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TECHNICAL PAPERS

Dynamic Stress of a Circular Cavity Buried in a Semi-Infinite Functionally Graded Material Subjected to Shear Waves

[+] Author and Article Information
Xue-qian Fang1

Department of Aerospace Engineering & Mechanics, Harbin Institute of Technology, Harbin 150001, Chinafangxueqian@163.comDepartment of Aerospace Engineering & Mechanics, Harbin Institute of Technology, Harbin 150001, China and School of Aerospace Engineering and Mechanics, Tongji University, Shanghai, 200092, Chinafangxueqian@163.comDepartment of Aerospace Engineering & Mechanics, Harbin Institute of Technology, Harbin 150001, Chinafangxueqian@163.com

Chao Hu, Shan-yi Du

Department of Aerospace Engineering & Mechanics, Harbin Institute of Technology, Harbin 150001, ChinaDepartment of Aerospace Engineering & Mechanics, Harbin Institute of Technology, Harbin 150001, China and School of Aerospace Engineering and Mechanics, Tongji University, Shanghai, 200092, ChinaDepartment of Aerospace Engineering & Mechanics, Harbin Institute of Technology, Harbin 150001, China

1

Corresponding author.

J. Appl. Mech 74(5), 916-922 (Aug 16, 2006) (7 pages) doi:10.1115/1.2712238 History: Received May 18, 2006; Revised August 16, 2006

The multiple scattering of shear waves and dynamic stress in a semi-infinite functionally graded material with a circular cavity is investigated, and the analytical solution of this problem is derived. The analytical solutions of wave fields are expressed by employing the wave function expansion method, and the expanded mode coefficients are determined by satisfying the boundary condition of the cavity. The image method is used to satisfy the traction-free boundary condition of the material structure. As an example, the numerical solution of the dynamic stress concentration factors around the cavity is also presented. The effects of the buried depth of the cavity, the incident wave number, and the nonhomogeneity parameter of materials on the dynamic stress concentration factors are analyzed. Analyses show that when the nonhomogeneity parameter of materials is <0, it has less influence on the maximum dynamic stress around the cavity; however, it has greater influence on the distribution of dynamic stress around the cavity. When the nonhomogeneity parameter of materials is >0, it has greater influence on both the maximum dynamic stress and the distribution of dynamic stress around the cavity, especially in the case that the buried depth is comparatively small.

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Copyright © 2007 by American Society of Mechanical Engineers
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Figures

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Figure 11

Effect of incident wave number parameter on dynamic stress concentration factor with θ=π∕2,b∕a=5.0

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Figure 1

Schematic of the buried cavity and the incident elastic waves in a semi-infinite graded material

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Figure 2

Distribution of dynamic stress concentration factor around the cavity (β=0,b∕a=1.1)

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Figure 3

Distribution of dynamic stress concentration factor around the cavity (β=0,b∕a=5.0)

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Figure 4

Distribution of dynamic stress concentration factor around the cavity (βa=−0.2,b∕a=1.1)

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Figure 5

Distribution of dynamic stress concentration factor around the cavity (βa=−0.2,b∕a=5.0)

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Figure 6

Distribution of dynamic stress concentration factor around the cavity (βa=0.2,b∕a=1.1)

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Figure 7

Distribution of dynamic stress concentration factor around the cavity (βa=0.2,b∕a=5.0)

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Figure 8

Effect of nonhomogeneity parameter on dynamic stress concentration factor with θ=π∕2,b∕a=1.1

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Figure 9

Effect of nonhomogeneity parameter on dynamic stress concentration factor with θ=π∕2,b∕a=5.0

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Figure 10

Effect of incident wave number parameter on dynamic stress concentration factor with θ=π∕2,b∕a=1.1

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