Non‑gradient Robust Topology Optimization Method Considering Loading Uncertainty

摘要

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