Optimisation for ultralight and high-stiffness hierarchical structures with tailored lattice metamaterials

Abstract

This research aims to develop advanced optimisation frameworks for the optimal design of ultralight and high-stiffness hierarchical structures with tailored lattice metamaterials, with the consideration of manufacturing effects, i.e., additive manufacturing building direction effects, and structural safety, i.e., yield criterion. Lattice structures are a type of bioinspired hierarchical lightweight structures with high stiffness-to-weight ratio and high strength-to-weight ratio. The scale decomposition method is adopted in this research to decompose lattice structures into two hierarchies, being the lower-hierarchical-level structures of lattice cells constructed with networks of struts and the higher-hierarchical-level structures composed of lattice metamaterials with effective material properties (e.g., effective elasticity tensors). To develop the optimisation frameworks, the following studies have been conducted. Firstly, a new framework has been developed to simultaneously optimise the distributions of relative densities, effective elastic moduli, and anisotropy of metamaterials in lattice structures. In this framework, a numerical homogenisation method is adopted to characterise the anisotropic effective elasticity tensors of lattice metamaterials, and neural-network-based surrogate models are developed to bridge the geometric information, i.e., lattice strut radii, of the lower-hierarchical-level lattice cells and the effective material properties of lattice metamaterials at the higher-hierarchical-level. Thus, the tailoring of relative densities, effective elastic moduli, and anisotropy can be enabled by optimising the lattice strut radii. A robust optimisation platform integrating multiple commercial software has been developed to implement the proposed optimisation framework. Case study results confirm that the structural efficiency (the stiffness-to-weight ratio) of graded lattice structures can be effectively improved by tailoring the anisotropy of lattice metamaterials. Secondly, a framework of conformal lattice structural optimisation has been developed to enable the optimisation of orientations of lattice cells to allow them to be not only conformal to the curved boundaries of higher-hierarchical-level structural features to achieve a better approximation of the boundary curvatures but also aligning with the paths of major principal stresses. This framework is implemented into open-source software, FEniCS (finite element solver) and IPOPT (sensitivity solver). Case study results demonstrated that conformal lattice structures can achieve higher structural efficiency than non-conformal lattice structures. Thirdly, the effects of building direction (BD) on the effective Young’s moduli of lattice metamaterials, fabricated using selective laser melting, have been investigated through conducting quasi-static uniaxial compression tests at room temperature. A surrogate model has been developed to describe the BD effects on the effective Young’s moduli of lattice metamaterials as a function of their relative densities and strut overhang angles. This surrogate model has been integrated into the optimisation framework to enable the BD effects to be considered during optimising cell orientations for conformal lattice structures. Finally, yield stress constrained lattice structural optimisation framework has been developed to ensure the structural safety of optimised lattice structures with respect to yield failure. Fillets are introduced to the strut joint regions of lattice cells to effectively enhance the yield stresses of the lattice metamaterials. The effective properties (the effective Young’s moduli, the effective Poisson’s ratios, and the effective yield stresses) of the lattice metamaterials have been experimentally characterised through conducting quasi-static uniaxial compression tests at room temperature. A yield stress constraint for lattice structural optimisation has been derived based on the von Mises yield criterion. Case study results show that by introducing the yield stress constraint, the structural safety of optimised lattice structures with respect to yield failure can successfully be guaranteed. The results also demonstrate that the strength-to-weight ratio of the optimised lattice structures can be effectively improved by introducing fillets to the strut joint regions of lattice cells.