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

Highlights: • A new lattice structural optimization framework is developed by innovatively integrating fillet designs, and yield and buckling constraints. • The constraints are developed based on modified Hill's yield criterion as well as Euler and Johnson buckling formulae. • The yield and buckling constraints guarantee the safety of the optimized Messerschmitt-Bolkow-Blohm beams composed of BCC or PC lattices. • For both lattice types, introducing fillets has resulted in reduced compliance and stress concentration for the optimized beams. To reduce the stress concentration and ensure 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 buckling constraints. Both relative strut radii and fillet parameters are defined as design variables, for BCC and PC lattices. Numerical homogenization 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. Yield and buckling constraints, based on modified Hill's yield criterion as well as Euler and Johnson buckling formulae respectively, are developed as functions of lattice geometric variables. A new optimization framework is proposed with both yield and buckling constraints integrated. A case study on minimizing the compliance of a Messerschmitt-Bolkow-Blohm beam, composed of either BCC or PC lattices, is conducted. The yield and buckling constraints guarantee the structural safety of the optimized lattice beams. The optimized beams composed of filleted lattices, compared with non-filleted lattices in the corresponding type, show reduced proportions subject to high modified Hill's stress (${\sigma }^{\mathrm{Hill}}\ge 0.95$) with 6 ~ 7% reductions in compliance.