A mesh evolution algorithm based on the level set method for geometry and topology optimization

Authors:
Grégoire Allaire;Charles Dapogny;Pascal Frey
Affiliations:
Centre de Mathématiques Appliquées (UMR 7641), École Polytechnique, Palaiseau, France 91128;UMR 7598, Laboratoire J.-L. Lions, UPMC Univ Paris 06, Paris, France 75005 and Renault DREAM-DELT'A, Guyancourt, France;UMR 7598, Laboratoire J.-L. Lions, UPMC Univ Paris 06, Paris, France 75005
Venue:
Structural and Multidisciplinary Optimization
Year:
2013

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Abstract

We propose an approach for structural optimization which combines the flexibility of the level set method for handling large deformations and topology changes with the accurate description of the geometry provided by an exact mesh of the shape. The key ingredients of our method are efficient algorithms for (i) moving a level set function on an unstructured mesh, (ii) remeshing the surface corresponding to the zero level set and (iii) simultaneously adaptating the volumic mesh which fits to this surfacic mesh.