Topology optimization of periodic structures under multiple dynamic uncertain loads

Abstract

Periodic structures have attracted considerable attention in lightweight design due to their high specific strength and stiffness. Despite this, existing topology optimization research on these structures typically focuses on deterministic, single-load cases. To address the limitations arising from real-world, variable load conditions, this study presents a robust method for the topology optimization of periodic structures under both multiple and uncertain load cases. The proposed model integrates the uncertainty of the load magnitude, direction, and excitation frequency, employing the weighted sum of the mean and standard deviation of the dynamic structural compliance modulus as the objective function, constrained by the volume fraction of the structure. A method for uncertainty quantification is introduced, utilizing the bivariate dimension reduction technique and Gauss-type quadrature. Leveraging the displacement superposition principle in linear elastomers, we provide a method to calculate the mean and standard deviation of the dynamic structural compliance modulus under these complex load cases. Additionally, the sensitivity of the objective function concerning design variables is derived. The effectiveness of the proposed method is verified through numerical examples, revealing the effect of load uncertainty on the topology optimization of periodic structures.