Multiscale Optimization of 3D-Printed Beam-Based Lattice Structures through Elastically Tailored Unit Cells

Herein, a numerical multiscale tool is developed to design 3D periodic lattice structures. The work is motivated by the high design freedom of additive manufacturing technologies, which enable complex multiscale lattice structures to be printed. A finite-element-based free-material optimization method is used to determine the ideal orthotropic material properties of a 3D macrostructure space. Subsequently, a population-based algorithm is established to design optimized microscopic lattice unit cells with the desired structural properties. The design variables are the coordinates of lattice skeleton nodes defined within the 3D lattice unit cell space, and the connectivities between them resulting in a truss skeleton. For the calculation of the mechanical properties of the individual lattice cells, an effective Timoshenko beam-based finite element calculation method is developed. The macroscale structure can be constructed by periodically filling the domain with the customized unit cell representing a metamaterial. The method is demonstrated by 3D beam problems with compliance constraints. These macroscopic demonstrators of the developed lattice structures were also 3D-printed. The benefit regarding the weight-specific structural performance is validated through benchmarking with periodic lattice design solutions using well-known standard lattice cells.