Coupled optimization of macroscopic structures and lattice infill
Article dans une revue avec comité de lecture
Journalinternational Journal for Numerical Methods in Engineering,
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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