Optimization of Oriented and Parametric Cellular Structures by the Homogenization Method

Abstract

We present here a topology optimization method based on a homogenization approach to design oriented and parametrized cellular structures. The present work deals with 2-D square cells featuring a rectangular hole, because their structure is close to that of rank-2 sequential laminates, which are optimal for compliance optimization. For several cells, the value and the parametric sensitivities of their effective elastic tensor can easily be computed, by the resolution of a cell problem. The obtained results can be used to build a surrogate model for the homogenized constitutive law. Moreover, we add the local orientation of the cells to our problem. Then, an optimal composite shape is computed thanks to an alternate directions algorithm. The crucial ingredient of the methodology is the extraction of a quasi-periodic and additive manufacturable structure from the previously obtained composite shape, based on the introduction of a space transformation.