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Applied Mathematics and Mechanics (English Edition) ›› 2013, Vol. 34 ›› Issue (10): 1201-1224.doi: https://doi.org/10.1007/s10483-013-1739-6

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Basic solutions of multiple parallel symmetric mode-III cracks in functionally graded piezoelectric/piezomagnetic material plane

泮世东 周振功 吴林志   

  1. Center for Composite Materials and Structures, Harbin Institute of Technology, Harbin 150080, P. R. China
  • 收稿日期:2012-03-01 修回日期:2013-03-25 出版日期:2013-09-29 发布日期:2013-09-23

Basic solutions of multiple parallel symmetric mode-III cracks in functionally graded piezoelectric/piezomagnetic material plane

 PAN Shi-Dong, ZHOU Zhen-Gong, WU Lin-Zhi   

  1. Center for Composite Materials and Structures, Harbin Institute of Technology, Harbin 150080, P. R. China
  • Received:2012-03-01 Revised:2013-03-25 Online:2013-09-29 Published:2013-09-23

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561

被引次数

5

摘要： The Schmidt method is adopted to investigate the fracture problem of multiple parallel symmetric and permeable finite length mode-III cracks in a functionally graded piezoelectric/piezomagnetic material plane. This problem is formulated into dual integral equations, in which the unknown variables are the displacement jumps across the crack surfaces. In order to obtain the dual integral equations, the displacement jumps across the crack surfaces are directly expanded as a series of Jacobi polynomials. The results show that the stress, the electric displacement, and the magnetic flux intensity factors of cracks depend on the crack length, the functionally graded parameter, and the distance among the multiple parallel cracks. The crack shielding effect is also obviously presented in a functionally graded piezoelectric/piezomagnetic material plane with multiple parallel symmetric mode-III cracks.

关键词: functionally graded piezoelectric/piezomagnetic material, multiple parallel symmetric crack, crack shielding effect, solid mechanics

Abstract: The Schmidt method is adopted to investigate the fracture problem of multiple parallel symmetric and permeable finite length mode-III cracks in a functionally graded piezoelectric/piezomagnetic material plane. This problem is formulated into dual integral equations, in which the unknown variables are the displacement jumps across the crack surfaces. In order to obtain the dual integral equations, the displacement jumps across the crack surfaces are directly expanded as a series of Jacobi polynomials. The results show that the stress, the electric displacement, and the magnetic flux intensity factors of cracks depend on the crack length, the functionally graded parameter, and the distance among the multiple parallel cracks. The crack shielding effect is also obviously presented in a functionally graded piezoelectric/piezomagnetic material plane with multiple parallel symmetric mode-III cracks.

Key words: null, functionally graded piezoelectric/piezomagnetic material, multiple parallel symmetric crack, crack shielding effect, solid mechanics

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