The need to simultaneously optimize the structural design properties, and attain a satisfactory vibroacoustic performance for composite structures, has been a challenging task for modern structural engineers. This work is aimed at developing a statistical energy analysis (SEA) based numerical scheme for computing the optimal design parameters of each individual layer of layered curved shells having arbitrary complexities and layering. The main novelty of the work focuses on the computation of SEA properties for curved composite shells and derive the sensitivities of the acoustic transmission coefficient, expressed through the computed SEA properties, with respect to the structural design characteristics to be optimized. A wave finite element approach is employed to calculate the wave propagation constants of the curved shell. The calculated wave constants are then applied to compute the vibroacoustic properties for the curved shell using a SEA approach. Sensitivity analyses are conducted on the vibroacoustic properties to estimate their response to changes in the structural properties. Gradient vector is then formulated and hence the Hessian matrix, which is employed to formulate a Newton-like optimisation algorithm for optimizing the properties of the layered composite shell. The developed scheme is applied to a sandwich shell; optimal design parameters of [Formula: see text] and [Formula: see text] are obtained for the facesheet and the core of the shell whose base parameters are [Formula: see text] and [Formula: see text], respectively. This simultaneously optimizes the structure with maximum stiffness and minimum mass and attains a satisfactory dynamic performance for acoustic transmission through the sandwich shell. The principal advantage of the scheme is the ability to accurately model composite panels of arbitrary curvature at a rational computational time.
