Topology optimization of periodic beam lattices using Cosserat elasticity

Abstract

This paper presents a novel method based on the Cosserat theory to optimize the topology of metamaterials made of slender beams. First, we filled the gap in the literature and compared the optimal topology of discrete Euler–Bernoulli beam lattices with counterparts obtained using the homogenized Cosserat theory. We investigated the effect of material and numerical parameters on the optimization results and the global stiffness. Finally, the paper highlights the importance of second-order models for slender lattice structures through different macroscopic geometries. For the first time, we presented an excellent quantitative agreement between continuum Cosserat and discrete beam results. We demonstrated that the Cosserat theory is necessary and sufficient to optimize slender, lightweight designs with lattice-based microstructures. Furthermore, the results showed that the locally allowed volume fraction was the most critical limiting parameter when maximizing global stiffness. Finally, we found that the reinforced honeycomb lattice is the stiffest microstructure for a given mass among the investigated forms.