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Coupled optimization of macroscopic structures and lattice infill

Article dans une revue avec comité de lecture
Author
GEOFFROY‐DONDERS, Perle
86289 Laboratoire Procédés et Ingénierie en Mécanique et Matériaux [PIMM]
ALLAIRE, Grégoire
89626 Centre de Mathématiques Appliquées - Ecole Polytechnique [CMAP]
MICHAILIDIS, Georgios
1123846 Helic ANSYS Hellas [Helic ANSYS Hellas S.A.]
PANTZ, Olivier
199970 Laboratoire Jean Alexandre Dieudonné [JAD]

URI
http://hdl.handle.net/10985/22479
DOI
10.1002/nme.6392
Date
2020-05-16
Journal
international Journal for Numerical Methods in Engineering,

Abstract

This article is concerned with the coupled optimization of the external boundary of a structure and its infill made of some graded lattice material. The lattice material is made of a periodic cell, macroscopically modulated and oriented. The external boundary may be coated by a layer of pure material with a fixed prescribed thickness. The infill is optimized by the homogenization method while the macroscopic shape is geometrically optimized by the Hadamard method of shape sensitivity. A first original feature of the proposed approach is that the infill material follows the displacement on the exterior boundary during the geometric optimization step. A second key feature is the dehomogenization or projection step which build a smoothly varying lattice infill from the optimal homogenized properties. Several numerical examples illustrate the effectiveness of our approach in 2-d, which is especially convenient when considering design-dependent loads.

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