Robust multiscale optimization accounting for spatially-varying material uncertainties

Abstract

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.