Using the extended finite element method to integrate the level-set method to simulate the stress concentration factor at the circular holes near the material boundary of a functionally-graded material plate

Several numerical methods have developed into indispensable and effective tools for solving science-technology problems. The finite element method has particularly become a popular and effective technology, among others—a method that cannot be separated from technical programming MATLAB codes. In order to simulate the discontinuity boundary, enrichment functions have been added to the displacement field expression of the finite element method to produce the extended finite element method.This research introduced the application of MATLAB codes combined with extended finite element method based on the level-set method to simulate the stress concentration factor at circular holes near the material boundary. Both cases were compared with the following analytical results: the stress intensity factors of the finite functionally-graded material isotropic plate had a crack with an average error of 3.37%; the stress concentration factor of the isotropic plate had a circular hole near the material boundary with an error of 4.19%. In particular, the extended finite element method had significant errors compared to the Exact and experimental methods