Non-gradient Robust Topology Optimization Method Considering Loading Uncertainty

To effectively tackle the robust topology optimization (RTO) problem of continuum structure considering the uncertainties of loading magnitude and direction under the premise of avoiding gaining the sensitivity information, a non-gradient RTO method was proposed by combining the improved proportional topology optimization (IPTO) algorithm with multiple methods (including the probabilistic approach, the superposition principle of linear theory, the Monte Carlo method and the weighted combination method). Among these, the probabilistic approach was used to describe the uncertainties of loading magnitude and direction. The weighted combination method was employed to establish the RTO model with the objective function of minimizing the weighted sum of the expectation and standard deviation of structural compliance. The calculation method of the expectation and standard deviation of structural compliance was given by applying the superposition principle of linear theory and the Monte Carlo method. Subsequently, the core equations of the IPTO algorithm (without requiring the sensitivity information) were redesigned to ensure that the structural RTO problem can be tackled. Finally, the numerical examples were used and other RTO methods were compared to demonstrate the effect of the RTO method proposed. The results show that the new RTO method not only can effectively address the structural RTO problem considering loading uncertainty, but also has advantages over other RTO methods in terms of some performance during solving the structural RTO problem. Moreover, the different values of control parameters in the new RTO method also have an effect on structural optimization results.