[en] This paper presents and describes an intermediate approach which takes its place
between the two classical methods of shape and topology optimization. It is based on using
the recent Level Set description of the geometry and the novel eXtended Finite Element Method
(X-FEM). The method benefits from the fixed mesh work using X-FEM and from the curves
smoothness of the Level Set description. Design variables are shape parameters of basic geometric
features. The number of design variables of this formulation remains small whereas
various global and local constraints can be considered. A key problem which is investigated
here is the sensitivity analysis and the way it can be carried out precisely and efficiently. Numerical
applications revisit some classical 2D (academic) benchmarks from shape optimization
and illustrate the great interest of using X-FEM and Level Set description together. The paper
presents the results of stress constrained problems using the proposed X-FEM and Level Set
based formulation. A central issue is the sensitivity analysis (related to the compliance and/or
the stresses) and the way it can be carried out efficiently. A special attention is also paid to
stress constrained problems which are often neglected in other Level Set Methods works.