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Topology and geometry optimization of elastic structures by exact deformation of simplicial mesh

Abstract : We propose a method for structural optimization that relies on two alternative descriptions of shapes: on the one hand, they are exactly meshed so that mechanical evaluations by finite elements are accurate; on the other hand, we resort to a level-set characterization to describe their deformation along the shape gradient. The key ingredient is a meshing algorithm for building a mesh, suitable for numerical computations, out of a piecewise linear level-set function on an unstructured mesh. Therefore, our approach is at the same time a geometric optimization method (since shapes are exactly meshed) and a topology optimization method (since the topology of successive shapes can change thanks to the power of the level-set method).
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Grégoire Allaire, Charles Dapogny, Pascal Frey. Topology and geometry optimization of elastic structures by exact deformation of simplicial mesh. Comptes Rendus Mathématique, Elsevier Masson, 2011, 349 (17-18), pp.999--1003. ⟨hal-00784047⟩

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