Linear smoothed extended finite element method
Abstract
The extended finite element method (XFEM) 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. Moreover, in the case of open surfaces and singularities, special, usually nonpolynomial functions must also be integrated. 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 (SmXFEM) [1], for example, makes numerical integration elegant and simple by transforming volume integrals into surface integrals. However, it was reported in [1, 2] that the strain smoothing is inaccurate when nonpolynomial functions are in the basis. This is due to the constant smoothing function used over the smoothing domains which destroys the effect of the singularity. In this paper, we investigate the benefits of a recently developed Linear smoothing procedure [3] which provides better approximation to higher order polynomial fields in the basis. Some benchmark problems in the context of linear elastic fracture mechanics (LEFM) are solved to compare the standard XFEM, the constantsmoothed XFEM (SmXFEM) and the linearsmoothed XFEM (LSmXFEM). We observe that the convergence rates of all three methods are the same. The stress intensity factors (SIFs) computed through the proposed LSmXFEM are however more accurate than that obtained through SmXFEM. To conclude, compared to the conventional XFEM, the same order of accuracy is achieved at a relatively low computational effort.
 Publication:

International Journal for Numerical Methods in Engineering
 Pub Date:
 December 2017
 DOI:
 10.1002/nme.5579
 arXiv:
 arXiv:1701.03997
 Bibcode:
 2017IJNME.112.1733S
 Keywords:

 Mathematics  Numerical Analysis
 EPrint:
 21 pages, 13 figures, 1 table