A study of functionally graded lattice structural design and optimisation

Abstract

Artificially designed lattice based structures, enabled by additive manufacturing are promising in various engineering applications due to their high stiffness and strength with low density and attractive multifunctional properties. In this work, a robust framework has been developed for structural optimisation by generating graded lattice structures. The goal of optimisation was to achieve the minimum structural weight while satisfying the stiffness requirement. Periodic representative volume element (RVE) homogenisation method was employed to calculate the effective mechanical properties of a unit cell of the lattice structure. A metamaterial model was determined to represent the relationship between the effective elastic constants and the geometric parameter, i.e. the strut radius of quasi-isotropic BCC lattice unit cell. Mesh effect analysis was carried out to capture the optimal Finite Element (FE) mesh size for numerical simulation, taking into consideration of the trade-off between accuracy and efficiency. The optimisation process was conducted through commercial software optistruct by applying the feasible directions (MFD) algorithm for optimisation, to achieve the optimal distribution of lattice strut radii. In post-processing, local maximum radius values were applied to joints of lattice unit cells to avoid sharp changes of strut radii between adjacent unit cells. Finally, a case study of 3-point bending beam was conducted to examine this framework and it was found that the proposed optimisation framework is valid for design and optimising graded lattice structures.