Cracks problem for non-homogeneous composite material subjected to dynamic loading

In this paper, we present a method to analyse the dynamic and steady response of non-homogeneous composite materials. Di€ering from the existing works reported in literature, the present method can be used for arbitrarily varying material properties through thickness direction and the crack number can be larger than one. It is assumed that the composite material is orthotropic and all the material properties depend only on the coordinates y (along the thickness direction). The material non-homogeneity is simulated by dividing the plate into a number of layers, each layer is assigned slightly di€erent material properties. The method is based upon the Fourier and Laplace transforms to reduce the boundary value problem to a system of generalized singularity integral equations in the Laplace transform domain. The singular integral equations for the problem are derived and numerically solved by weighted residual value methods. By utilized numerical Laplace inversion the time-dependent full ®eld solutions are obtained. As the numerical illustrates, three di€erent cracked specimens, a functionally graded material, a metal- ceramic joint with functionally graded interlayer, and a metal substrate/functionally graded ®lm structure are presented for various material non-homogeneity parameters and/or functionally graded layer thickness. The results obtained demonstrate that the present model is an ecient tool in the fracture analysis of composite materials with properties varying in the thickness direction