Robust topology optimization for structures under interval uncertainty

Abstract

This paper proposes a new non-probabilistic robust topology optimization approach for structures under interval uncertainty, as a complementarity of the probabilistic robust topology optimization methods. Firstly, to avoid the nested double-loop optimization procedure that is time consuming in computations, the interval arithmetic is introduced to estimate the bounds of the interval objective function and formulate the design problem under the worst scenario. Secondly, a type of non-intrusive method using the Chebyshev interval inclusion function is established to implement the interval arithmetic. Finally, a new sensitivity analysis method is developed to evaluate the design sensitivities for objective functions like structural mean compliance with respect to interval uncertainty. It can overcome the difficulty due to non-differentiability of intervals and enable the direct application of gradient-based optimization algorithms, e.g. the Method of Moving Asymptotes (MMA), to the interval uncertain topology optimization problems. Several examples are used to demonstrate the effectiveness of the proposed method.