  To reduce the stress concentration and ensure the structural safety for
lattice structure designs, in this paper, a new optimization framework is
developed for the optimal design of graded lattice structures, innovatively
integrating fillet designs as well as yield and elastic buckling constraints.
Both strut and fillet radii are defined as design variables. Homogenization
method is employed to characterize the effective elastic constants and yield
stresses of the lattice metamaterials. Metamaterial models are developed to
represent the relationships between the metamaterial effective properties and
lattice geometric variables. A yield constraint, based on the modified Hills
yield criterion, is developed as a function of relative strut radii and fillet
parameters. An elastic buckling constraint, based on the Euler buckling formula
and the Johnson formula, is developed as a function of relative strut radii.
Both yield and buckling constraints are integrated into an optimization problem
formulation; a new optimization framework is proposed and a case study of
minimizing the compliance of a Messerschmitt-Bolkow-Blohm beam is conducted.
The yield and buckling constraints guarantee the safety of the optimized beams
composed of BCC and PC lattices. Reductions in compliance and stress
concentration are achieved by the optimized MBB beams.
