Optimisation design of graded lattice structures for natural frequency

In this study, a design approach is presented to optimise the layout of lattice structures for natural frequency in dynamic problems. For an optimisation framework, the design domain is periodically configured by a series of predefined microstructures with variable thickness of structures. An interpolation scheme was employed to estimate the mechanical properties of the unit cells with respect to their thicknesses. To achieve an optimised design ready for additive manufacturing, the constraint of the minimum length scale is considered in the optimisation process, and a post-processing scheme is developed to smooth the mismatches between the unit cells with different thicknesses of microstructures. Two numerical examples are investigated to demonstrate the feasibility of the proposed approach for designing manufacturable lattice structures with practical significance.