Robust topology optimization for concurrent design of dynamic structures under hybrid uncertainties

Abstract

Abstract A new robust topology optimization method based on level sets is developed for the concurrent design of dynamic structures composed of uniform periodic microstructures subject to random and interval hybrid uncertainties. A Hybrid Dimensional Reduction (HDR) method is proposed to estimate the interval mean and the interval variance of the uncertain objective function based on a bivariate dimension reduction scheme. The robust objective function is defined as a weighted sum of the mean and standard variance of the dynamic compliance under the worst case. The sensitivity information of the robust objective function with respect to the macro and micro design variables can then be obtained after the uncertainty analysis. Several examples are used to validate the effectiveness of the proposed robust topology optimization method.