Efficient strategy for topology optimization of stochastic viscoelastic damping structures

In this study, the dynamic topology optimization (TO) of stochastic viscoelastic damping structures (VDSs) is performed for the first time. However, the expensive computation cost seriously hinders the TO process. To address this problem, an efficient strategy is proposed. On the one hand, in the stochastic structural response analysis, a fully adaptive method based on direct probability integral method is presented to determine the number and locations of samples. Meanwhile, to improve the computational efficiency of structural response for each sample, a piecewise model-order reduction method based on Krylov subspace is adopted to generate the orthonormal basis and project the original large-scale system onto a low-order system. On the other hand, to overcome the optimization challenge arising from large number of design variables in the density-based topology method, a material-field series-expansion method is employed to describe the topology layout and significantly reduce the number of design variables. Moreover, the sensitivity of the optimization model is derived by the adjoint method and the method of moving asymptotes (MMA) is used to efficiently update the design variables. Some numerical examples comprehensively demonstrate the effectiveness and efficiency of the proposed strategy. The results indicate that the uncertainty of structural parameters greatly affect both the topology layout of VDS and vibration damping capacity.