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Basic solutions of a 3-D rectangular limited-permeable crack or two 3-D rectangular limited-permeable cracks in piezoelectric materials

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Abstract

The solutions of a 3-D rectangular limited-permeable crack or two 3-D rectangular limited-permeable cracks in piezoelectric materials were given by using the generalized Almansi’s theorem and the Schmidt method. At the same time, the electric permittivity of the air inside the rectangular crack was considered. The problem was formulated through Fourier transform as three pairs of dual integral equations, in which the unknown variables are the displacement jumps across the crack surfaces. To solve the dual integral equations, the displacement jumps across the crack surfaces were directly expanded as a series of Jacobi polynomials. Finally, the effects of the electric permittivity of the air inside the rectangular crack,the shape of the rectangular crack and the distance between two rectangular cracks on the stress and electric displacement intensity factors in piezoelectric materials were analyzed.

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Authors and Affiliations

  1. Center for Composite Materials and Structures, Harbin Institute of Technology, P. O. Box 3010, No. 2, Yikuang Street, Harbin, 150080, China

    Zhen-Gong Zhou, Jia-Yi Liu & Lin Zhi Wu

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  1. Zhen-Gong Zhou
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  2. Jia-Yi Liu
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  3. Lin Zhi Wu
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Correspondence to Zhen-Gong Zhou.

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Zhou, ZG., Liu, JY. & Wu, L.Z. Basic solutions of a 3-D rectangular limited-permeable crack or two 3-D rectangular limited-permeable cracks in piezoelectric materials. Meccanica 47, 109–134 (2012). https://doi.org/10.1007/s11012-010-9418-5

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  • DOI: https://doi.org/10.1007/s11012-010-9418-5

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