The intrinsic XFEM: A method for arbitrary discontinuities without additional unknowns

Thomas Peter Fries*, Ted Belytschko

*Korrespondierende/r Autor/-in für diese Arbeit

Publikation: Beitrag in einer FachzeitschriftArtikelBegutachtung

Abstract

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.

Originalspracheenglisch
Seiten (von - bis)1358-1385
Seitenumfang28
FachzeitschriftInternational Journal for Numerical Methods in Engineering
Jahrgang68
Ausgabenummer13
DOIs
PublikationsstatusVeröffentlicht - 24 Dez. 2006

ASJC Scopus subject areas

  • Ingenieurwesen (sonstige)
  • Angewandte Mathematik
  • Numerische Mechanik

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