Optimisation of three-dimensional hierarchical structures with tailored lattice metamaterial anisotropy

Abstract

This paper presents a new framework for optimising three-dimensional hierarchical structures with tailored relative densities and anisotropy of lattice metamaterials. The effective properties of the lattice metamaterials are characterised with numerical homogenisation. Artificial neural network based surrogate models are developed to quantitatively relate lattice struts radii with the effective properties of the lattice metamaterials to improve the computational efficiency of the framework. A new platform integrating user-defined functions with multiple robust and efficient commercial software is developed to implement the proposed optimisation framework. The framework and its implementation are tested using three case studies featuring multiple lattice types and configurations. Case study results show that, compared with results from classical topology optimisation and optimising quasi-isotropic lattice metamaterials, optimised structures composed of tailored anisotropic lattice metamaterials achieved superior structural efficiency. This is attributed to the concurrent optimisation of the intermediate relative densities and anisotropy in the lattice metamaterials. The optimised struts radii distributions approximately align with the paths of the principal stresses. It is also found that the orthogonal struts and diagonal struts especially contribute to the bending and torsion resistance of beams, respectively.