A non-gradient multi-material robust topology optimization approach to multi-material structures considering load uncertainty

The robust topology optimization (RTO) design of multi-material structures holds significant practical implications and theoretical value. The main contribution of this paper is to study the RTO problem of multi-material structures considering load uncertainty, and to propose an innovative non-gradient multi-material RTO approach to multi-material structures considering load uncertainty. To this end, the alternating active-phase algorithm (AAPA) is first applied to decouple this RTO problem, and combined with these approaches (probabilistic approach, density-based approach, and linear combination approach) to construct the RTO model of multi-material structures considering load uncertainty and taking the linear combination of the mean and standard deviation of the structural compliance as the objective function. Subsequently, the superposition principle of linear theory, Monte Carlo simulation (MCS), and orthogonal diagonalization of a symmetric matrix are applied to derive the computational equation for the objective function suitable for an improved proportional topology optimization (IPTO) approach. Based on this, the IPTO approach is employed to solve this RTO model, thereby forming an innovative multi-material non-gradient RTO approach. Finally, two numerical examples are applied to illustrate the efficacy of this new approach and the influence of the filtering radius on the structural RTO design. The results showcase that this new approach can tackle the robust optimization design issues of multi-material structures and yield an optimal structure with enhanced robustness. Moreover, the proposed approach's filtering radius directly influences the shape of the optimized structure.