Based on hybrid cellular automata (HCA), we present a two-scale optimization model for heterogeneous structures with non-uniform porous cells at the microscopic scale. The method uses the K-means clustering algorithm to achieve locally nonperiodicity through easily obtained elemental strain energy. This energy is used again for a two-scale topological optimization procedure without sensitivity analysis, avoiding drastically the computational complexity. Both the experimental tests and numerical results illustrate a significant increase in the resulting structural stiffness with locally nonperiodicity, as compared to using uniform periodic cells. The effects of parameters such as clustering number and adopted method versus classical Optimality Criteria (OC) are discussed. Finally, the proposed methodology is extended to 3D two-scale heterogeneous structure design.

基于混合细胞自动机（HCA），我们在微观尺度上提出了具有非均匀多孔细胞的异质结构的两尺度优化模型。该方法使用K-均值聚类算法通过容易获得的元素应变能来实现局部非周期性。该能量再次用于两级拓扑优化过程，无需进行敏感性分析，从而极大地避免了计算复杂性。实验测试和数值结果均表明，与使用均匀周期电池相比，具有局部非周期性的结构刚度显着增加。讨论了聚类数和采用的方法等参数与经典最佳标准（OC）等参数的影响。最后，将所提出的方法扩展到3D两尺度异质结构设计。