Topology optimization of damping layers in shell structures subject to impact loads for minimum residual vibration

Abstract This paper studies optimum distributions of damping material in shell structures subject to impact loads by topology optimization. The optimization aims at reducing the residual vibration responses after the application of impact loads. In particular, the dependence of both structural forced vibration and residual vibration on the damping layer distribution is considered by transient dynamic responses based optimization approach. Until now, optimum distributions of damping material are always carried out based on frequency domain responses or structural dynamic characteristics. But for the studied problem, transient responses based optimization is more straightforward when the impact loads are known. When involving transient responses, the calculations of structural responses and sensitivities are always difficult and time-consuming. To deal with these problems, we use an integrated square performance measure of residual vibration as the objective function, which can be greatly simplified by Lyapunov equation, and use an efficient adjoint method to calculate the sensitivities. The topology optimization is implemented using the common solid isotropic material with penalization (SIMP) method. Numerical examples are carried out to illustrate the validity and utility of the proposed approach, and the numerical results also show the advantages of transient dynamic responses based optimization for the studied problem.