| Basic solution of two parallel non-symmetric permeable cracks in piezoelectric materials |
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| 作者姓名： | 周振功 王彪 |
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| 作者单位： | Center for Composite Materials Harbin Institute of Technology，Harbin 150001，P. R. China，School of Physics and Engineering，Sun Yat-Sen University，Guangzhou 510275，P. R. China |
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| 基金项目： | 国家自然科学基金;黑龙江省自然科学基金 |
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| 摘 要： | The behavior of two parallel non-symmetric cracks in piezoelectric materials subjected to the anti-plane shear loading was studied by the Schmidt method for the permeable crack electric boundary conditions. Through the Fourier transform, the present problem can be solved with two pairs of dual integral equations ip which the unknown variables are the jumps of displacements across crack surfaces. To solve the dual integral equations, the jumps of displacements across crack surfaces were directly expanded in a series of Jacobi polynomials. Finally, the relations between electric displacement intensity factors and stress intensity factors at crack tips can be obtained. Numerical examples are provided to show the effect of the distance between two cracks upon stress and electric displacement intensity factors at crack tips. Contrary to the impermeable crack surface condition solution, it is found that electric displacement intensity factors for the permeable crack surface conditions are much smaller than those for the impermeable crack surface conditions. At the same time, it can be found that the crack shielding effect is also present in the piezoelectric materials.
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| 关 键 词： | 压电材料 平行非对称裂纹 对偶积分方程 反平面剪切负荷 应力强度 |
| 收稿时间： | 2006-11-08 |
| 修稿时间： | 2007-01-25 |
Basic solution of two parallel non-symmetric permeable cracks in piezoelectric materials |
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| Zhou?Zhen-gong,Wang?Biao.Basic solution of two parallel non-symmetric permeable cracks in piezoelectric materials[J].Applied Mathematics and Mechanics(English Edition),2007,28(4):417-428. |
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| Authors: | Zhou Zhen-gong Wang Biao |
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| Institution: | 1. Center for Composite Materials, Harbin Institute of Technology, Harbin 150001, P. R. China
2. School of Physics and Engineering, Sun Yat-Sen University, Guangzhou 510275, P. R. China |
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| Abstract: | The behavior of two parallel non-symmetric cracks in piezoelectric materials subjected to the anti-plane shear loading was studied by the Schmidt method for the permeable crack electric boundary conditions. Through the Fourier transform, the present problem can be solved with two pairs of dual integral equations ip which the unknown variables are the jumps of displacements across crack surfaces. To solve the dual integral equations, the jumps of displacements across crack surfaces were directly expanded in a series of Jacobi polynomials. Finally, the relations between electric displacement intensity factors and stress intensity factors at crack tips can be obtained. Numerical examples are provided to show the effect of the distance between two cracks upon stress and electric displacement intensity factors at crack tips. Contrary to the impermeable crack surface condition solution, it is found that electric displacement intensity factors for the permeable crack surface conditions are much smaller than those for the impermeable crack surface conditions. At the same time, it can be found that the crack shielding effect is also present in the piezoelectric materials. |
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| Keywords: | piezoelectric materials parallel non-symmetric cracks dual-integral equations intensity factor |
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