Topology optimization of bi-material curved shell structures for minimizing time-domain sound radiation

So far, the research on topology optimization against noise has mainly addressed frequency-domain problems, while time-domain analysis is also widely used in practical engineering. Nonetheless, the topology optimization work on the latter was rarely reported due to its complexity. This article presents a new topology optimization scheme of bi-material curved shell structure to reduce the time-domain noise generated by transient vibration. A finite element formulation for an eight-node curved shell element is presented. The Newmark integral method is employed to calculate transient responses, and the obtained results are input into the time-domain boundary element method to predict transient sound pressure. In the optimization model, the volumetric densities of material in a bi-material interpolation model constructed by the solid isotropic material with penalization model are chosen as the design variables; the time integral of the squared sound pressure on structural surfaces or prescribed reference points in acoustic medium over a specified time interval of interest is taken as the objective function; and the constraint on material volume is considered. A volume-preserving Heaviside penalization is introduced to suppress gray elements. Furthermore, the calculation of time-domain sound radiation sensitivity is transformed into the following two processes: (a) the derivation of transient response based on the Newmark integral method; (b) the derivation of transient sound pressure based on the discrete time-domain boundary integral equation. Numerical examples demonstrate the validity of the approach proposed in this article. The influences of volume-preserving Heaviside penalization, volume constraint, loading position and form, and selection of objective function on the optimal design are discussed.