Concurrent topology optimization of multiscale structure under uncertain dynamic loads

Abstract

This study proposes a robust concurrent topology optimization method with considering dynamic load uncertainty for the design of structures composed of periodic microstructures based on the bi-directional evolutionary structural optimization (BESO) method. The objective function is formulated as the summation of the mean and standard deviation of the structural dynamic compliance modulus. The constraints are imposed on the macrostructure and material microstructure volumes, respectively. The hybrid dimension reduction method and Gauss integral (HDRG) method is proposed to quantify and propagate load uncertainty to estimate the objective function. By the HDRG method, robust topology optimization with uncertainty modeled by probabilistic methods can be handed uniformly. To reduce the computational burden, a decoupled sensitivity analysis method is proposed to calculate the sensitivities of objective function with respect to the microstructure design variables. Five numerical examples are used to validate the effectiveness of the proposed robust concurrent topology optimization method and demonstrate the influence of load uncertainty on the design results. Results illustrate that the proposed methods can obtain the clear topologies of macro and micro structures, and the dynamic load uncertainty has a significant impact on the design results.