Multiscale optimisation of dynamic properties for additively manufactured lattice structures

Abstract

A framework for tailoring the dynamic properties of functionally graded lattice structures through the use of multiscale optimisation is presented in this thesis. The multiscale optimisation utilises a two scale approach to allow for complex lattice structures to be simulated in real time at a similar computational expense to traditional finite element problems. The micro and macro scales are linked by a surrogate model that predicts the homogenised material properties of the underlying lattice geometry based on the lattice design parameters. Optimisation constraints on the resonant frequencies and the Modal Assurance Criteria are implemented that can induce the structure to resonate at specific frequencies whilst simultaneously tracking and ensuring the correct mode shapes are maintained. This is where the novelty of the work lies, as dynamic properties have not previously been optimised for in a multiscale, functionally graded lattice structure.

Multiscale methods offer numerous benefits and increased design freedom when generating optimal structures for dynamic environments. These benefits are showcased in a series of optimised cantilever structures. The results show a significant improvement in dynamic behavior when compared to the unoptimised case as well as when compared to a single scale topology optimised structure. The validation of the resonant properties for the lattice structures is performed through a series of mechanical tests on additive manufactured lattices. These tests address both the micro and the macro scale of the multiscale method. The homogeneous and surrogate model assumptions of the micro scale are investigated through both compression and tensile tests of uniform lattice samples. The resonant frequency predictions of the macro scale optimisation are verified through mechanical shaker testing and computed tomography scans of the lattice structure. Sources of discrepancy between the predicted and observed behavior are also investigated and explained.