Multiscale topology optimization of 3D structures: A micro-architectured materials database assisted strategy

Abstract This article presents a datadriven multiscale optimization method for solving 3D problems under given boundary conditions. The topology is represented by an extended level-set function that allows the nucleation of new holes throughout the process making it less sensitive to the initial guess. The two scales involved are the structural (macro) scale and the material (micro) scale. For the macro scale, the stiffness is maximized while reducing the weight of the structure; while for the micro scale, the homogenized elasticity tensor is prescribed and the weight is also minimized. In order to decrease the significant computational cost of multi-scale optimization, a datadriven approach is proposed. The method consists in two main steps: (1) an offline step to build a database (catalog of optimal micro-architectured materials indexed by their effective elasticity) for a wide range of desired elasticity tensors, and (2) an online step aiming to optimize the 3D structure at the macroscale. The precomputed catalog is thus interrogated in order to find the best micro-architectured material within the macroscale optimization. This method performs a two scales weight minimization and leads to a significantly light structure design. The optimization formulation is first introduced. Then a few 3D benchmark tests are given for the multi-scale optimization using micro-architectured materials.

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