Shape optimization with a level set based mesh evolution method

Grégoire Allaire (1, 2) , Charles Dapogny (3, 4) , Pascal Frey (3)

1 DeFI - Shape reconstruction and identification
2 CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique
3 LJLL - Laboratoire Jacques-Louis Lions
4 Technocentre Renault [Guyancourt]

In this article, we discuss an approach for geometry and topology optimization of structures which benefits from an accurate description of shapes at each stage of the iterative process - by means of a mesh amenable for mechanical analyses - while retaining the whole versatility of the level set method when it comes to accounting for their evolution. The key ingredients of this method are two operators for switching from a meshed representation of a domain to an implicit one, and conversely; this notably brings into play an algorithm for generating the signed distance function to an arbitrary discrete domain, and a mesh generation algorithm for implicitly-defined geometries.

Mots clés: Linear elasticity; Signed distance function; Geometry and topology optimization; Level set method; Meshing and Remeshing

Domaines: Optimisation et contrôle [math.OC]

Grégoire Allaire, Charles Dapogny, Pascal Frey. Shape optimization with a level set based mesh evolution method. Computer Methods in Applied Mechanics and Engineering, 2014, pp.doi:10.1016/j.cma.2014.08.028. ⟨hal-00933545v2⟩