Coupled optimization of macroscopic structures and lattice infill

Perle Geoffroy-Donders (1) , Grégoire Allaire (1) , Georgios Michailidis , Olivier Pantz (1)

1 CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique

This paper 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 ho-mogenization 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.

Domaines: Analyse numérique [math.NA]; Optimisation et contrôle [math.OC]; Mécanique des structures [physics.class-ph]

Perle Geoffroy-Donders, Grégoire Allaire, Georgios Michailidis, Olivier Pantz. Coupled optimization of macroscopic structures and lattice infill. International Journal for Numerical Methods in Engineering, 2020, 123 (13), pp.2963-2985. ⟨10.1002/nme.6392⟩. ⟨hal-02429166⟩