Two-Scale Optimization and Generation of Anisotropic Cellular Designs in the Context of Additive Manufacturing

Abstract

Within the context of gradient-based optimization of cellular structures, we aim to optimize designs in a two-scale setting and generate respective geometric descriptions that are additively manufacturable in powder-bed systems. We analyze representative unit cells for their suitability and present a workflow to generate cellular designs by means of a parameterized unit cell, for which an implicit surface description is described. After performing homogenization-based optimization, we compare the predicted performance of the homogenized model to a full-resolution finite element (FE) analysis. Throughout the whole process, special attention is paid to the consistent integration of manufacturing limitations in terms of horizontal overhang and feature size.We discuss the performance of cellular components with maximized stiffness. Our numerical experiment for a single-load scenario demonstrates that using isotropic micro-structures is not beneficial, even when graded. We further observe that using anisotropic micro-structures leads to improvements only in very specific cases, e.g. with a uniformly distributed load. However, the conclusion may be different for anisotropic cells with non-uniform parameterization and other loading scenarios. Instead of conducting further tedious investigations for stiffness maximization, we finally demonstrate the benefit of cellular designs for a thermo-mechanical example.