Optimization flutter response of laminated smart nanocomposite truncated conical shell under supersonic aerodynamic pressure using hybrid IGWO-DQHFEM

Abstract

Given the wide application of conical shells in the aerospace and aircraft industry, there comes a need for dynamic analysis and optimum design of these structures against supersonic aerodynamic forces, which induce a phenomenon called flutter. As the key contribution of this paper, a new method has been developed and applied to optimize the dynamic and flutter control of truncated conical shells under supersonic aerodynamic loads. Here, a truncated conical shell with a layered configuration is considered for the optimization of supersonic aerodynamic conditions with smart control, shape, and size optimum design, wherein every layer is reinforced with carbon nanotubes (CNTs). Moreover, a conical shell is considered with piezoelectric properties to smartly control the aerodynamic behavior of the structure, so by applying voltage, it will be possible to control flutter or critical aerodynamic pressure and frequency. The objective of the optimization model is defined based on aerodynamic pressure and frequency of conical shells. Mathematical modeling of the structure with high accuracy is carried out to optimize the model. The supersonic aerodynamic force is considered employing piston theory, where seven variables are used through a high-order shear deformation theory. In the new numerical method, the differential quadrature hierarchical finite element method (DQHFM) is used for the solution of the coupled electro- dynamic equations of the structure and computing the frequency of the structure along with the flutter or critical aerodynamic pressure. The optimization model obtained by the DQHFM method is applied to search the optimum conditions using an Improved Grey Wolf Optimization (IGWO) method. In IGWO, the local search condition is proposed based on the optimum positions and statistical properties of agents in previous positions. Finally, the optimum size, shape, and smart control parameters of the structure such as the length and radius of the cone, cone apex angle, external voltage, CNTs volume fraction, number of layers, and airflow angle are drawn out and discussed by IGWO and DQHFM. The results show that by increasing the cone angle from 30 ^o to 60 ^o, the optimum voltage that has to be applied decreases. On the other hand, an optimal radius stabilizes at around 1 m and the optimum volume fraction of the CNTs is 10 %.