Explicit and efficient topology optimization of frequency-dependent damping patches using moving morphable components and reduced-order models

Abstract

Viscoelastic materials have been widely applied as the lightweight structures are growingly used in many industrial sectors in order to improve the cost-efficiency of products. The present work is devoted to minimize the kinetic energy of thin-shell structures subjected to harmonic excitations within a certain frequency range by seeking the optimal layouts of frequency-dependent viscoelastic damping patches under a prescribed area constraint. An explicit topology optimization approach based on the moving morphable components (MMC) is applied, where the number of design variables is substantially reduced compared to the traditional density-based implicit framework. This is achieved by introducing a set of geometry parameters (i.e. design variables) to explicitly describe the boundary of structural components which are viscoelastic patches in this paper. Meanwhile, the unnecessary degrees of freedom (DOFs) related to void regions from the finite element (FE) model are removed at every step of numerical optimization thanks to the explicit boundary evolution. The adjoint method is adopted to derive the sensitivity of the objective function with respect to a design variable. Furthermore, an adaptive model order reduction (MOR) technique for the frequency-dependent system is provided to simplify the computational complexity of the dynamical equation and the adjoint equation as well. With the MMC to reduce the number of design variables in the topology formulation and the MOR to reduce the number of DOFs in the FE model, the optimization simulation can be largely sped up. Numerical examples are presented to demonstrate that the combination of the MMC- and MOR-technique is able to distribute constrained-layer damping patches reasonably and very efficiently.