Optimization of graded filleted lattice structures subject to yield and buckling constraints

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.