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.

本文提出了一种新的框架，用于优化具有定制相对密度和晶格超材料各向异性的三维分层结构。晶格超材料的有效特性以数值均匀化为特征。开发了基于人工神经网络的替代模型，以定量地将晶格支柱半径与晶格超材料的有效特性相关联，以提高框架的计算效率。开发了一个将用户定义的功能与多个强大且高效的商业软件集成在一起的新平台，以实现所提出的优化框架。该框架及其实现使用具有多种晶格类型和配置的三个案例研究进行测试。案例研究结果表明，与经典拓扑优化和优化准各向同性晶格超材料的结果相比，由定制的各向异性晶格超材料组成的优化结构实现了更高的结构效率。这归因于同时优化晶格超材料中的中间相对密度和各向异性。优化后的支柱半径分布与主应力路径大致对齐。还发现正交支柱和对角支柱分别对梁的抗弯和抗扭特别有贡献。这归因于同时优化晶格超材料中的中间相对密度和各向异性。优化后的支柱半径分布与主应力路径大致对齐。还发现正交支柱和对角支柱分别对梁的抗弯和抗扭特别有贡献。这归因于同时优化晶格超材料中的中间相对密度和各向异性。优化后的支柱半径分布与主应力路径大致对齐。还发现正交支柱和对角支柱分别对梁的抗弯和抗扭特别有贡献。