In this work we demonstrate a methodology
for performing robust optimization using multivariable
parameterized lattice microstructures. By introducing
material uncertainties at the microscale, we are able to
simulate the variations in geometry that occur during
the manufacturing stage and design structures which are
tolerant to variations in the microscale geometry. We
impose both uniform and spatially-varying, non-uniform
material uncertainties to generate structures which, in
terms of standard deviation, are up to 77% more robust
in the non-spatially uncertainty varying case, and 74%
more robust in the spatially-varying case. We also explore the utility of imposing spatially-varying material
uncertainties compared to using homogeneous, uniform
material uncertainties, which are much less computationally expensive. It is found that when designs that
have been optimized assuming uniform uncertainties are
subject to spatially-varying uncertainties, their standard
deviations of compliance are similar to designs optimized
assuming spatially-varying uncertainties. However, their
mean compliances are far higher in comparison to designs generated by assuming spatially-varying material
uncertainties.