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. | XFEM fracture analysis by applying smoothed weighted functions with compact support Engineering Solid Mechanics 6 2018 227-240 Contents lists available at GrowingScience Engineering Solid Mechanics homepage esm XFEM fracture analysis by applying smoothed weighted functions with compact support Song-Il Ham and Hyon-Sik Hong Institute of Mechanics State Academy of Sciences Pyongyang DPR of Korea A R T I C L EI N F O ABSTRACT Article history In this paper a smoothed weighted function with the compact support is suggested to improve Received 10 January 2018 the numerical accuracy of blending elements for the extended finite element method XFEM Accepted 29 May 2018 applied to the crack problem. Such a weight function consists of the shape functions used for Available online the meshless method reflecting the characteristics of the enriched bases inside the blending 29 May 2018 Keywords element. The effectiveness of this weight function is validated through the numerical examples. Crack Analysis XFEM Meshfree Shape Function Smoothed Weighted Function Compact Support 2018 Growing Science Ltd. All rights reserved. 1. Introduction Numerical methods for solving discontinuous problems are still being attracted by many researchers in the field of computational fracture mechanics. Instead of traditional finite element method combining with adaptive meshing many studies have been conducted in order to improve the numerical accuracy of global and local solutions for discontinuous problems Bittencourt et al. 1996 Bourdin et al. 2000 Hansbo amp Hansbo 2004 Karihalloo amp Xiao 2003 Loehnert amp Belytschko 2007 Miehe amp Gurses 2007 Moёs et al. 1999 Oliver 1989 Areias et al. 2009 . Moreover an efficient method to initiate and propagate cracks in 2D models was offered independently of the constitutive and element specific technology Areias et al. 2016 Areias et al. 2015 Areias et al. 2013 Areias amp Rabczuk 2013 . Even though these studies are known to be .
