Robust topology optimization with interval field model: on the spatially varied non-probabilistic uncertainty of material property, loading and geometry

In this work, we introduce the non-probabilistic uncertainties of spatial variation into the topology optimization problem. We investigate the material properties, geometry and loading uncertainties. A recently emerged interval field model is employed for modeling these spatially varied uncertainties. Based on the robust topology optimization framework, we propose an interval-field based perturbation analysis (IFPA) method for predicting the median and radius of structural compliance under uncertainty, and the sensitivity analysis is developed accordingly. Three numerical examples are presented, in which topology optimization problems with uncertainty aroused from material properties, loading and geometry are discussed separately. Comparing the results with those of Monte Carlo simulations, we illustrate the accuracy and efficiency of the IFPA in predicting structural compliance. The topology optimization results demonstrate the merit of emphasizing spatial dependence in topology optimization with non-probabilistic uncertainty.