LI Lin, ZHOU Zhen-gong, WANG Biao. Scattering of Anti-Plane Shear Waves in a Functionally Graded Material Strip With an Off-Center Vertical Crack[J]. Applied Mathematics and Mechanics, 2006, 27(6): 646-654.
 Citation: LI Lin, ZHOU Zhen-gong, WANG Biao. Scattering of Anti-Plane Shear Waves in a Functionally Graded Material Strip With an Off-Center Vertical Crack[J]. Applied Mathematics and Mechanics, 2006, 27(6): 646-654.

# Scattering of Anti-Plane Shear Waves in a Functionally Graded Material Strip With an Off-Center Vertical Crack

• Rev Recd Date: 2006-02-26
• Publish Date: 2006-06-15
• The scattering problem of anti_plane shear waves in a functionally graded material strip with an off_center crack is investigated by use of Schmidt method.The crack is vertically to the edge of the strip.By using the Fourier transform,the problem can be solved with the help of a pair of dual integral equations that the unknown variable is the jump of the displacement across the crack surfaces.To solve the dual integral equations,the jump of the displacement across the crack surfaces was expanded in a series of Jacobi polynomials.Numerical examples were provided to show the effects of the parameter describing the functionally graded materials,the position of the crack and the frequency of the incident waves upon the stress intensity factors of the crack.
•  [1] Erdogan F,Wu B H. The surface crack problem for a plate with functionally graded properties[J].Journal of Applied Mechanics,1997,64(3):449—456. [2] Delale F,Erdogan F.On the mechanical modeling of the interfacial region in bonded half-planes[J].ASME Journal of Applied Mechanics,1988,55(2):317—324. [3] Jin Z H, Batra R C.Interface cracking between functionally graded coating and a substrate under antiplane shear[J].International Journal of Engineering Science,1996,34(15):1705—1716. [4] Bao G, Cai H. Delamination cracking in functionally graded coating/metal substrate systems[J].Acta Materialia,1997,45(3):1055—1066. [5] Erdogan F, Wu H B. Crack problems in FGM layer under thermal stress[J].Journal of Thermal Stress,1996,19(3):237—265. [6] Parameswaran V,Shukla A.Crack-tip stress fields for dynamic fracture in functionally graded materials[J].Mechanics of Materials,1999,31(9):579—596. [7] WANG Bao-lin,HAN Jie-cai,DU Shan-yi.Crack problem for non-homogeneous composite materials subjected to dynamic loading[J].International Journal of Solids and Structures,2000,37(9):1251—1274. [8] Parameswaran V, Shukla A. Dynamic fracture of a functionally graded material having discrete property variation[J].Journal of Materials Science,1998,31(6):1641—1657. [9] Morse P M, Feshbach H.Methods of Theoretical Physics[M].Vol 1.New York:McGraw-Hill,1958. [10] Srivastava K N, Palaiya K N, Karaulia D S. Interaction of shear waves with two coplanar Griffith cracks situated in an infinitely long elastic strip[J].International Journal of Fracture,1983,23(1):3—14. [11] Chen E P. Impact response of a finite crack in a finite strip under anti-plane shear[J].Engineering Fracture Mechanics,1977,9(4):719—724. [12] Gradshteyn I S, Ryzhik I M.Table of Integrals, Series and Products[M].New York:Academic Press,1980,923—967. [13] Erdelyi A.Tables of Integral Transforms[M].Vol 1.New York:McGraw-Hill,1954,68—105. [14] ZHOU Zhen-gong,HAN Jie-cai,DU Shan-yi.Two collinear Griffith cracks subjected to uniform tension in infinitely long strip[J].International Journal of Solids and Structures,1999,36(4):5597—5609. [15] 周振功，王彪.位于两不同正交各向异性半平面间张开型界面裂纹的性能分析[J].应用数学和力学，2004,25(7):667—676. [16] 周振功，王彪.压电材料中两平行对称可导通裂纹断裂性能分析[J].应用数学和力学，2002,23(12):1211—1219.

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