Multi-scale collaborative optimization of lattice structures using laser additive manufacturing

• A multi-scale collaborative optimization method is proposed for lattice structures. • A proposed parametric interpolation model is superior in terms of computational cost. • The proposed method enables intermediate densities to have actual physical meaning. • Optimized graded lattice structures have higher stiffness under compressive load. In the present work, an effective and efficient design approach is proposed to obtain a three-dimensional multi-scale graded lattice structure by virtue of multiple control parameters via density-based topology optimization. To balance the computational accuracy and cost, a Parameterized Interpolation of Lattice Structure (PILS) model was established, and the math formula combined two novel designing parameters: relative density at macro-scale and aspect ratio at micro-scale. A multinomial function was employed to describe the explicit association between control parameters and equivalent elastic constants with regard to relative density and aspect ratio, which avoided tedious homogenization computation burden in the structural optimization process. Consequently, the multi-scale collaborative design approach could optimize the macro material density distribution and the micro cell topology in an integrated manner. Numerical examples with respect to compliance optimization were offered to validate the benefits of the proposed approach. Finally, the quasi-static and dynamic compression tests were respectively implemented by universal testing machine and Split Hopkinson Pressure Bar (SHPB) system on lattice structures manufactured by laser powder bed fusion (LPBF). The outcomes reveal that graded lattice structures exhibit remarkably improved load-bearing performance than the uniform lattice structures.