A fully smoothed XFEM for analysis of axisymmetric problems with weak discontinuities |
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| Authors: | Detao Wan Dean Hu Sundararajan Natarajan Stéphane PA Bordas Gang Yang |
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| Affiliation: | 1. State Key Laboratory of Advanced Design and Manufacturing for Vehicle Body, Hunan University, Changsha, China;2. Department of Mechanical Engineering, Indian Institute of Technology, Chennai, India;3. Cardiff School of Engineering, Institute of Mechanics and Advanced Materials Theoretical, Applied and Computational Mechanics, Cardiff University, Cardiff, Wales, UK |
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| Abstract: | 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. |
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| Keywords: | SmXFEM indefinite integral Gaussian divergence theorem mass matrix weak discontinuity axisymmetric problem |
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