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Advances in modeling of discrete models have allowed the development of approaches for direct mesh modeling and modification. These tools mainly focus on modeling the visual appearance of the shape which is a key criterion for animation or surgical simulation. Most of the time, the resulting mesh quality as well as the semantics preservation capabilities are not considered as key features. These are the limits we overcome in this paper to enable fast and efficient mesh modifications when carrying out numerical simulations of product behaviors using the Finite Element (FE) analysis. In our approach, the modifications involve the resolution of an optimization problem where the constraints come from the shapes of the operating tools and the FE groups (sets of mesh entities) used to support the semantic information (e.g. boundary conditions, materials) contained in the FE mesh model and required for FE simulation. The overall mesh quality, a key point for accurate FE analysis, is guaranteed while minimizing an objective function based on a mechanical model of bar networks which smoothes the repositioning of nodes. Principle of the devised mesh operators is exemplified through the description of a 2D/3D mesh drilling operator. The proposed mesh modification operators are useful in the context of fast maintenance studies and help engineers to assess alternative design solutions aimed at improving the physical behavior of industrial machinery.