Gradient porous structured materials possess significant potential of being applied in many engineering fields. To accelerate the design process of infill graded microstructures of uniform local density, a novel asymptotic homogenisation topology optimisation method was proposed by Zhu et al. (J Mech Phys Solids 124:612–633, 2019), aiming for (1) significantly enriching the pool of representable graded microstructures; and (2) deriving an homogenised formulation for stress analysis in consistency with fine-scale results. But the work is severely confined from being widely applied, mainly due to the following two reasons. Firstly, to circumvent macroscopically pointwise computation for solving various microscopic cell problems, linearisation had to be adopted for its numerical implementation, and this significantly reduces the design freedom. Secondly, lacking of sensitive analysis, genetic algorithm was chosen for optimisation, inevitably decreasing the computational efficiency. To address these bottleneck challenging issues, a zoning scheme empowered by computational parallelism is introduced, and the sensitivity analysis associated with the new asymptotic framework is conducted. Through comparisons with fine-scale simulation results, the proposed algorithm is shown to be an effective tool for evaluating the mechanical behaviour of graded microstructures. As an optimisation tool, the mapping function takes a concise and explicit form. But its parameterisation still needs further investigation, so as to improve the solution optimality of the present approach, especially in comparison with another recently proposed method (Groen and Sigmund, Internat J Numer Methods Engrg 113(8):1148–1163, 2018). Optimisation results for three-dimensional graded microstructures are also shown, which are not frequently discussed in literature, possibly because of the high computational cost generated.

梯度多孔结构材料具有在许多工程领域中应用的巨大潜力。为了加快均匀局部密度的填充梯度微结构的设计过程，Zhu等人提出了一种新的渐近均匀化拓扑优化方法。（J Mech Phys Solids 124：612–633，2019），旨在（1）显着丰富可代表的渐变微结构库；（2）得出均质的应力分析公式，与精细结果一致。但是，由于以下两个原因，使得该工作受到严格限制而无法广泛应用。首先，为了解决宏观的逐点计算以解决各种微观单元问题，必须在其数值实现中采用线性化，这大大降低了设计自由度。其次，由于缺乏敏感性分析，选择了遗传算法进行优化，不可避免地降低了计算效率。为了解决这些瓶颈挑战性问题，引入了一种由计算并行性授权的分区方案，并进行了与新渐近框架相关的灵敏度分析。通过与精细仿真结果的比较，该算法被证明是一种用于评估梯度微结构力学性能的有效工具。作为优化工具，映射功能采用简洁明了的形式。但是其参数化仍需要进一步研究，以提高本方法的最优解，尤其是与最近提出的另一种方法相比（Groen和Sigmund，Internat J Numer Methods Engrg 113（8）：1148–1163，2018年）。还显示了三维梯度微结构的优化结果，这在文献中不经常讨论，可能是因为产生了很高的计算成本。