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

Abstract 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.