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Analysis for Multiple Cracks in 2D Piezoelectric Bimaterial Using the Singular Integral Equation Method

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Abstract

A singular integral equation method is proposed to analyze the two-dimensional (2D) multiple cracks in anisotropic piezoelectric bimaterial. Using the Somigliana formula, a set of singular integral equations for the multiple crack problems are derived, in which the unknown functions are the derivatives of the generalized displacement discontinuities of the crack surfaces. Then, the exact analytical solution of the extended singular stresses and extended stress intensity factors near the crack tip is obtained. Singular integrals of the singular integral equations are computed by the Gauss–Chebyshev collocation method. Finally, numerical solutions of the extended stress intensity factors of some examples are presented and discussed.

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Acknowledgements

The authors would like to express their special thanks to the National Natural Science Foundation of China (Project No. 11172320).

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Authors and Affiliations

  1. College of Engineering, China Agricultural University, Beijing, 100083, China

    Ting Cao

  2. Department of CAE, BYD Auto Industry Co., Ltd, Shenzhen, 518118, China

    Xiaobin Feng

  3. College of Science, China Agricultural University, Beijing, 100083, China

    Taiyan Qin

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  1. Ting Cao
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  2. Xiaobin Feng
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  3. Taiyan Qin
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Correspondence to Taiyan Qin.

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Cao, T., Feng, X. & Qin, T. Analysis for Multiple Cracks in 2D Piezoelectric Bimaterial Using the Singular Integral Equation Method. Acta Mech. Solida Sin. 35, 261–272 (2022). https://doi.org/10.1007/s10338-021-00281-5

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  • DOI: https://doi.org/10.1007/s10338-021-00281-5

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