[en] This paper presents an intermediate approach between parametric
shape optimization and topology optimization. It is based on using
the recent Level Set description of the geometry and the novel
eXtended Finite Element Method (XFEM). The method takes benefit of
the fixed mesh work using XFEM and of the smooth curves
description of the Level Set method. Design variables are shape
parameters of basic geometric features like circles, triangles
etc. The number of design variables of this formulation is small
whereas various global and local constraints can be considered.
The Level Set description allows to modify the connectivity of the
structure as geometric features can merge or separate from each
other. However no new entity can be introduced by the programme. A
central problem that is investigated here is the sensitivity
analysis and the way it can be carried out efficiently. Numerical
applications revisit some classical (academic) benchmarks from
shape and topology optimization.
