Structural Engineering and Mechanics

  • 제23권1호
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  • Pages.63-74
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  • 2006
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  • 1225-4568(pISSN)
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  • 1598-6217(eISSN)
테크노프레스 (Techno-Press)
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DOI QR코드

DOI QR Code

The nonlocal theory solution for two collinear cracks in functionally graded materials subjected to the harmonic elastic anti-plane shear waves

  • Zhou, Zhen-Gong (Center for fomposite Materials, Harbin Institute of Technology) ;
  • Wang, Biao (School of Physics and Engineering, Sun Yat-Sen University)
  • 투고 : 2005.10.26
  • 심사 : 2006.12.15
  • 발행 : 2006.05.10
⟨ 이전 논문 다음 논문 ⟩

초록

In this paper, the scattering of harmonic elastic anti-plane shear waves by two collinear cracks in functionally graded materials is investigated by means of nonlocal theory. The traditional concepts of the non-local theory are extended to solve the fracture problem of functionally graded materials. To overcome the mathematical difficulties, a one-dimensional non-local kernel is used instead of a two-dimensional one for the anti-plane dynamic problem to obtain the stress field near the crack tips. To make the analysis tractable, it is assumed that the shear modulus and the material density vary exponentially with coordinate vertical to the crack. By use of the Fourier transform, the problem can be solved with the help of a pair of triple integral equations, in which the unknown variable is the displacement on the crack surfaces. To solve the triple integral equations, the displacement on the crack surfaces is expanded in a series of Jacobi polynomials. Unlike the classical elasticity solutions, it is found that no stress singularities are present at crack tips.

키워드

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피인용 문헌

  1. Two collinear Mode-I cracks in piezoelectric/piezomagnetic materials vol.29, pp.1, 2008, https://doi.org/10.12989/sem.2008.29.1.055
  2. The nonlocal theory solution of a Mode-I crack in functionally graded materials vol.52, pp.4, 2009, https://doi.org/10.1007/s11431-008-0152-3
  3. Investigation of the behavior of a mode-I crack in functionally graded materials by non-local theory vol.45, pp.2-8, 2007, https://doi.org/10.1016/j.ijengsci.2007.03.018