The introduction of cellular materials models in topology optimization allows designers to achieving significant weight reductions in structural applications. However, higher material savings and increased performance can be achieved if the material and the structure topologies are concurrently designed. The objective of this paper is to incorporate and establish a design methodology to obtaining optimal macro-scale structures and the corresponding optimal meso-scale periodic material designs in continuum design domains. The proposed approach makes use of homogenization theory to establish communication bridges between both material and structural scales. The periodicity constraint makes such cellular materials manufacturable. Penalization methods are used to obtaining binary solutions in both scales. This proposed methodology is demonstrated in the design of compliant mechanisms and structures of minimum compliance. The results demonstrate potential benefits when this multi-scale design algorithm when applied to the design of ultra-lightweight structures.

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