  Gradient porous structured materials possess significant potential of being
applied in many engineering fields. To accelerate the design process of infill
graded microstructures, a novel asymptotic homogenisation topology optimisation
method was proposed by Zhu et al.(2019), aiming for 1) significantly enriching
the pool of representable graded microstructures; 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 the 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 by Groen et al (2018). The
high computational efficiency shown by the proposed scheme is also demonstrated
with optimisation results for three-dimensional graded microstructures, which
are not frequently discussed in literature, possibly because of the high
computational cost generated.
