An efficient multiscale topology optimization method for frequency response minimization of cellular composites

Abstract

It is vital to control the vibration of cellular composites under harmonic excitation in engineering. Due to numerous design variables and expensive frequency domain integration operation, the majority of multiscale topology optimization methods for frequency response minimization of cellular composites tend to be conservative, where a small number of types of microstructures are considered. This paper proposes an efficient multiscale topology optimization method to minimize the frequency response of cellular composites over specified frequency intervals. This method utilizes multiclass graded lattice unit cells (LUCs) as design candidates, offering great design space to improve the dynamic performance of cellular composites. At microscale, the proposed method leverages Kriging metamodels to replace the the homogenization method in each iteration step, thus accelerating the performance estimation of multiclass graded LUCs. At macroscale, the second-order Krylov subspace with moment-matching Gram-Schmidt orthonormalization (SOMMG) method is introduced to expedite the frequency response analysis of cellular composites. Two types of design variables are employed to construct the Kriging metamodel assisted Uniform Multiphase Materials Interpolation (KUMMI) model, facilitating the concurrent updating of LUCs’ classes and relative densities. Several numerical examples are presented to validate the effectiveness and efficiency of the proposed method in minimizing the frequency response of cellular composites.