Topology optimization of viscoelastic damping layers for attenuating transient response of shell structures

This paper presents topology optimization of viscoelastic damping layers attached to shell structures for attenuating the amplitude of transient response under dynamic loads. The transient response is evaluated using an implicit time integration scheme. Dynamic performance indices are defined to measure the transient response. In the optimization formulation, three different types of the performance indices are considered as the objective function. The density-based topology optimization scheme is applied to find the optimal distribution of the viscoelastic material. The artificial densities of the shell elements of the viscoelastic layers are taken as the design variables. The constraint is the maximum volume fraction of the viscoelastic material. A sensitivity analysis method of the transient response is developed based on the adjoint variable method. Several numerical examples are presented to demonstrate the validity of the proposed method. The transient responses of the optimized structures are compared to those of the uniformly distributed structures to show the effectiveness of the proposed method. Also, the influences of the performance indices are discussed.