Use of XTFEM based on the consecutive interpolation procedure of quadrilateral element to calculate J-integral and SIFs of an FGM plate

Abstract

An extended twice - interpolation finite element method (XTFEM) based on the consecutive interpolation procedure (CIP) of quadrilateral element in two-dimensional (2D) with continuous nodal stress for stress fields near material interface and geometry boundary such as inclusion and hole is presented. In contrast to the traditional approaches, the approximation shape functions constructed based on the CIP involve both nodal values and averaged nodal gradients as interpolation conditions. The CIP for quadrilateral element is developed recently by Tinh Quoc Bui, et al., 2014.In this research, we exhibit a pioneering extension of CIP – based consecutive-interpolation quadrilateral element enhanced by enrichment in terms of local partition of unity method to precisely model of a functionally graded material (FGM) plate had a single-edge crack a, and the influence of holes and inclusions near the crack was investigated in 2D structure to calculate the stress intensity factors (SIFs), an important parameter in predicting the direction of the crack even when the crack is no longer growing, taking advantages of the strengths and making use all the desirable features of both techniques, the CIP and the local enriched partition of unity method. Using MATLAB codes combined with XTFEM based on CIP of quadrilateral element. The accuracy and performance of the proposed XTFEM are compared to standard finite element method (FEM) (ANSYS). The comparison revealed the following analytical results: SIFs of the FGM isotropic plate had a crack a with an average error of 2.55% and the J-integral of 2.86%. The XTFEM gave better errors than FEM compared to the Exact and Experimental methods.