Abstract
Topology optimization is a technique used in engineering to determine the optimal distribution of material within a defined design domain. This technique has been applied to the design of cellular materials to create an efficient microstructural arrangement that meets the necessary performance criteria and minimizes the weight of the material. This article presents an innovative approach that combines topology optimization, a homogenization method based on the unit cell concept and finite-volume theory to design highly efficient periodic cellular materials with optimized macroscopic elastic properties. To determine the optimal microstructural topology, specific linear combinations of components of the homogenized elastic matrix are considered to obtain optimized elastic properties, such as maximum shear/bulk moduli, considering a prescribed volume fraction constraint of solid material. Numerical examples are analysed, and the results demonstrate the exceptional performance of this approach in achieving optimal designs of cellular materials characterized by chequerboard-free patterns without filtering techniques.
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