Buckling and free vibration of grid-stiffened composite conical panels using Extended Kantorovich Method

Abstract

This paper develops very accurate closed-form solutions for buckling and free vibration of grid-stiffened composite conical panels using a semi-analytical method. On the base of first-order shear deformation theory (FSDT), the governing formulations are derived while an appropriate unit cell is used to derive the material properties of the lattice from their bulk properties. Multiple systems of ordinary differential equations (ODEs) are obtained by applying the Extended Kantorovich Method (EKM) to solve the governing system of partial differential equations (PDEs). The resulting ODEs are then solved using semi-analytical closed-form solutions to study buckling and free vibration of grid-stiffened panels. It is interesting to note that due to the general formulation of the conical panel, it is very easy to obtain other useful geometries including cylindrical panels, and even rectangular plates with general unit cell configurations. Regarding stability, fast convergence, and very low computing cost, the effectiveness of the proposed technique is investigated. The accuracy of the critical buckling loads and natural frequencies for various cases is studied which shows very good agreement in comparison with results obtained from the commercial finite element code ANSYS.