[en] This paper deals with the alternative representation of parametric CAD models in the context of the
Extended Finite Element Method (X-FEM) [1]. Partition of unity methods like the X-FEM allows to
embed in finite element functional spaces any discontinuity. It is so theoretically possible to simulate a
complete model without any of its geometrical features appearing in the mesh. Nevertheless, X-FEM
was at first only used in geometrically simple application (e.g. cracks) due to the lack of method to
make features of a complex CAD model to implicitly appear in the functional spaces. The geometry of
the crack was originally modeled using Level Sets because of their ability to handle complex surfaces
and naturally take into account changes in topology and geometry encountered with moving interfaces.
Level Sets modelling has been recently extended in combination with a Constructive Solid Geometry
(CSG) approach [2] but this method is still limited by the use of globally defined Level Sets.
The proposed algorithm extends the Level Sets modelisation of the geometry using the Boundary
Representation (B-Rep) of the object. In this case, Level Sets are only locally defined (Fig a). A sub-
mesh is then obtained by cutting a primary fixed mesh (encompassing the CAD model) along with
isozero of each Level Set (Fig b). Resulting sub-elements are then sorted to build a temporary topology.
One of the difficulties involved is then to match the temporary topology with the original B-Rep topology
(Fig c). The aim is to recover unmodified entities and detect deleted or new entities that could appear
during the deformation of the object. Finally, examples of computations in linear elasticity will be
shown.
Disciplines :
Mechanical engineering
Author, co-author :
Mouton, Thibaud ; Université de Liège - ULiège > Département d'aérospatiale et mécanique > Conception géométrique assistée par ordinateur
Béchet, Eric ; Université de Liège - ULiège > Département d'aérospatiale et mécanique > Conception géométrique assistée par ordinateur
Language :
English
Title :
Conversion of a B-Rep CAD model to an implicit representation in the context of the X-FEM
Publication date :
November 2011
Event name :
Fifth International Conference on Advanced COmputational Methods in ENgineering (ACOMEN)