Topology Optimization of Periodic Materials employing the Finite- Volume Theory

Resumo

This paper presents a computational tool for designing composite materials with periodic
microstructures for optimal effective elastic properties. The effective elastic properties of the periodic porous
material are evaluated through a combination of the homogenization method and finite-volume theory analysis.
The finite-volume theory results are employed in the topology optimization procedure, combining this technique
with the dual optimization algorithm of convex programming. In this approach, to find the optimal microstructural
topology for the periodic unit cell, specific linear combinations of the components of the effective elastic tensor
are considered to obtain extreme elastic properties, such as the maximum shear or bulk modulus under a prescribed
volume constraint. Some numerical examples involving materials with periodic porous microstructures are
analyzed, and the results demonstrate the finite-volume theory formulation’s performance for the optimal design
of composite porous materials.