2001. On stress singularities in an anisotropic wedge for varies boundary conditions. Composite Structures, 54, 87-102.
    [78] Chue, C.H., Liu, C.I., 2001. A general solution on stress singularities in an anisotropic wedge. International Journal of Solids and Structures, 38, 6889-6906.
    [79] Chue, C.H., Liu, C.I., 2002. Stress singularities in a bimaterial anisotropic with arbitrary fiber orientation. Composite Structures, 58, 49-56.
    [80] Li, X.F., Fan, T.Y., 2000. Semi-infinite anti-plane crack in a piezoelectric material. International Journal of Fracture, 102, L55-L60.
    [81] Li, X.F., Fan, T.Y., 2001. Mode III interface edge crack between two bonded quarter-planes of dissimilar piezoelectric materials. Archive of Applied Mechanics, 71, 703-714.
    [82] Xu, X.L., Rajapakse, R.K.N.D., 2000. On singularities in composite piezoelectric wedges and junctions. International Journal of Solids and Structures, 37, 3253-3275.
    [83] Chue, C.H., Chen, C.D., 2002. Decoupled formulation of piezoelectric elasticity under generalized plane deformation and its application to wedge problems. International Journal of Solids and Structures, 39, 3131-3158.
    [84] Chue, C.H., Chen, C.D., 2003. Antiplane stress singularities of a bonded bimaterial piezoelectric wedge. Archive of Applied Mechanics, 72, 673-685.
    [85] Chen, C.D., Chue, C.H., 2003. Singular electro-mechanical fields near the apex of a piezoelectric bonded wedge under antiplane shear. International Journal of Solids and Structures, 40, 6513-6526.
    [86] Chue, C.H., Wei, W.B., Liu, T.J.C., 2003. The antiplane electro-mechanical field of a piezoelectric wedge under a pair of concentrated forces and free charges. Journal of the Chinese Institute of Engineers, 26, 575-583.
    [87] Faal, R.T., Fotuhi, A.R., Fariborz, S.J., Daghyani, H.R., 2004. Antiplane stress analysis of an isotropic wedge with multiple cracks. International Journal of Solids and Structures, 41, 4535-4550.
    [88] Lin, R.L., Ma, C.C., 2004. Theoretical full-field analysis of dissimilar isotropic composite annular wedges under anti-plane deformations. International Journal of Solids and Structures, 41, 6041-6080.
    [89] Chang, J., Xu, J.Q., 2007. The singular stress field and stress intensity factors of a crack terminating at a bimaterial interface. International Journal of Mechanical Sciences, 49, 888-897.
    [90] Shin K.C., Kim, W.S., Lee, J.J., 2007. Application of stress intensity to design of anisotropic/isotropic bi-materials with a wedge. International Journal of Solids and Structures, 44, 7748-7766.
    [91] Sue, W.C., Liou, J.Y., Sung, J.C., 2007. Investigation of the stress singularity of a magnetoelectroelastic bonded antiplane wedge. Applied Mathermatical Modelling, 31, 2313-2331.
    [92] Decolon, C., 2002. Analysis of Composite Structures. Hermes Penton Science, London.
    [93] Barber, J.R., 1992. Elasticity. Kluwer Academic Publishers, Dordrecht.
    [94] Boresi, A.P., Chong, K.P., 2000. Elasticity in Engineering Mechanics. John Wiley & Sons, New York.
    [95] Ting, T.C.T., 1996. Anisotropic Elasticity Theory and Applications. Oxford University Press, New York.
    [96] Sneddon, I.N., 1972. The Use of Integral Transforms. McGraw-Hill, New York.
    [97] Gerald, C.F., Wheatley, P.O., 1999. Applied Numerical Analysis (6th edition). Addison-Wesley, Massachusetts.
    [98] Farlow, S.J., 1982. Partial Differential Equations for Scientists and Engineers. John Wiley & Sons, New York.
    [99] Wunsch, A.D., 1994. Complex Variables with Applications (2nd edition). Addison-Wesley, Massachusetts.
    [100] Pageau S.S., Joseph, P.F., Biggers, S.B.Jr., 1995. Singular antiplane stress fields for bonded and disbonded three-material junctions. Engineering Fracture Mechanics, 52, 821-832.
    [101] Bui, H.D., 2006. Fracture Mechanics Inverse Problems and Solutions. Springer, Dordrecht.
    [102] Carpinteri, A., Paggi, M., Pugno, N., 2006. Numerical evaluation of generalized stress-intensity factors in multi-layered composites. International Journal of Solids and Structures, 43, 627-641.
    [103] Giner, E., Tur, M., Fuenmayor, F.J., 2009. A domain integral for the calculation of generalized stress intensity factors in sliding complete contacts. International Journal of Solids and Structures, 46, 938-951.
    [104] Liu, D., Wang, S., Li, L., 2000. Investigation of fracture behaviour during rock mass failure. International Journal of Rock Mechanics and Mining Sciences, 37, 489-497.
    [105] Chen, C.H., Wang, C.L., 2009. A solution for an isotropic sector under anti-plane shear loadings. International Journal of Solids and Structures, 46, 2444-2452.
    [106] Chen, C.H., Wang, C.L., 2007. A fracture mechanics stability analysis of a rock slope with a tensile crack. Electronic Journal of Geotechnical Engineering, 12, Bundle C.
    [107] Sih, G.C., 1973. A special theory of crack propagation, in Methods of Analysis and Solutions of Crack Problems. Sih, G.C. (ed.), Noordhoof, Netherlands.
    [108] Smith, R.N.L., 1987. Second-order terms and strain energy density for the angled crack problem. Engineering Fracture Mechanics, 26, 463-469.
    [109] Gross, D., Seelig, T., 2006. Fracture Mechanics With an Introduction to Micromechanics. Springer, Berlin.
    [110] Kanninen, M.F., Popelar, C.H., 1985. Advanced Fracture Mechanics. Oxford University Press, New York.
    [111] Spiegel, M.R., 1968. Mathematical Handbook of Formulas and Tables. McGraw-Hill, New York.
    [112] Tuma, J.J., 1979. Engineering Mathematics Handbook (2nd edition). McGraw-Hill, New York.
    [113] Ting, T.C.T., 1998. The remarkable nature of cylindrically anisotropic elastic materials exemplified by an anti-plane deformation. Journal of Elasticity, 49, 269-284.

    下載圖示 校內：2012-07-03公開
    校外：2012-07-03公開
    QR CODE