A fully smoothed XFEM for analysis of axisymmetric problems with weak discontinuities. (22nd September 2016)

• Record Type: Journal Article
• Authors: Wan, Detao; Hu, Dean; Natarajan, Sundararajan; Bordas, Stéphane P.A.; Yang, Gang
• Is Part Of: International journal for numerical methods in engineering. Volume 110:Number 3(2017)
• Page Start: 203
• Page End: 226
• Publication Date: 2016-09-22
• Subjects: SmXFEM -- indefinite integral -- Gaussian divergence theorem -- mass matrix -- weak discontinuity -- axisymmetric problem; Numerical analysis -- Periodicals; Engineering mathematics -- Periodicals; 620.001518
• DOI: 10.1002/nme.5352
• Languages: English
• ISSNs: 0029-5981

Abstract

Summary: In this paper, we propose a fully smoothed extended finite element method for axisymmetric problems with weak discontinuities. The salient feature of the proposed approach is that all the terms in the stiffness and mass matrices can be computed by smoothing technique. This is accomplished by combining the Gaussian divergence theorem with the evaluation of indefinite integral based on smoothing technique, which is used to transform the domain integral into boundary integral. The proposed technique completely eliminates the need for isoparametric mapping and the computing of Jacobian matrix even for the mass matrix. When employed over the enriched elements, the proposed technique does not require sub‐triangulation for the purpose of numerical integration. The accuracy and convergence properties of the proposed technique are demonstrated with a few problems in elastostatics and elastodynamics with weak discontinuities. It can be seen that the proposed technique yields stable and accurate solutions and is less sensitive to mesh distortion. Copyright © 2016 John Wiley & Sons, Ltd.