Analysis using higher-order XFEM: implicit representation of geometrical features from a given parametric representation

¹ ESIEE-Amiens, 14 quai de la Somme, 80082 Amiens Cedex 2, France
² School of Engineering, Institute of Mechanics and Advanced Materials, Cardiff University, Queen’s Buildings, The Parade, Cardiff CF24 3AA, UK

^a Corresponding author:mohammed.moumnassi@ymail.com
^b stephane.bordas@alum.northwestern.edu

Received: 21 June 2013
Accepted: 3 May 2014

Abstract

We present a promising approach to reduce the difficulties associated with meshing complex curved domain boundaries for higher-order finite elements. In this work, higher-order XFEM analyses for strong discontinuity in the case of linear elasticity problems are presented. Curved implicit boundaries are approximated inside an unstructured coarse mesh by using parametric information extracted from the parametric representation (the most common in Computer Aided Design CAD). This approximation provides local graded sub-mesh (GSM) inside boundary elements (i.e. an element split by the curved boundary) which will be used for integration purpose. Sample geometries and numerical experiments illustrate the accuracy and robustness of the proposed approach.