Robust topology optimization of multi-material structures under load uncertainty using the alternating active-phase method

The synergy between different constituent materials can drastically improve the performance of composite structures. The optimal design of such structures for practical applications is complicated by the oftenencountered non-deterministic loading conditions. This paper proposes an efficient method for robust multimaterial topology optimization problems of continuum structures under load uncertainty. Specifically, the weighted sum of the mean and standard deviation of structural compliance is minimized under volume constraints for each material phase. Based on the theory of linear elasticity and using the orthogonal diagonalization of real symmetric matrices, the Monte Carlo sampling is separated from the topology optimization procedure and an efficient procedure for sensitivity analysis is established. By employing an alternating active-phase algorithm of the Gauss-Seidel version, the multi-material topology optimization problem is split into a series of binary topology optimization sub-problems, which can be easily solved using the modified SIMP model. Several 2D examples are presented to demonstrate the effectiveness of the proposed method.