The present work aims to investigate the effect of an edge crack on the stress concentration around the circular hole surrounded by Functionally Graded Material (FGM) in an infinite plate subjected to uniaxial tensile load. The numerical investigation has been carried out using Extended Finite Element Method (XFEM). Two cases have been analysed in this work, i.e. the whole plate made up of radial FGM and homogeneous material plate having radial FGM layer around the hole. Young’s modulus of FGM varies according to exponential and power law function. The relations of stress intensity factor (SIF) and stress concentration factor (SCF) with normalised crack length, Young’s modulus ratio, FGM layer thickness and power law index have been presented. It has been observed that the FGM layer case has low SCF around hole than FGM plate case in presence of an edge crack.

In this paper, a smoothed weighted function with the compact support is suggested to improve the numerical accuracy of blending elements for the extended finite element method (XFEM) applied to the crack problem. Such a weight function consists of the shape functions used for the meshless method, reflecting the characteristics of the enriched bases inside the blending element. The effectiveness of this weight function is validated through the numerical examples.