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Structural Engineering and Mechanics
  Volume 23, Number 1, May10 2006 , pages 63-74
DOI: https://doi.org/10.12989/sem.2006.23.1.063
 


The nonlocal theory solution for two collinear cracks
in functionally graded materials subjected to the
harmonic elastic anti-plane shear waves
Zhen-Gong Zhou and Biao Wang

 
Abstract
    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.
 
Key Words
    crack; nonlocal theory; functionally graded materials; lattice parameter; stress waves.
 
Address
Zhen-Gong Zhou; P.O. Box 1247, Center for Composite Materials, Harbin Institute of Technology, Harbin 150001, P. R. China
Biao Wang; School of Physics and Engineering, Sun Yat-Sen University, Guangzhou 510275, China
 

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