Fracture analysis of functionally graded material by hybrid meshless displacement discontinuity method

The recent progress in the development and research of functionally graded materials (FGMs) has prompted the development of numerical methods in engineering analysis for continuously non-homogeneous media. This paper presents the hybrid Meshless Displacement Discontinuity Method (MDDM) for a cracked structure with functionally graded materials. The fundamental solutions of displacement discontinuity for an isotropic homogenous body form a part of the general solutions for non-homogenous materials, in order to create the gap on the crack surface. The governing equations are satisfied by using the Meshless Local Petrov-Galerkin method (MLPG) at the scattered nodes in the domain. The stress intensity factors (SIFs) are evaluated by either crack opening displacement (COD) method or equivalent stress technique. The crack growth paths with different FGMs gradient parameters are investigated and compared with the solutions given by the finite element method (FEM). The efficiency and accuracy of hybrid MDDM are demonstrated by four examples and comparisons have been e with other analytical and numerical methods.