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Linear smoothed extended finite element method

Surendran, M., Natarajan, Sundararajan, Bordas, Stephane P. A. and Palani, G. S. 2017. Linear smoothed extended finite element method. International Journal for Numerical Methods in Engineering 112 (12) , pp. 1733-1749. 10.1002/nme.5579

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Abstract

The extended finite element method was introduced in 1999 to treat problems involving discontinuities with no or minimal remeshing through appropriate enrichment functions. This enables elements to be split by a discontinuity, strong or weak, and hence requires the integration of discontinuous functions or functions with discontinuous derivatives over elementary volumes. A variety of approaches have been proposed to facilitate these special types of numerical integration, which have been shown to have a large impact on the accuracy and the convergence of the numerical solution. The smoothed extended finite element method (XFEM), for example, makes numerical integration elegant and simple by transforming volume integrals into surface integrals. However, it was reported in the literature that the strain smoothing is inaccurate when non‐polynomial functions are in the basis. In this paper, we investigate the benefits of a recently developed Linear smoothing procedure which provides better approximation to higher‐order polynomial fields in the basis. Some benchmark problems in the context of linear elastic fracture mechanics are solved and the results are compared with existing approaches. We observe that the stress intensity factors computed through the proposed linear smoothed XFEM is more accurate than that obtained through smoothed XFEM.

Item Type: Article
Date Type: Publication
Status: Published
Schools: Engineering
Publisher: Wiley
ISSN: 0029-5981
Date of Acceptance: 8 May 2017
Last Modified: 05 Jul 2018 13:58
URI: http://orca.cf.ac.uk/id/eprint/111995

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