Random Dynamic Analysis of a Crack in a Functionally Graded Materials Layer for Plane Problem Using Shear Stress

Abstract

Dynamic analysis is performed for a crack in a functionally graded materials layer for plane problem using shear stress. The material properties of the functionally graded materials layer vary randomly in the thickness direction, and the cracks are parallel to the materials faces. A pair of dynamic loadings applied on the elastic planes faces are treated as stationary stochastic processes of time. By dividing the functionally graded materials layer into several sub-layers, this problem is reduced to the analysis of laminated composites containing a crack, the material properties of each layer being random variables. A fundamental problem is constructed for the solution. Based on the use of Laplace and Fourier transforms, the boundary conditions are reduced to a set of singular integral equations, which can be solved by the Chebyshev polynomial expansions. The stress intensity factor history with its statistics is analytically derived. Numerical calculations are provided to show the effects of related parameters.