A multi-scale topology optimization approach with implicit function-based micro-structures

Topology optimization is a design method that afford an optimal layout with the minimization of a function, which describe a functional aspect, under prescribed constraints. The most common problem analysed in topology optimization is the compliance minimization, i.e. maximization of stiffness, under prescribed volume constraint. Here, we propose a multiscale approach with multi-material formulation where several microstructures, which differ in terms of material and topology, are generated using an implicit function. This approach, based on the theory of ho-mogenization, allows to account for different microstructures and enables to obtain functionally graded structures. Several numerical examples are shown to illustrate the main features and advantages of the proposed multi-scale topology optimization approach.