Lightweight design with displacement constraints using graded porous microstructures

A multi-scale approach of topology optimization is proposed to design lightweight components for given loads and displacement limits. Hexagonal close-packed arrangements of circular/spherical holes allow defining 2D/3D isotropic/transversely isotropic microstructures whose macroscopic elastic properties depend on the radius of the cavities, namely the density of the porous material. An interpolation law is implemented to handle two-material structures with void, distributing both solid and graded material within a certain density range. An Augmented Lagrangian approach is adopted to handle multiple displacement constraints, along with the enforcement of a minimum amount of graded porous microstructure to be used in the optimal design. The proposed method defines: (i) boundaries of the component, and, (ii) possible internal arrangements of circular/spherical holes with graded radius. Also, when boundaries of a hollow component are prescribed, the method can be used to equip it with an optimal infill. Numerical examples are presented, concerning two- and three- dimensional problems, for different types of loads. Features of the proposed procedure are discussed, as well as peculiar properties of the optimal solutions, with special regard to coated structures. Fabrication of the porous layouts by means of additive manufacturing techniques is outlined.