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Higher-order crack tip fields for functionally graded material plate with transverse shear deformation

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Abstract

The crack tip fields are investigated for a cracked functionally graded material (FGM) plate by Reissner’s linear plate theory with the consideration of the transverse shear deformation generated by bending. The elastic modulus and Poisson’s ratio of the functionally graded plates are assumed to vary continuously through the coordinate y, according to a linear law and a constant, respectively. The governing equations, i.e., the 6th-order partial differential equations with variable coefficients, are derived in the polar coordinate system based on Reissner’s plate theory. Furthermore, the generalized displacements are treated in a separation-of-variable form, and the higher-order crack tip fields of the cracked FGM plate are obtained by the eigen-expansion method. It is found that the analytic solutions degenerate to the corresponding fields of the isotropic homogeneous plate with Reissner’s effect when the in-homogeneity parameter approaches zero.

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Authors and Affiliations

  1. Institute of Command and Information Systems, PLA University of Science and Technology, Nanjing, 210007, China

    Dianhui Hou

  2. Changping School of Noncommissioned Officer, PLA Academy of Equipment, Beijing, 102200, China

    Xiao Chong

  3. Army 73111, Xiamen, 361025, China

    Guixiang Hao

  4. Academy of Armored Force Engineering, Beijing, 100072, China

    Yao Dai

Authors
  1. Dianhui Hou
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  2. Xiao Chong
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  3. Guixiang Hao
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  4. Yao Dai
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Corresponding author

Correspondence to Yao Dai.

Additional information

Project supported by the National Natural Science Foundation of China (Nos. 90305023 and 11172332)

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Hou, D., Chong, X., Hao, G. et al. Higher-order crack tip fields for functionally graded material plate with transverse shear deformation. Appl. Math. Mech.-Engl. Ed. 37, 695–706 (2016). https://doi.org/10.1007/s10483-016-2083-6

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  • DOI: https://doi.org/10.1007/s10483-016-2083-6

Keywords

Chinese Library Classification

2010 Mathematics Subject Classification

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