The intrinsic XFEM: a method for arbitrary discontinuities without additional unknowns
Article first published online: 16 MAY 2006
Copyright © 2006 John Wiley & Sons, Ltd.
International Journal for Numerical Methods in Engineering
Volume 68, Issue 13, pages 1358–1385, 24 December 2006
How to Cite
Fries, T.-P. and Belytschko, T. (2006), The intrinsic XFEM: a method for arbitrary discontinuities without additional unknowns. Int. J. Numer. Meth. Engng., 68: 1358–1385. doi: 10.1002/nme.1761
- Issue published online: 20 NOV 2006
- Article first published online: 16 MAY 2006
- Manuscript Accepted: 20 MAR 2006
- Manuscript Received: 2 MAR 2006
- Army Research Office. Grant Number: W911NF-05-1-0049
- Office of Naval Research. Grant Number: N00014-98-1-0578
A new method for treating arbitrary discontinuities in a finite element (FE) context is presented. Unlike the standard extended FE method (XFEM), no additional unknowns are introduced at the nodes whose supports are crossed by discontinuities. The method constructs an approximation space consisting of mesh-based, enriched moving least-squares (MLS) functions near discontinuities and standard FE shape functions elsewhere. There is only one shape function per node, and these functions are able to represent known characteristics of the solution such as discontinuities, singularities, etc. The MLS method constructs shape functions based on an intrinsic basis by minimizing a weighted error functional. Thereby, weight functions are involved, and special mesh-based weight functions are proposed in this work. The enrichment is achieved through the intrinsic basis. The method is illustrated for linear elastic examples involving strong and weak discontinuities, and matches optimal rates of convergence even for crack-tip applications. Copyright © 2006 John Wiley & Sons, Ltd.