Topological and morphological design of additively-manufacturable spatially-varying periodic cellular solids

The focus of this research is to create a methodology to systematically generate spatially-varying, periodic, cellular microstructures that are tailored to attain optimized performance of the macrostructure. The unit cell lattice is represented by Fourier series expansions, and the corresponding amplitudes and phase spectrum are obtained. Then, the material distribution (topology) and orientation of each cell (morphology) are optimized for multiple load cases. The phase of the spatial harmonics is updated based on the optimized orientation, and the analog response is thresholded with the optimized material distribution to find the binary lattices. The framework is tested for three types of lattices with various periodicities. The square cell with a rectangular hole shows the exploitation of the cell's orthotropic properties for structures subjected to a single load case; the triangular cell with the triangular lattice depicts the applicability of other types of cells and lattices to transfer shear for the structures subjected to multiple load cases; and the square cell with pentagonal lattices shows the versatility of the framework. An optimized triangular cellular solid is additively manufactured, and it is validated experimentally that 12% higher stiffness and 57% higher strength can be achieved compared to the conventional topology optimization design. (c) 2020 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http:// creativecommons.org/licenses/by-nc-nd/4.0/).