Multigrid reduced-order topology optimization scheme for structures subjected to stationary random excitations

Topology optimization methods for structures subjected to random excitations are difficult to widely apply in aeronautic and aerospace engineering, primarily due to the high computational cost of frequency response analysis for large-scale systems. Conventional methods are either unsuitable or inefficient for large-scale engineering structures, especially for structures consisting of multi-materials with non-proportional damping systems. To address this challenge, an accurate and highly efficient reduced-order method (ROM) based on the second-order Krylov subspace and the multigrid method is proposed in this paper, which is applicable to non-proportional damping systems. Moreover, a novel multigrid reduced-order topology optimization scheme for structures subjected to stationary random excitations is proposed based on the pseudo-excitation method (PEM). Two 3D numerical examples demonstrate the accuracy and efficiency of the proposed scheme for multi-material topology optimization. For a cantilever beam with about 6.7 x 10(5) degrees of freedom (DOFs), compared against the original reduced-order method, the efficiency of pseudo-harmonic analysis of the multigrid reduced-order method is improved by about 91% with sufficient accuracy, and the efficiency of the whole optimization process of the multigrid reduced-order method is improved by more than 71%. For a pedestal structure with about 3.5 x 10(5) DOFs, compared against the original reduced-order method, the efficiency of pseudo-harmonic analysis of the multigrid reduced-order method is improved by about 61%.