Robust topological design of actuator-coupled structures with hybrid uncertainties

Based on the bidirectional evolutionary structural optimization method, a robust topology optimization (RTO) algorithm is developed for actuator-coupled structures with hybrid uncertainties. The hybrid interval random variables model is adopted to simulate the uncertainty of the mechanical and piezoelectric parameters. The worst case of the compliance is set as the robust objective function. A hybrid uncertainty perturbation analysis method (HUPAM) is proposed to estimate the expectation and standard variance of the robust objective function. The density-based interpolation scheme is employed to establish the design variables, and the sensitivity of the robust objective function with respect to the design variables is derived. The robust topologies of the host structure and the optimal placement of the coupled actuators are obtained by the proposed RTO approach. Several numerical examples are presented to show the effectiveness of the proposed method, and the Monte Carlo method is used to validate the accuracy of the HUPAM.