  This paper studied a robust concurrent topology optimization (RCTO) approach
to design the structure and its composite materials simultaneously. For the
first time, the material uncertainty with imprecise probability is integrated
into the multi-scale concurrent topology optimization (CTO) framework. To
describe the imprecise probabilistic uncertainty efficiently, the type I hybrid
interval random model is adopted. An improved hybrid perturbation analysis
(IHPA) method is formulated to estimate the expectation and stand variance of
the objective function in the worst case. Combined with the bi-directional
evolutionary structural optimization (BESO) framework, the robust designs of
the structure and its composite material are carried out. Several 2D and 3D
numerical examples are presented to illustrate the effectiveness of the
proposed method. The results show that the proposed method has high efficiency
and low precision loss. In addition, the proposed RCTO approach remains
efficient in both of linear static and dynamic structures, which shows its
extensive adaptability.
