Robust topology optimization of vibrating structures considering random diffuse regions via a phase-field method

This paper investigates a robust topology optimization method for structural dynamic problems by considering random diffuse-region widths between different material phases using a phase-field model. Herein, the spatial distribution of the widths of diffuse regions in a multi-material structure is first represented by a random field and then discretized into uncorrelated stochastic variables using the expansion optimal linear estimation method; stochastic response analysis is then conducted with polynomial chaos expansion. Furthermore, a robust topology optimization formulation of structural dynamic problems is proposed on the basis of the phase-field method, where the design domain is represented with the phase-field function and the explicit phase-field curve is updated by solving the Allen–Cahn equation. A weighted summation of the mean value and standard deviation of the structural dynamic performance is taken as the objective function of the robust optimization problem, where three types of the dynamic performance functions are considered, including the structural dynamic compliance, the fundamental frequency or frequency gap, and the transient displacement under impact loads. The stochastic structural dynamic responses and the corresponding sensitivities are evaluated by polynomial chaos expansion based on finite element analysis at each sampling point. Numerical examples show that the proposed method generates meaningful optimal topologies for structural dynamic robust optimization problems with the framework of the phase-field method. Additionally, some influence factors that affect the optimal solutions are discussed.